(See Energy Level Diagrams for 12C and Isobar Diagram)
< r2matter >1/2 ≈ 2.35-2.48 fm; i.e., see (1985TA18, 2001OZ04, 2011AL23, 2016KA37).
12C*(4.44): Q = 6 ± 3 e ⋅ fm2, indicating a substantial oblate deformation (1983VE01).
gJ (12C5+)[electronic g-factor] = 2.0010415963 (10)exp (44)me (2002BE82).
The γ0-3 excitation functions from the 6Li + 6Li capture reaction were measured for Ecm = 1 to 8 MeV (1991EU01). Evidence is found for a state at Ex = 30.33 MeV with Γ ≈ 0.8 MeV. A comparison with other data, mainly from other 6Li + 6Li decay channels and 9He(3He, γ) suggests the resonance results from a concentration of Jπ; T = 2+; 0 and 2-; 1 strength.
The excitation functions for some final states in 11B and 11C (reactions (a) and (b)) are structureless while others (to states with Jπ = 3/2-, 5/2-, 5/2+) exhibit pronounced structures. The most prominent of these is observed at E(6Li) = 8.4 MeV [12C*(32.4)] in the p2 and n2 yields with a width Γcm ≈ 1 MeV (1987DO05). Reaction (d) has been studied in kinematically complete experiments at E(6Li) = 2.4 to 6.7 MeV (1988LA11) and at E(6Li) = 2.5 and 3.1 MeV (2015SP01, 2015TU06). See also (1984LA19, 1987LA25). For reactions (e) and (f) see (1983WA09). Broad structures have been observed in the elastic scattering at E(6Li) ≈ 13 and 26 MeV: see (1980AJ01). See also (1990AJ01).
This reaction and the Hoyle state 12C*(7.65) resonance state are of great importance to nucleosynthesis and the formation of heavy elements; see (1985CA41, 1987DE13, 1998TH07, 2000FI14, 2001CS04, 2010OGZX, 2010UM01, 2013EP01, 2013NG01, 2015FI03, 2016ME03, 2016SU25). In (2010UM01), non-resonant capture to a linear configuration that transitions to a triangular orientation is suggested. Production rate sensitivities to stellar environment variables are investigated in (2010DE18, 2011AU01), and the impact of time variation of the fundamental constants is studied in (2012CO19). Also see a prediction for the Jπ = 03+ state at Eres = 1.66 MeV in (2010KAZK).
Excitation functions and angular distribution studies have been carried out at E(3He) = 1.0 to 6.0 MeV (1972BL17: γ0, γ1, γ2), E(3He) = 1.5 to 11 MeV (1972LI29: γ0, γ1, γ2, γ3), E(3He) = 2 to 4.5 MeV (1964BL12: γ0, γ1) and E(3He) = 3 to 26 MeV (1974SH01: γ0, γ1, γ2, γ3). Observed resonances are shown in 12.15 (in PDF or PS). See (1980AJ01) for references.
12C*(28.2) appears to be formed by s- and d-wave capture. The γ0 and γ2 transitions to the 0+ states 12C*(0, 7.7) are strong and show a similar energy dependence. A strong non-resonant contribution is necessary to account for the γ1 yield (1972BL17). The resonance structure reported by (1974SH01) appears to confirm the role of 3p-3h configurations for 12C excitations somewhat above the giant resonance region. The γ3 yield is relatively unstructured (1972LI29, 1974SH01: to E(3He) = 26 MeV). See also (1975AJ02).
(1970BL09) had reported a capture resonance at E(3He) = 1.74 MeV which subsequently decayed via 12C*(15.11) and which was assumed to correspond to the first Jπ = 0+; T = 2 state in 12C [Ex = 27.585 ± 0.005 MeV]. However, neither (1972HA63) nor (1972WA18) have been able to repeat this observation: Γ3HeΓγ/Γ < 1.5 meV (1972WA18), < 2 meV (1972HA63).
Excitation functions for neutrons, production cross sections for 11C and polarization observables have been measured at E(3He) = 1.2 to 10 MeV for several neutron groups. No sharp structure is observed, but there is some suggestion, from angular distribution data and the excitation function at forward angles, for a structure (Γ ≈ 350 keV) at E(3He) ≈ 2 MeV: Ex = 27.8 MeV (1963DU12, 1965DI06). The total cross section for 11C production shows a broad maximum, σ = 113 mb at E(3He) = 4.3 MeV. In the range E(3He) = 5.7 to 40.7 MeV the yield decreases monotonically. Excitation functions and angular distributions for protons (reaction (b)) have been measured for E(3He) = 1.0 to 10.2 MeV for a number of proton groups. No pronounced structures are reported.
Analyzing powers have been measured at E(pol. 3He) = 33.3 MeV for nine deuteron groups (reaction (c)). The cross section for ground-state tritons (reaction (d)) increases monotonically for E(3He) = 2.5 to 4.2 MeV and then shows a broad maximum at E(3He) ≈ 4.5 MeV. See also (1993AR14, 1996AR07: E = 22.3 to 34 MeV).
The excitation function for elastic scattering (reaction (e)) decreases monotonically for E(3He) = 4.0 to 9.0 MeV and 15.0 to 21.0 MeV. See also (1992AD06: E = 50, 60 MeV). At θcm = 111° a slight rise is observed for E(3He) = 19 to 21 MeV. Polarization observables have been reported at E(3He) = 18, 31.4 and 32.8 MeV.
Excitation functions for the α0 group (reaction (f)) have been reported for E(3He) = 2 to 10 MeV (1978BI15): evidence is found for a resonance at Ex ≈ 29.3 MeV. See also (1992AD06). Analyzing powers have been measured at E(pol. 3He) = 33.3 MeV. For reaction (g) see (1986LA26, 1987WA25).
Neutron groups have been observed to 12C*(0, 4.4, 7.7, 9.6, (10.1), (10.8)). Angular distributions of neutrons, mainly for n0-3, have been measured at energies in the range Eα = 1.75 to 32 MeV. Gamma-ray angular distributions have been studied by (1955TA28, 1959SM98, 1963SE04). Observation of the γ-decay of the 15.1 MeV level is reported by (1954RA35, 1957WA04). At Eα = 35 MeV the members of the Kπ = 0+ band and 12C*(9.63) are strongly populated (1981HAZV).
Doppler shift measurements on the transition 12C*(4.4 → g.s.) yield mean life values of τm = 50 ± 6 fsec (1961DE38); 57+23-17 fsec, Γγ = (11.5+5-3.2) meV (1966WA10); < 48 ± 10 fsec (1967CA02). The internal pair conversion coefficient indicates an E2 transition (1954MI68): the pair angular correlation permits M1 or E2 and favors the latter (1954HA07, 1956GO1K, 1956GO73, 1958AR1B). Angular distributions of n1 and n1-γ correlations strongly indicate a direct interaction mechanism even at Eα = 3.3 and 5.5 MeV (1960GA14, 1962KJ01); also see correlation studies at Eα = 1.4 to 4.5 MeV (2010GI07). 12C*(7.65[Jπ = 0+]) decays predominantly into 8Be + α with a small radiative branch. In (1960AL04, 1972OB01) the pair decay is measured Γπ/Γ = (6.9 ± 2.1) × 10-6; this supercedes the earlier value Γπ/Γ = (6.6 ± 2.2) × 10-6 (1959AL97, 1960AJ04, 1960AL04, 1961GA03). However, see 12.14 (in PDF or PS).
Neutron catalyzed helium burning, i.e. 4He(αn, γ)9Be(α, n)12C, is analyzed in (1994WR01, 1996KU07, 2009GI03, 2011GI05). The ratio, Yield(Eγ = 4.44 MeV)/Yield(neutrons) = 0.596 ± 0.017, was measured for an AmBe source in (2004MO18). The energy dependent reaction cross sections have been evaluated at E < 10 MeV for actinide-Be neutron source energy distributions (2003SH22). Also see (1997HE11, 2000MI34, 2007AH07, 2007MA58, 2015VL01).
Reaction (b) was measured at Eα = 22 to 30 MeV, along with 12C(α, 3α)4He, in search of 12C resonances above Ex = 7 MeV that could have structures related to the Hoyle state (2011FR02). The analysis separately considered both events populating natural parity states involving 12C* → 8Beg.s.(Jπ = 0+) + α and events that excluded 12C* → 8Beg.s. + α. Known states at Ex = 9.64, 10.84, 11.83, 12.71, 14.08 are observed in the 9Be(α, 12C) reaction along with a state consistent with Ex = 13.3 ± 0.2 MeV and Γ = 1.7 ± 0.2 MeV. Analysis of the angular correlations from the 12C(α, 3α) reaction support Jπ = 4+ for the new state.
At E(6Li) = 32 MeV angular distributions have been studied to 12C*(0, 4.4, 7.7, 9.6, 10.8, 11.8, 12.7, 14.1); 12C*(9.64) is relatively strongly populated. There is no indication of the T = 1 states (1986AS02: FRDWBA). Similar results are found for E(9Be) = 26 MeV in (1975VE10).
At E(9Be) = 40 MeV, angular distributions to 12C*(0, 4.44, 7.65, 9.64, 13.35, 14.08) were measured (1992CO05); the data are consistent with direct 3He cluster transfer. Cluster spectroscopic factors are deduced. Also see measurements at E(9Be) = 26 MeV, θ = 10° to 12C*(4.4, 7.7, 9.6) (1975VE10).
At E(10C) = 10.7 MeV, the α-particle correlations from 12C*(7.65, 9.64) were studied in search of evidence supporting direct 3-body breakup (2012MA10), as suggested in (2011RA43). Results were consistent with 100% decay via 8Beg.s. + α in both cases.
At E(3He) = 13 MeV neutron groups are observed to 12C*(0, 4.4, 7.7, 16.1, 17.8) and to excited states at Ex = 23.53 ± 0.04 [Γ < 0.4 MeV] and 27.611 ± 0.020 MeV. The latter is formed with a 0° cross section of ≈ 200 μb/sr and is taken to be the first 0+; T = 2 state of 12C (1974GO23).
The (d, γγ) excitation function [via the Jπ = 1+; T = 1 state at Ex = 15.1 MeV] has been measured for Ed = 2.655 to 2.84 MeV. The non-resonant yield of 15 MeV γ-rays is due to direct capture processes or to a very broad resonance: no sharp resonances are observed corresponding to the Ex ≈ 27.6, T = 2 state reported in other reactions [Γd0Γγ/Γ ≲ 0.2 eV] (1970BL09).
The thin-target excitation function, measured at Ed = 0.3 to 4.6 MeV, shows some indication of a broad resonance in the forward direction near Ed = 0.9 MeV. Above Ed = 2.4 MeV, the cross section increases rapidly to 210 mb/sr at 3.8 MeV and then remains constant to 4.6 MeV (1954BU06, 1955MA76). Also see activation measurements reported at Ed = 0.5 to 6 MeV (1990MI11). The 0° excitation function for ground state neutrons shows no structure for Ed = 3.2 to 9.0 MeV (1967DI01). Excitation functions have been measured for Ed = 7.0 to 16.0 MeV (1981AN16). The excitation function for neutrons to 11C*(6.48) increases monotonically for Ed = 4.0 to 4.8 MeV (1972TH14). The branching ratios at 90° for the transitions to the ground states of 11C and 11B [n0/p0] have been measured for Ed = 1.0 to 2.0 MeV by (1973BR24). At Ed = 1 to 5 MeV, cross sections have been obtained for the neutrons and protons to the second, third, fourth, and fifth excited states of the 11B and 11C mirror nuclei (1967SC1K). The angular distributions all show a sharp peak around 20° and a smaller contribution in the backward direction; DWBA produces a satisfactory fit to these distributions (1967DI01).
Polarization measurements have been carried out for Epol. d = 2.5 to 4.0 MeV (1967ME1N), Epol. d = 1.20 to 2.90 MeV (1968BR26: n0) and Epol. d = 2.4 to 4.0 MeV (1972ME06: n0, n1, n2+3). The transitions to 11C*(0, 4.32 + 4.80) appear to involve a direct reaction mechanism (1972ME06).
Cross sections and astrophysical S-factors for n0 are reported for Ed < 160 keV (2008ST10). Thick-target yields and astrophysical S-factors are reported for neutrons at Ed = 24 to 111 keV (2001HO23) and for 4.3 MeV γ-rays at Ed = 111 to 170 keV (1982CE02).
Angular distributions and yields of protons have been measured for Ed = 0.9 to 2 MeV (2007KO69) and Ed = 15.3 MeV (2005GA59); also see results reported at Ed = 0.18 to 3.1 MeV (1959AJ76), 0.14 to 12 MeV (1968AJ02) and 0.7 to 2.9 MeV (1975AJ02). Although the excitation functions show several broad peaks, no clear resonances can be identified, and it is assumed that many overlapping resonances are involved (1956MA69) except possibly at Ed = 2.3 MeV (Ex = 27.1 MeV) where the effect of a broad resonance influences the cross section of the p1 and p3 groups. An analysis given in (2005RU16) suggests the broad peaks correspond to fragmented Jπ = 1- components of the GDR at Eres(cm) = 0.38, 0.61, 1.61 MeV with Γ = 0.37, 0.37 and 1.24 MeV, respectively, as well as a Jπ = 2+ contribution from the GQR at Eres(cm) = 1.36 MeV with Γ = 710 keV. The p2-γ-ray correlations were measured in (2005GA59). Cross section ratios for the (d, n) and (d, p) reactions to mirror states have been measured by (1967SC1K, 1973BR24).
The yield of elastically scattered deuterons has been measured for Ed = 1.0 to 2.0 MeV: resonances at Ed = 1.0 and 1.9 MeV are suggested by (1969LO01). Excitation functions for the deuterons to 10B*(1.74, 2.16) [Jπ; T = 0+; 1 and 1+; 0, respectively] have been measured at several angles for Ed = 4.2 to 16 MeV: they are characterized by rather broad, slowly varying structures. The ratio σ1.74/σ2.16 varies from (0.69 ± 0.04)% at Ed = 6.5 MeV to (0.16 ± 0.04)% at Ed = 12.0 MeV corresponding, respectively, to isospin impurities of ≈ 2% and ≈ 0.5% (1974ST01). No resonance structure is observed in the elastic yield for Ed = 14.0 to 15.5 MeV (1974BU06). Polarization measurements are reported at Epol. d = 12.5 MeV (1975ZA08) and at 15 MeV (1974BU06).
Excitation functions have been measured for the α0 and α1 groups for Ed = 0.4 to 12 MeV [see (1968AJ02, 1975AJ02, 1980AJ01)] and for Ed = 0.9 to 2.0 MeV (2007KO70: α0). Maxima in the α0 yields are reported at Ed = 1, 2, 4.5 and (6) MeV. The first is attributed to an s-wave resonance corresponding to a state with Ex ≈ 26.0 MeV, Γ ≈ 0.5 MeV (1968FR07). The resonance structures at ≈ 2.0 and 4.5 MeV (Γ ≳ 1 MeV) may both involve the isoscalar giant resonance: Ex ≈ 28 MeV, Γ ≈ 4 MeV (1978BU04). No evidence for the T = 2 state was found in the α0 and α1 yield curves taken in 2 keV steps for 27.35 < Ex < 27.65 MeV (1970BL09). For yields of the α-particles to 8Be*(17.6, 18.1) see (1970CA12). Cross sections, angular distributions and S-factors are deduced in (2001HO22: Ed = 120 to 340 keV) and (1993CE02, 1997YA02, 1997YA08: Ed = 57 to 141 keV).
Reaction (b) has been studied for Ed = 2.7 to 5.0 MeV (1975RO09, 1975VA04, 1977GO16), Ed = 0.36 MeV (1977NO10), Ed = 2.5 and 3 MeV (1992KO26), Ed = 13.6 MeV (1981NE08, 1992PU06) and Ed = 48 MeV (1993PA31). The work of (1977NO10) suggests that Jπ = 3- and 4+ 12C compound states with unidentifiable energies and widths contribute dominantly to the sequential decay. Also see (1990NE15, 1991AS02).
Observed proton groups are displayed in 12.16 (in PDF or PS). Angular distributions of many of these groups have been measured for E(3He) = 2.0 to 3.0 MeV (1965BH1A), 3.7 MeV (1962BR10), 10.1 MeV (1962AL01) and 14 MeV (1967CO1F). Also see 12.17 (in PDF or PS), which has results from complete kinematics studies of 10B(3He, p3α) and 11B(3He, d3α) given in (2007BO49, 2009KI13, 2010KI08, 2011AL28, 2012AL22, 2012KI07, 2013KI07). 12.14 (in PDF or PS) summarizes the electromagnetic decay parameters of some of the excited states of 12C including results below.
Pair emission from 12C*(7.65) has been measured: Γπ/Γ = (6.6 ± 2.2) × 10-6 [see 12.14 (in PDF or PS)] as has the cascade through 12C*(4.4): Γγ/Γ = (3.3 ± 0.9) × 10-4 (1961AL27). By observation of 12C recoils, a value Γrad/Γ = (3.5 ± 1.2) × 10-4 is found by (1964HA23).
For 12C*(12.71) Γγ0/Γ = (1.93 ± 0.12)%, Γγ1/Γγ0 = (15.0 ± 1.8)% and Γα/Γ = (97.8 ± 0.1)% (1977AD02). See earlier reported results of Γγ/Γα = (3 ± 1)% (1958MO99) and (2 ± 1)% (1959AL96): the γ-decay branching ratios are reported; see comments in 12.16 (in PDF or PS). The α breakup of 12C*(12.71) shows a triple-peaked α-particle spectrum, characteristic of the breakup of a Jπ = 1+ state (1967BH1B).
For 12C*(14.08) the branching ratio Γα0/Γ is 0.1 - 0.4. Proton-α correlations require J ≥ 2 (1966WA16).
12C*(15.11: Jπ = 1+; T = 1) decays by γ-emission mainly to 12Cg.s. and has weaker transitions to 12C*(4.4, 7.7, (10.3), 12.7) (1972AL03, 2009KI13): see 12.16 (in PDF or PS). Earlier measurements reported the feeding to 12Cg.s. as 97% and to 12C*(4.4) as (3.1 ± 0.6)% (1959AL96), (4 ± 1)% (1960AL14); Γα/Γ < 0.2 (1960MI1E), < 0.05 (1965AL1B), < 0.10 (1966WA16), respectively. The strong inhibition of the transition to 8Be*(2.9) is cited as evidence for a high isospin purity (1965AL1B). For a study of the charge-dependent matrix element between 12C*(12.7, 15.1) see 12.18 (in PDF or PS).
Decays of 12C*(16.11, 16.57) populate both 8Be*(0, 2.9). The consequent assignment of natural parity is consistent with Jπ = 2+ for the former but not with the accepted Jπ = 2- for the latter. For 12C*(16.1) Γγ1/Γ = (2.42 ± 0.29) × 10-3, Γγ0/Γγ1 = (4.6 ± 0.7)%, Γγ(16.1 → 9.6)/Γγ1 = (2.4 ± 0.4)%, and Γγ(16.1 → 12.7)/Γγ1 = (1.46 ± 0.25)% (1976AD03, 1977AD02). Also see (1974AN19) who reported Γp/Γ = (3.24 ± 0.27) × 10-3 and Γγ/Γ = (3.23 ± 0.50) × 10-3. Reported values of Γα0/Γ are 0.05 - 0.12; the decay to 3α occurs rarely, if at all (1966WA16: see however, 11B(p, α)8Be: (1965DE1A)).
An unpublished result at E(3He) = 14 MeV, referenced in (1968AJ02), reported two peaks in the giant resonance excitation region corresponding to 12C* ≈ 20.6 and 24.5 MeV, with Γ ≈ 200 and 50 keV, respectively; the angular distributions show forward maxima.
Reactions (c) and (d) have been studied by (1970BO39). The latter, at E(3He) = 11 MeV, appears to proceed via a state in 12C at Ex = 20.5 ± 0.1 MeV, which is suggested to be Jπ = 3+; T = 1. The relative intensities of the decays of 12C states with 20 < Ex < 25 MeV via channels (c) and (d) is estimated. The α0-decay is very small, consistent with the expected population of T = 1 states (1970BO39).
Angular distributions of the deuterons corresponding to 12C*(0, 4.4) have been measured at Eα = 15 to 31 MeV [see references in (1968AJ02, 1980AJ01, 1985AJ01, 1990AJ01)]. The dγ4.4 angular correlations have been measured for Eα = 19 to 30 MeV [see references in (1975AJ02, 1990AJ01)], and see (1989VA07, 2001LE50: Eα = 25 MeV). Thick target γ-ray yields were measured in (1995HE40, 1997HE11). At Eα = 39.9 MeV, the relative populations of 12C*(12.71, 15.11) [both 1+; the latter isospin forbidden] leads to the value of 285 ± 30 keV (1977LI02) for the charge-dependent matrix element between these two states. The spin-tensor components for 12C*(4.44) formation (1990BO54, 1991BA23, 1998GA46) and induced polarization effects (1999GA43, 2003ZE06) are deduced from analysis of angular distributions at Eα = 25 and 30 MeV.
At E(6Li) = 4.9 MeV (1966MC05) angular distributions have been obtained for the α-particles to 12C*(0, 4.4, 7.7, 9.6); the population of 12C*(11.8, 12.7) is also reported. At E(6Li) = 3.8 MeV the intensity ratio for populating the isospin forbidden 12C*(15.11; T = 1) state is (3 ± 2)% of the intensity to 12C*(12.7; T = 0) (1964CA18).
(a) Measurements relevant to the astrophysical capture reaction have been carried out at Ep = 40 to 180 keV (1992CE02), Epol. p = 80 to 100 keV (2000KE10), Ep = 140 to 260 keV (1993AN06) and Ep = 160 to 310 keV (2016HE05). (1992CE02) produced γ0 and γ1 yields and S-factor related to the measured α-particle yields. A study of the Ex = 16.1 MeV state in (2016HE05) found Eres = 150.0 ± 0.5 keV and Γ = 5.0 ± 0.8 keV. See related discussion in (1990BR12, 1996RE16, 1999AN35, 2000LI06, 2012CO19, 2012MI24, 2014DU09).
In (2012DI19, 2012FY01), a kinematic energy reconstruction of the 3α energy was used to study α-unbound states populated in the γ-decay of 12C*(16.1, 16.57). Capture reactions with Ep = 165 keV and 350 keV beams populated the higher-states, while 12C*(9.63, 10.8, 12.7) were observed in the low-energy region of the 3α spectrum. In (2012DI19), the Ex = 11.5-12 MeV region shows evidence for a state that may be associated with Jπ = 2+ strength. An update of this work, (2016LA27) observed evidence for 12C*(16.1) decay to 12C*(10.8) with Γγ = 0.48 ± 0.04 (stat.) ± 0.11 (sys.) eV; in that work, they gave an overview of the partial decay widths for 12C*(16.1). At Ep = 0.675, 1388, 2626 keV (Ex = 16.58, 17.23, 18.37 MeV), the relative intensities of the capture γ rays to 12C*(0, 4.44, 7.65, 9.64, 12.71, 15.11) were measured at θlab = 55° (1990ZI02). See also (1992HO11).
In the range 4 < Ep < 14.5 MeV, σ(γ0) is dominated by the giant dipole resonance at Ep = 7.2 MeV (Ex = 22.6 MeV, Γcm = 3.2 MeV), while the giant resonance in γ1 occurs at Ep ≈ 10.3 MeV (Ex = 25.4 MeV, Γcm ≈ 6.5 MeV): see (1964AL20). Absolute cross-section measurements from Ep = 5 to 14 MeV suggest that dσ/dΩ(90°) = 13.1 ± 1.3 μb/sr be used as a standard at the Ep = 7.25 MeV peak of the GDR (1982CO11; also derived σ(E2) for Ep = 7 to 14 MeV). The E2 strength is found to be centered near Ep = 12 MeV: it exhausts ≳ 30% of the isoscalar E2 sum rule (1976MAZG, 1976MAZL).
A study of the giant dipole resonance region with polarized protons (Epol. p = 6 to 14 MeV) sets limits on the configuration mixing in the γ0 giant resonance (1972GL01). The analysis of γ1 is more complicated: the asymmetry results are constant either with a single Jπ = 2- state or with interference of pairs of states such as (1-, 3-), (2-, 3-) and (1-, 2-) (1972GL01). The 90° yield of γ0, γ1, γ2 and γ3 [to 12C*(0, 4.4, 7.7, 9.6)] has been studied by (1977SN01): the γ2 yield shows a peak at Ep ≈ 14.3 MeV with a cross section ≈ 2.3% that of γ0 [in γ0 yield, Eres = 15.0 MeV (1977SN01)] and perhaps a low-intensity structure at Ep = 11.8 MeV as well. The γ3 yield exhibits two asymmetric peaks at Ep = 12.5 and 13.8 MeV (Γ ≈ 0.7 and 2.5 MeV) and a weaker structure at ≈ 9.8 MeV (1977SN01).
Resonances populated with Ep = 7 to 24.5 MeV beams were studied via γ-γ techniques by measuring the cascades feeding into the 12C*(15.1) state. In (2008CH13) peaks were found in the excitation function corresponding to E1 transitions from Ex = 24.41 ± 0.15 and 28.81 ± 0.10 MeV with Γcm = 1.3 ± 0.3 MeV and 2.0 ± 0.2 MeV, and (2J + 1) Γp0Γγ/Γ = 20.8 ± 2.8 and 150 ± 18 eV, respectively. The peaks were found on a smooth excitation function that had previously been analyzed in (2004CH06).
(1983AN09, 1983AN16) have measured the cross sections for γ0 and γ1 for Ep = 18 to 43 MeV. They report giant resonances based on various excited states of 12C at Ex = 22.5 and 25.5 MeV (γ0), 25.5, 27.4 and (31) MeV (γ1), 27.4, 31 and (37) MeV (γ3), as well as in the γ-yield to higher states. At Ep = 40, 60 and 80 MeV, radiative capture is observed to a state, or a narrow group of states, at Ex = 19.2 ± 0.6 MeV (1979KO05); see also (1982WE08). At Epol. p = 50 MeV, angular distributions and analyzing power measurements are reported to 12C*(0, 4.4, 9.6, 18.8 ± 0.5 [u], 22.3 ± 1.0 [u]) by (1985NO01) [u = unresolved].
At Ep = 98 MeV, radiative capture to 12C*(0,4.4, 7.6, 9.6, 12.7, 15.1, 16.1 + 16.6, ≈ 19) (1990HO23, 1992HO04, 1996BR20: Ep = 98 and 176 MeV) and internal pair production to 12C*(0, 4.4, 9.64) (1993HO07, 1997TR01) are studied to gain insight into exchange current effects. See also (2000LI06). See other measurements in (1991CA25: Ep = 14.24 MeV, 1992KE03: Ep = 7 MeV, 1998MA85: Ep = 7.2 MeV).
(b) In (1993HO07, 1997TR01) radiative capture at Ep = 98 MeV followed by decay via internal pair conversion to 12C*(0, 4.4, 9.64) was measured; the internal conversion cross section was roughly two times larger than expected. At Ep = 1.6 MeV, the pair decay of 12C*(17.2) was studied (1996DE51) in a search for evidence of a massive neutral boson. See also (1994VA17).
(c) Excitation functions have been measured for Ep = 0.15 to 18.9 MeV (see 1975AJ02), 35.4 keV to 18 MeV (see 1980AJ01), 4.5 to 24 MeV (see 1985AJ01). Also see references listed below and in the comments of 12.19 (in PDF or PS), 12.20 (in PDF or PS) and 12.21 (in PDF or PS).
Astrophysically relevant 11B(p, α) cross sections were measured in (1993AN06: Ep = 17 to 134 keV); see additional comments on electron screening in (1993AN06, 1997BA95, 2002HA51, 2002BA77) and other discussions in (1995YA07, 1996RA14, 2004RO27, 2004SP03, 2008LA18, 2010LA11, 2011ST01, 2012CO19, 2013KI06). The use of this reaction for clean fusion energy generation is discussed in (1996YU04: Ep = 0.165 to 2.58 MeV, 1998LI51: Ep = 667 and 1370 keV, 1999LI13, 2015BE28). Surface analysis techniques and related cross sections are given in (1991BA61: Ep = 660 keV, 1992LA08: Ep = 650 keV, 1996VO23: Ep = 160 to 800 keV, 1998MA54: Ep = 1.7 to 2.7 MeV, 2002LI29: Ep = 0.4 to 1.6 MeV, 2010KO33: Ep = 2.2 to 4.2 MeV). See additional theoretical analysis in (1992KO26, 1994SH21, 2006DM01).
The total cross section shows the 162 keV resonance and a broad peak centered at 600 keV. At Ecm = 300 keV σ(α0) = 1.03 ± 0.06 mb and σ(α1) = 165 ± 10 mb (1987BE17). The parameters of the 162 keV resonance are Eres(cm) = 148.3 ± 0.1 keV, Γcm = 5.3 ± 0.2 keV (1987BE17), 149.8 ± 0.2 keV, 5.2+0.5-0.3 keV (1979DA03). Derived S-values lead to S(0) = 197 ± 12 MeV ⋅ b (1987BE17).
The reaction proceeding via 3α breakup into the 3-body continuum is of astrophysical importance; however the reaction proceeds predominantly by sequential two-body decays via 8Be*(0, 2.9). In past reviews, the reactions 11B(p, α)8Be and 11B(p, α)4He4He were distinct in that experiments grouped with the later reaction detected both α particles from the decay of 8Be.
In (2016LA27) the 3-body decay of 12C*(16.11) was analyzed using Dalitz plots, which indicated primarily sequential decay. Analysis of the multiplicity = 2α and 3α events yields Γα0/Γ = 0.054 ± 0.011 and 0.051 ± 0.005 respectively. The text includes discussion on the "ghost" of the ground state; it is suggested that a correction for the "ghost" could raise the Γα0/Γ value by ≈ 25% to around 0.065, as in (2012AL22).
Beams of Ep = 0.675 and 2.64 MeV protons were used to study the decay mechanisms of 12C*(16.576, 18.38) (2011ST01); the decays were found to proceed primarily via l = 3 and 1 α1 emission, respectively.
At higher energies, resonances are observed at Ep = 4.68, 5.10, 6.08, 6.58 and 7.11 MeV [Ex = 20.25 to 22.47 MeV] (1983BO19) and some broad structures are reported by (1983BU06). Contributions from 12C*(23.0, 23.6, 25.4) are reported in (1975VA04). A wide resonance-like structure centered at Ep = 13 MeV [12C*(28)] with Γ ≈ 6 MeV is reported by (1977BU07): the angular distributions of α0 show prominent backward peaking. No marked structure is observed above Ex = 28 MeV (1972TH1C: Ph.D. thesis).
The parameters of the observed resonances are displayed in 12.19 (in PDF or PS) and 12.20 (in PDF or PS). The following summarizes the information on the low-lying resonances: for a full list of references see (1968AJ02, 1980AJ01).
Ep = 0.16 MeV [12C*(16.11)]. This is the Jπ = 2+; T = 1 analog of the first excited states of 12B and 12N. The γ-decay is to 12C*(0, 4.4, 9.6): the angular distribution of γ3, together with the known α-decay of 12C*(9.6), fix Jπ = 3- for the latter (1961CA13).
Ep = 0.67 MeV [12C*(16.58)]. The proton width [Γp ≈ 150 keV] indicates s-wave protons and therefore Jπ = 1- or 2-. This is supported by the near isotropy of the two resonant exit channels, α1 and γ1. The α1 cross section indicates 2J + 1 ≥ 5: therefore Jπ = 2-. [This is consistent with the results of an α-α correlation study via 8Be*(2.9) (1972TR07)]. The γ1 E1 transition has |M|2 ≈ 0.01 W.u., suggesting T = 1 (1957DE11, 1965SE06). (1962BL10) report a γ branch to 12C*(12.71) (≈ 6% of the intensity of the γ1 transition). Such a branch may also be present for 12C*(17.23).
Ep = 1.4 MeV [12C*(17.23)]. (2J + 1) Γγ0 ≥ 115 eV. This indicates Jπ = 1-, with T = 1 most probable (1965SE06). Jπ = 1- is also required to account for the interference at lower energies in α0 and γ0: see (1957DE11) and is consistent with the α-α correlation results of (1972TR07). Two solutions for Γp are possible; the larger (chosen for 12.19 (in PDF or PS) and 12.20 (in PDF or PS)) is favored by elastic scattering data (1965SE06).
Ep = 2.0 MeV [12C*(17.76)]. The resonance in the yield of α0 requires natural parity, the small α-widths suggest T = 1. For Jπ = 1- or 3- the small γ-widths would be surprising; Jπ = 2+ would lead to a larger anomaly than is observed. Jπ is then 0+; T = 1 (1965SE06). A study of Ep = 0.82 to 2.83 MeV reports that Ex = 17.80 MeV [Γcm = 96 ± 5 keV] decays via a 5.10 ± 0.03 MeV γ-ray to 12C*(12.71): Γγ = 3.7 ± 1.5 eV. The angular distribution is isotropic, as expected (1982HA12).
Ep = 2.37 MeV [12C*(18.13)]. Seen as a resonance in the yield of 15.1 MeV γ-rays: σR = 0.77 ± 0.15 μb, Γcm = 600 ± 100 keV, (2J + 1) Γγ ≥ 2.8 ± 0.6 eV. The results are consistent with Jπ = 1+; T = 0, but interference with a non-resonant background excludes a definite assignment (1972SU08).
Ep = 2.64 MeV [12C*(18.38)]. The resonance for α0 requires natural parity; the presence of a large P4 term in the angular distribution requires J ≥ 2 and lp ≥ 2. The assignment Jπ = 3- is consistent with the data (1965SE06, 1972CH35, 1972VO01, 1974GO21). (1982HA12) report Ex = 18.38 MeV, Γcm ≈ 400 keV, Γγ (to 12C*(9.6)) = 5.7 ± 2.3 eV, consistent with Jπ = 3-; T = 1. The total peak cross section is 4.2 ± 1.7 μb. Transitions to 12C*(0, 4.4) are also observed: Γγ ≈ 2 × 10-3 eV and 3.2 ± 1.0 eV, respectively.
Ep = 2.66 MeV [12C*(18.40)] is not observed in these reactions: see 11B(p, p).
Ep = 3.12 MeV [12C*(18.80)]. The angular distribution of γ0 indicates E2 radiation, Jπ = 2+. This assignment is supported by the angular correlation in the cascade γ1 and by the behavior of σ(α0); T = 1 is suggested by the small Γα (1965SE06). The yield of γ3 (to 12C*(9.6)) shows a peak corresponding to Ex ≈ 18.9 to 19.0 MeV. It may be due to 12C*(18.8) with an energy shift due to interference (1982WR01).
The structure near Ep = 3.5 to 3.7 MeV [12C*(19.2, 19.4)] seems to require at least two levels. The large Γγ0 requires that one be Jπ = 1-; T = 1 and interference terms in σ(α0) require the other to have even spin and even parity: Jπ = 2+; T = 0 is favored (1963SY01, 1965SE06). (1982WR01) do not observe any evidence for an isospin mixed doublet near Ex = 19.5 MeV [Ep = 2.9 to 4.6 MeV (60° and 90°)].
Levels at Ep = 4.93 and 5.11 MeV, seen in σ(γ1) (1955BA22) also appear in σ(α1), but not in σ(α0). Angular distributions suggest Jπ = 2+ or 3- for the latter [12C*(20.64)]; the strength of γ1 and absence of γ0 favors Jπ = 3-; T = 1 (1963SY01, 1965SE06).
The first seven T = 1 states in 12B and 12C have been identified by comparing reduced proton widths obtained from this reaction and reduced widths obtained from the (d, p) and (d, n) reactions: see 12.12 (in PDF or PS) of (1980AJ01) and (1971MO14, 1974AN19).
Excitation functions have been studied at Ep = 2 to 5, 2.6 to 5.5, 3 to 4, 4 to 11.5, 4 to 14 and 4.9 to 11.4 MeV [see (1968AJ02)], from threshold to 6.0, 5.4 to 7.5 and 10.87 to 27.50 MeV [see (1985AJ01)], Ep = 13.7 to 14.7 and 16 to 26 MeV [see (1990AJ01)]. At the higher energies the excitation function decreases essentially monotonically (1981AN16). At the lower energies many peaks are observed whose positions correspond with structures seen in 11B(p, γ)12C and 11B(p, α)8Be and 12C(γ, n) and 12C(γ, p) reactions, suggesting that resonances, and not fluctuations, are involved; see 12.21 (in PDF or PS). Angular distributions do not change as rapidly as might be expected from the pronounced structures in the excitation function (1965OV01). The strength of the pronounced peak at Ep = 6.03 MeV (Ex = 21.49 MeV) appears to demand J ≥ 4 (1961LE11). See also (1994SH21, 1995SH44, 1999AN35, 2009EL09).
Polarization measurements have been carried out for Epol. p = 186 MeV (1994RA23, 1994WA22, 1995YA12) and 295 MeV (1995WA16) and at Epol. p = 7.0 to 26.5 MeV [see articles cited in (1975AJ02, 1980AJ01, 1985AJ01)]. For high-energy interactions see (1994GA40, 1994GA49) and work cited in (1990AJ01).
States shown in 12.21 (in PDF or PS) are revealed in the excitation functions, which have been studied at Ep = 0.3 to 1.0, 0.6 to 2.0, 2 to 5.3 MeV [see (1959AJ76)], Ep = 0.5 to 4.0, 1.8 to 4.1 MeV [see (1968AJ02)], Ep = 1.9 to 3.0, 3.5 to 10.5, 7.5 to 21.5 MeV [see (1975AJ02)], Ep = 1.8 to 3.1, 1.9 to 3.0, 3.0 to 5.2, 3 to 8, 7.5 to 10.5 and 19.2 to 47.4 MeV [see (1980AJ01)], Ep = 4.5 to 7.5, and 5.4 to 7.0 MeV [see (1985AJ01)], and Ecm ≈ 0.15 to 1.1 MeV (1990AJ01), Ep = 0.3 to 1.05 MeV (2011AM02), 0.5 to 3.3 MeV (2001CH78), 1.7 to 2.7 MeV (1998MA54), 2.2 to 4.2 MeV (2010KO33). No pronounced structure is observed above Ex = 28 MeV (1969TH1B, 1971TH1F, 1972TH1C). It is reported that in all the channels and throughout this energy range a strong 2+ background is observed. It is suggested that it may be the low-energy tail of the isoscalar giant quadrupole resonance (1983BO19).
Polarization measurements are reported in (1975AJ02, 1980AJ01, 1990AJ01) and in (2003HA11, 2003HA12, 2004KA53). For studies of high-energy interactions see (2004KA53, 2004KA56). Applied uses of this reaction are discussed in (1990BO15, 1994MI21, 1998MA54, 2010KO33) Also see (1994SH21, 1998DO16, 2013HA17).
Angular distributions of the neutrons to many 12C states up to Ex = 17.23 MeV have been reported (see 12.22 (in PDF or PS)) for energies in the range Ed = 0.5 to 10 MeV [see (1968AJ02)], Ed = 2.5 to 4 MeV (1972ME06), Ed = 5.5, 6 and 11.8 MeV [see (1975AJ02)], Ed = 0.9 and 1.2 MeV (1975SI22), Ed = 7 to 16 MeV (1981AN16), Ed = 12 MeV (1983NE11), Epol. d = 79 MeV (1985FO05, 1987FO22), and Ed = 111 keV (2001HO23), Ed = 120 to 160 keV (2006PA27) and Ed < 5 MeV (2013CO12).
Proton- and α-decay from excited states are reported in (1965OL01, 1985NE01). Jπ = 3- for the 9.64 MeV state is favored on the basis of the angular distribution of the α-particles to 8Beg.s.. There is no evidence for direct 3α-decay of 12C levels in the range Ex = 9 to 13 MeV, nor does 12C*(10.3) appear to participate in this reaction (1965OL01). Relative spectroscopic factors obtained in several (d, n) and (3He, d) studies are summarized in (1975AJ02), but see (1971MU18) for a discussion of the problems involved in comparing spectroscopic factors obtained in these different reactions.
See a comparison of cross section calculations from the TALYS nuclear reaction code with reaction rates from the NACRE data base in (2012CO01). Angular correlations of neutrons and 4.4 MeV γ-rays and neutrons and 15.1 MeV γ-rays are reported in (1968AJ02, 1975AJ02). For polarization measurements see references in (1990AJ01).
Observed deuteron groups are displayed in 12.22 (in PDF or PS). Also see 12.17 (in PDF or PS), which has results from 10B(3He, p3α) and 11B(3He, d3α) complete kinematics studies given in (2007BO49, 2009KI13, 2010KI08, 2011AL28, 2012AL22, 2012KI07, 2013KI07). Angular distributions have been measured at E(3He) = 5.1 to 44 MeV [see (1968AJ02)], 10, 11, 12, 18 and 44 MeV [see (1975AJ02)], 23.2 MeV [see (1980AJ01)], 43.6 MeV [see (1985AJ01)], 18.3 and 22.3 MeV [see (1990AJ01)] and 44 MeV (2012SM06). The angular distributions exhibit characteristic direct interaction features (1967CR04). A Jπ = 2+ state at Ex = 11.16 was reported at E(3He) = 44 MeV in (1971RE03): the group appeared as an enhancement on the high energy side of the Ex = 10.84 MeV peak; however a study under the same kinematic conditions found no evidence for such a peak (2012SM06). The R-matrix analysis of (2012SM06) showed that the fit to their data was improved by including a Jπ = 2+ resonance at Ex = 9.7 MeV: note there is no visible peak in the spectrum at this energy. At E(3He) = 22.3 MeV, spectroscopic factors of S = 1.6 and 0.33 are deduced for 12C*(0,4.4), respectively (1993AR14); See 12.14 (in PDF or PS) in (1980AJ01) for earlier reported values and see (2010TI04, 2016CO14). The d1-γ angular correlations are studied in (1988IG03).
Angular distributions of t0-3 and to 12C*(12.7) have been measured at several energy between Eα = 15.1 to 120 MeV [see references in (1968AJ02, 1975AJ02, 1980AJ01, 1985AJ01 1990AJ01)]. Single-proton transfer seems to be the dominant reaction mode (1967DE1K). Angular correlation measurements of t1-γ are reported at Eα = 21 to 30 MeV: see (1972EL09, 1987VA04, 1988IG04). See also reaction mechanism studies in (1989BA86, 1990BO23, 1990BA62, 1991BA23, 1998GA46, 1999GA43, 1999LE48).
At E(7Li) = 18.3 and 28.3 MeV, angular distributions to 12Cg.s. were measured and analyzed via DWBA to determine the 6He + 12C and 7Li + 11B optical Model parameters (2009WU01). At E(7Li) = 34 MeV, angular distributions have been measured and spectroscopic factors deduced for the groups to 12C*(0, 4.4, 7.7, 9.6, 10.8, 11.8, 12.7, 15.1, 16.1, 18.35) (1983NE11, 1987CO16). It is concluded on the basis of these and other works, that the group corresponding to Ex = 18.35 ± 0.05 MeV (Γ = 350 ± 50 keV) consists of unresolved 12C states with Jπ = 3- (T = 1) and 2- (T = 0 plus some mixing of T = 1). No states were observed with Ex > 18.35 MeV.
Angular distributions involving 12C*(0, 4.4) and 10Be*(0, 3.4) have been measured at E(11B) = 11 MeV (1985PO02).
The 13N valence proton wave function was evaluated using the (13N, 12C) reaction on 11B at E(13N) = 29.5 and 45 MeV (1998DI14). States at 12C*(0, 4.44, 15.1) are found to participate, along with 3α unbound states. Further studies on 24Mg states, some of which are found to possess significant components of 3-1 + 3-1, 3-1 + 1-1 and 0+2 + 3-1, are given in (1999DI04, 2001DI12).
Angular distributions to 12Cg.s. were measured at E(14N) = 41, 77 and 113 MeV (1971LI11) and optical model parameters were deduced. For reaction (b), angular distributions to 12C*(0, 4.44, 9.6) have been measured at E(16O) = 27, 30, 32.5, 35 and 60 MeV (1972SC03): at the highest energy the ratio of relative spectroscopic factors, θ2/θ2g.s., for the transitions 11Bg.s. + p → 12C* is 0.12 and 0.05, respectively, for 12C*(4.4, 9.6). See (1975SC35) for analysis of reactions to the ground state at E(16O) = 27 to 35 MeV, and see (1992KA19) for analysis of multi-cluster transfer processes in the reaction.
The impact of reactions such as 11C(n, γ), 11C(n, α) and 11C(d, p) on nucleosynthesis is analyzed (2012CO01).
12B decay to 12C is complex. Most of the decay populates 12Cg.s. with small branches populating 12C*(4.4) and several α-particle unbound states (see 12.24 (in PDF or PS)). See general discussion in (1992BA11, 1993CH06). The ground state decay branch is determined by subtracting all other observed decay branches from unity. Early studies were motivated by evaluation of the 12B and 12N mirror decays to states in 12C and by parity violation studies. The decay rates to 12C*(4.4) measured in (1981KA31) are deduced while taking significant care to decrease systematic effects that could distort the results; they are the most precise and have been used as normalization factors in modern experiments to deduce the relative and absolute branching ratios of weaker decay branches. We adopt the branching ratios of (1981KA31) to 12C*(4.4).
Significant efforts have focused mainly on the ratio of the β-decay branches of 12B and 12N to 12C*(4.4) and the relevance of mirror asymmetries in β-decay; see 12.23 (in PDF or PS). In the case of 12N, the measurement is complicated because the high-energy 17.3 MeV β+ particles can produce Bremsstrahlung photons and give rise to a huge background. A lower Q-value in the case of 12B β--decay makes these measurements less complicated. Discussion on systematic effects in the measurements is given in (1974MC11, 1978AL01).
In (1963PE10, 1963WI05) the experimental layout used a scintillator β-counter that covered only part of the total solid angle along with NaI detectors; the β-γ coincidence data were analyzed. Other experimental efforts surrounded the targets with well-type scintillators while also detecting γ-rays in a NaI detector and analyzing the β-γ coincidence events (1972AL31, 1974MC11). The use of Ge(Li) and HPGe detectors significantly improved results from the measurements reported in (1978AL01, 1981KA31, 1988NA09). In most cases, the ratio of 12B-to-12N β-γ(4.44) coincidences was measured by using an essentially identical configuration for the two decays; then in some cases the configuration was modified to permit an absolute measurement of the 12B decay branch to 12C*(4.4) (1978AL01). In (1963PE10, 1981KA31) absolute 12N decay intensities were measured along with the mirror decay ratio.
In the early study of (1957CO59) β-delayed α particles were studied in an effort to validate the prediction of a narrow "3α" state located just above the breakup threshold. The Hoyle state was reported in 12B decay with the branching ratio (1.3 ± 0.4)%, Jπ = 0+ and Q(12C-8Be-α) = 278 ± 4 keV (Ex = 7.65 MeV). Analysis of a higher energy α group (1958CO66) was consistent with a broad Jπ = 0+ (or 2+) state near 10.1 MeV with a (0.13 ± 0.04)% branching ratio. Later, in (1963WI05) the α, β and γ products were measured and analyzed for evidence of states in the Ex = 9 to 12 MeV region; their best fit included states at Ex = 10.1 and ≈ 11.8 MeV. It is later pointed out in (1967AL03, 2009HY02) that the early works such as (1958CO66, 1963WI05) assigned too much intensity to the Ex = 10.3 MeV strength because they were unaware of the presence of the Ex = 12.71 MeV state. The work of (1966SC23) found evidence for 12C*(10.3 ± 0.3) decaying primarily to 8Beg.s. + α0 with a likely Jπ = 0+ and for 12C*(12.71) decaying > 96% to 8Be*(2+) + α, hence Jπ = 1+. The relative ratio of Iβ(10.3)/Iβ(12.7) was found as 0.20 ± 0.05.
On the other hand, the studies of (1962MA22, 1963GL04) used magnetic spectrometers to measure the β∓-particle energy spectra. While the main thrust of these measurements focused on the energy dependence of the shape factors, results on intensities to 12C*(7.65, 10.3) were also obtained in the analysis. See also (2015MO10).
In (1963AL15), the γ3.23-γ4.44 sequential de-excitation γ rays from 12C*(7.65) and the β-γ3.23-γ4.44 events are analyzed to determine Γγ/Γ(7.65) = (3.8 ± 1.5) × 10-4 and the (1.7 ± 0.5)% for the 12B β-decay branching ratio to 12C*(7.65). A similar measurement was carried out using the Gammasphere array (2016MU06); in that work (0.64 ± 11)% is determined for the β-decay branching ratio to 12C*(7.65) and Eγ = 3216.9 ± 0.4 (stat.) ± 0.7 (sys.) keV and 4439.5 ± 0.7 (sys.) keV are determined for the transitions between the Jπ = 0+2 → 2+1 and Jπ = 2+1 → 0+1 states. This corresponds to Ex = 7657.8 ± 1.0 keV, which is in poor agreement with the adopted value in 12.13 (in PDF or PS), Ex = 7654.07 ± 0.19 keV (1976NO02). In 12.24 (in PDF or PS) it is highlighted that some of the differences in published branching ratios are connected with the use of updated values in their computations.
In (1973BA73) the energy of the Hoyle state was determined by implanting 12B activity, produced via the 11B(d, 12B) reaction, into a thick Si detector and measuring the 3-α breakup energy, Q = 379.6 ± 2.0 keV.
Prior to development of rare isotope facilities, the 12B and 12N activities were typically produced in the target using the 11B(d, n) and 10B(3He, n) reactions, respectively. These approaches have the disadvantage of producing unwanted activities such as 11C, 13N and 14O in the targets. Renewed interest in the higher-lying Jπ = 0+ and 2+ states led to measurements where 12B and 12N were produced at rare isotope facilities. An early series of experiments (2002FY02, 2003FY02, 2003FY04, 2004BO43, 2004FY02, 2004FY03) focused on identifying 12C*(10.3) → 8Beg.s. + α and 12C*(12.71) → 8Be*(2+) + α1 as the dominant breakup mechanisms for these states by analyzing the α-particle correlations. These data also gave indications of important interference effects between the Ex = 7.65 and 10.3 MeV Jπ = 0+ states, as had been suggested in (1963WI05). In follow up measurements, two different experimental approaches enhanced the available data (2005DI16, 2009DI06, 2009HY01, 2009HY02, 2014TE01); in one case the ions were implanted into a thin carbon foil and the full decay kinematics of breakup α-particles was measured. Analysis yielded the decay intensity of 12C excited states along with an assessment of the decay mechanism. In the second approach, ions were implanted in a segmented strip detector whose thickness stopped the full decay energy of breakup α-particles; this calorimeter approach provided a measure of the energies populated in 12C with fewer systematic effects than prior experiments. The general shapes of spectra observed in (2009HY01, 2009HY02) were found in reasonable agreement with prior results. Implementation of HPGe detectors in the setups of (2009HY01, 2009HY02) permitted a simultaneous and absolute normalization of the β branching ratios to all unbound states using the known branching ratio to the 12C*(4.44) state. In this case, the total intensities of 12C*(12.71, 15.11) must be adjusted to account for the Γγ decay branches. See 12.24 (in PDF or PS).
The work of (2009HY01, 2009HY02, 2010HY01) focused on a search for unknown and unresolved Jπ = 0+ and 2+ strength in the Ex = 9-16 MeV region. Their analysis found that interference of the Jπ = 0+2 state with other Jπ = 0+ strength around Ex ≈ 11.2 MeV leads to "the very broad component from 8.5 to 11 MeV, which has been mistaken for a 10.3-MeV resonance with a 3-MeV width". Rather than attribute their observed strength to a 10.3 MeV group, they provided the β feeding strength for the Ex = 9-12 MeV and 12-16.3 MeV regions [excluding the 12.7 MeV state]. In (2010HY01), a multi-level many-channel R-matrix analysis of the data was carried out. The data was best fit with a Jπ = 0+ state at Ex = 11.2 ± 0.3 MeV with Γ = 1.5 ± 0.6 MeV and B(GT) = 0.06 ± 0.02 and a Jπ = 2+ state at Ex = 11.1 ± 0.3 MeV with Γ = 1.4 ± 0.4 MeV and B(GT) = 0.05 ± 0.03.
Violation of the Pauli exclusion principle could permit 12C to decay by converting a p-shell nucleon into as 1s1/2-shell nucleon followed by emission of a ≈ 20 MeV γ ray. The reaction has not been observed. The limit on the mean lifetime of 12C for this decay is τm ≥ 5.0 × 1031 yr (2010BE08); see also (1979LO13, 1998BA57, 1999AR22). Lifetimes for other 12Cg.s. exotic decays are > 8.9 × 1029 yr (2010BE08); see also (2003BA42).
The total absorption, mainly (γ, n) + (γ, p), is dominated by a giant resonance peak at Ex = 23.2 MeV, Γ = 3.2 MeV [σmax = 21 mb] and by a smaller structure at Ex = 25.6 MeV, Γ ≈ 2 MeV [σmax ≈ 13 mb]: see (1975AH06) and references tabulated in (1968AJ02, 1975AJ02).
The (γ, n) cross section shows a giant resonance, σmax ≈ 7 - 8 mb, centered at about 23 MeV and consisting of an ≈ 1 MeV-wide group at 22.3 MeV and an ≈ 2 MeV-wide group at ≈ 23.3 MeV. A secondary maximum occurs at 25.5 MeV, Γ ≈ 2 MeV with evidence for other structures at ≈ 30 - 31 and possibly at ≈ 35 MeV (1966FU02, 1966LO04); see also (1999AB39, 1999AB40, 2000AB35: Ebrem = 20 MeV), (2003CH80, 2016HE07) and the atlas of photo-neutron cross sections (1988DI02).
The (γ, n0) cross section has been measured at θ = 90° for 21 < Ex < 40 MeV and compared with the (γ, p0) cross section (1968WU01): the isospin mixing averages about 2% in intensity and shows structure at the giant resonance. Angular distributions of n0 measured over the giant resonance region indicate that the main excitation mechanism is of a 1p3/2 → d5/2 E1 single-particle character. No significant E2 strength is observed (1968RA21). At Eγ = 60 MeV a comparison of the (γ, n0) and (γ, p0) cross sections indicates the reaction mechanism is absorption and suggests the reaction is useful for studying correlated n-p pairs (1980GO13). A comparison of the 12C(γ, p)3H2α and 12C(γ, n)3He2α reactions at Eγ = 30 to 120 MeV is given in (2007AF02). See also results in (1993AN17: Ebrem = 58 MeV), (2001KO62: Ebrem = 70 to 140 MeV) and (1994RY03, 2000LE38, 2003VA20, 2011DZ02).
The (γ, 2n) cross section (reaction (b)) is much smaller than that for (γ, n): the highest value is 0.15% of the maximum value for reaction (a) in the energy range Eγ = 20 to 140 MeV (1970KA37). The reaction has been studied for Ebrem = 100 to 800 MeV with an emphasis on 11C production (1977JO02): see other references in (1975AJ02, 1980AJ01, 1985AJ01, 1990AJ01).
The photoproton cross section exhibits two broad peaks, the giant resonance peak at 22.5 MeV, Γ = 3.2 MeV, σmax = 13.1 ± 0.8 mb and a 2 MeV broad peak at 25.2 MeV, σmax = 5.6 ± 0.3 mb: see (1976CA21) and values listed in 12.19 (in PDF or PS) in (1968AJ02). The (γ, p0) cross section at the giant resonance is 11.0 ± 1.1 mb (1986KE06). While the E1 component dominates in the GDR, a 2% E2 contribution may be present (1976CA21). In contrast with the giant resonance peak in the (γ, n) cross section, the (γ, p) cross section shows a sharp peak in the center of the broad giant resonance peak. See also (1991IS09). Above 24.5 MeV the ground state (γ, p) and (γ, n) excitation functions have the same shape up to at least 36 MeV: see (1985FU1C).
The (γ, p) results of (1968FR12, 1968FR14, 1969CA22) are in good agreement with those of (1964AL20) for the inverse reaction, 11B(p, γ0)12C [see reaction 20], when the population of 11B*(4.4, 5.0) is taken into account: the required cross sections for the (γ, p2) and (γ, p3) processes peak at 1.5 mb at 29 and 30 MeV, respectively (1973DI1C, 1974DI17).
The population of 11B states has been determined at various energies. The ground state is predominantly populated in these reactions; see measurements and discussion in (1980AJ01, 1985AJ01, 1990AJ01) and (1986AN25, 1986MC15, 1990SP06, 1990VA07, 1990VA09, 1991IS09, 1993IR01, 1994NI04, 1994ZO01, 1995HA03, 1995MO18, 1996KU36, 1996RU15, 1997AS01, 1997ZO02, 1998KU23, 1998SO18, 2001ME29, 2006MO11). Nuclear transparency, as well as the roles of different reaction mechanisms, including quasi-deuteron knockout, are investigated in (1990VA07, 1992RY02, 1992VA01, 1993HA12, 1993IR01, 1994IR01, 1994NI04, 1994RY03, 1995MO18, 1996AS02, 1996JO15, 1996RU15, 1997AS01, 1997BO22, 1997JO07, 2000LE38, 2002ME17, 2005GL05, 2005KA54, 2006CO19, 2013RO17).
Reactions in the Δ resonance region are discussed in (1992BA57, 1992GL04, 1995CR04, 1997JO07, 1997LI30, 1998GL14, 1999FI01, 2000DE58, 2000GL08, 2001MA31, 2002ME17, 2003GL03, 2006AN22, 2008GL05, 2010GL02, 2012GL02, 2013GL03, 2014GL03). In this region peaks corresponding to the removal of s-shell or p-shell protons from 12C are observed in the missing mass spectrum, and quasi-free photo pion production is an important reaction mechanism. Searches for Δ components in the 12Cg.s. are discussed in (2001BY01, 2002BY03). Evidence for η-mesic 11B atoms is claimed in (1999SO18, 2000SO19, 2000YO02, 2002BA21); also see (1995LE26, 1996LE11, 1996RO06, 1997FI07, 1997HE14, 1998AB13, 1998EF09, 1998HE18, 1998PE12, 1999LE35, 1999TR09, 2000EF04, 2001BL13, 2001TR06, 2003HE18, 2003VA08, 2004MA27, 2005MO04, 2005NA17, 2005NA25, 2005NA35, 2006NA34, 2007HE29, 2008JI06, 2008ME15, 2015NE10).
Photo-pion production has been measured at Eγ = 111 to 160 MeV (1997BE22), 120 to 819 MeV (2008TA05), 130 to 165 MeV (1995VO17), 141 to 159 MeV (2008BA24), 170 to 177 MeV (1995GO27, 2008GO20), 200 to 350 MeV (2002KR02), 200 to 800 MeV (1998KR28, 2004KR16), 300 to 400 MeV (1991BE16) and 4.5 GeV (1993EG06). The 2π0 correlations were measured at Eγ = 200 to 820 MeV (2003ME32) and at 400 to 460 MeV (2002JA10, 2002ME22). General discussion, for example on photo-pion production in the Δ-resonance region, can be found in (1991TR02, 1992CA16, 1994BE31, 1994KO23, 1994OS02, 1995BA92, 1995HO12, 1996MA20, 1997EF03, 2000GL08, 2002BA23, 2004MU17, 2006DA17, 2007TR04, 2008CO04). Coherent photo-pion production is discussed in (1991BO26, 1993CA35, 1993LA07, 1993OL06, 1996TR07, 1997KA65, 1998PE09, 1999AB42, 1999DR17, 2005KR18, 2010NA04, 2012ZH39), and in-medium effects are discussed in (1996OS02, 1999LE35, 2002RO28, 2003RO20, 2003VI09, 2003VI11, 2005KR10, 2005RO13, 2006SC18). For 12C(γ, π+) see 12B reaction 23 and for 12C(γ, π-) see 12N reaction 8.
Cross sections and angular distributions of the deuterons corresponding to transitions to 10Bg.s. and/or low excited states have been measured at Eγ ≈ 40 MeV: the results are consistent with E2 strength. There is some evidence for the excitation of higher states of 10B via non-E2 transitions (1972SK08). For Ebrem = 90 MeV, the ratio of the yields of deuterons to protons is ≈ 2%, for particle energies 15 to 30 MeV. For higher particle energies, the ratio decreases (1962CH26). The excitation function for deuterons to Eγ = 1.4 GeV is given in (1969AN10, 1971AN15, 1972AN09, 1972AN22). The (γ, pn) reaction has been studied at Eγ = 83 to 133 MeV by (1988DA16), at Ebrem = 150 MeV by (1999KH06) and in the Δ-resonance region by (1987KA13, 1996HA17, 1996LA15, 1998HA01, 1998MA02, 1998YA05, 1999FR32, 2000WA20, 2001PO19); see also (1996OS01, 1998RY01, 1999IR01, 2000GR13, 2003WA01).
Momentum spectra for deuterons and tritons (reactions (a) and (c)) are reported at Eγ = 300 to 600 MeV by (1986BA07). The yield of tritons has been measured for Eγ = 35 to 50 MeV: see (1967KR05) and Eγ < 1.2 GeV (1972AN09). For reaction (d) see (1987VO08: Ebrem = 80 MeV), (1999MC06: Ebrem = 150 to 400 MeV) and (2007WA12: Epol. brem = 170 to 350 MeV).
A study of the α breakup cross section using quasi-monoenergetic and polarized beams with Eγ = 9.0 to 10.7 MeV found enhanced E2 strength corresponding to Ex = 10.03 ± 0.11 MeV with Γ = 0.80 ± 0.13 MeV and Γγ = 60 ± 10 meV (2013ZI03); in the analysis the α-8Be breakup angular distribution was analyzed to determine the E1/E2 contributions and the mixing phase. This state is interpreted as the Jπ = 2+ excitation of the Ex = 7.65 MeV astrophysically important Hoyle state. Also see (2011GA09, 2012GA39), (2016HA05: theory) and (1994OB03, 2011GA47, 2011IS14, 2013IS05, 2014IS06, 2015GA17: astrophys.).
At higher energies, the total cross section exhibits broad peaks at Ex = 17.47 ± 0.12 MeV with Γ = 6.12 ± 0.14 MeV and 27.12 ± 0.34 MeV with Γ = 4.56 ± 0.14 MeV (2008AF04). A pronounced minimum occurs at 20.5 MeV: to what extent the peaks have fine structure is not clear; see (1964TO1A) and references in (1968AJ02). Alpha energy distributions show surprisingly strong E1 contributions below Eγ ≈ 17 MeV (1955GO59, 1964TO1A). For Eγ < 22 MeV, transitions are mainly to 8Beg.s. and 8Be*(2.9) with the g.s. transition dominating for Eγ ≲ 14 MeV. For Eγ > 26.4 MeV, 8Be (T = 1) levels near 17 MeV are strongly excited (1955GO59, 2008AF04). The mechanism for formation of various 8Be excited states up to Ex ≈ 23 MeV was carefully studied for photon energies below Ebrem = 40 MeV (2008AF04), and resonances have been deduced; see 12.25 (in PDF or PS). See also (1992DZ02, 1993KI15, 1997GO16, 1998KO77, 2001KI33, 2002KO65).
Inelastic scattering has also been reported to 12C*(4.4, 9.6 ± 0.2, 11.8 ± 0.2, 12.7, 13.3 ± 0.2, 17.2 ± 0.2, 18.3 ± 0.2, 20.5 ± 0.2, 22-24 (giant resonance), 26.5 ± 0.4, 29.5 ± 0.3): see details in (1980AJ01) and (1980IS09, 1980IS13, 1982NOZV).
Resonance scattering and absorption by 12C*(15.11) have been studied by many groups: see 12.15 (in PDF or PS) in (1968AJ02). The branching ratios and partial widths are displayed in 12.9 (in PDF or PS) in (1975AJ02) and 12.14 (in PDF or PS). The scattering angular distribution indicates dipole radiation (1959GA09), the azimuthal distribution of scattered polarized radiation indicates M1 (1960JA01) and the large Γγ indicates T = 1. The branching ratio for the cascade decay via 12C*(4.4) was reported as (3.6 ± 0.7)% (1970AH02).
The ground-state width of 12C*(16.11) was first reported as Γγ0 = 7.5 ± 1.9 eV (1959KE19): see, however, 12.14 (in PDF or PS) which shows a much smaller accepted value. For 12C*(17.22), the scattering cross section is 1.0 ± 1.0 μb, consistent with Γγ from 11B(p, γ) (1963SC21).
At higher energies, elastic scattering studies show the giant resonance peak at ≈ 24 MeV. A considerable tail is visible, extending to > 40 MeV (1959PE32). At Eγ = 23.5 MeV, the peak of the giant resonance, the total photonuclear absorption cross section is 19.7 ± 0.4 mb (1983DO05), and Γ1/Γ0 = 0.23 ± 0.07.
In (1990SC02) the cross sections were measured for Eγ = 15 to 140 MeV using tagged Bremsstrahlung photons. At low energies, 12C*(15.1) and the GDR are prominent, while the scattering cross section is essentially flat above Eγ = 30 MeV. The 12C*(16.1) state and additional strength are observed in the inelastic scattering to 12C*(4.4). The ratio of dσ(150°)/dσ(60°) was studied in this range to reveal E1/E2 interference effects; E2 states are suggested near Ex = 28 and 32 MeV. Previous measurements of the cross section at θ = 90° and 135° for Eγ = 23.5 to 39 MeV indicated a significant E2 strength [1.9+0.8-0.7 total isoscalar + isovector energy weighted sum rule] in addition to the dominant E1 strength (1980DO04, 1983DO05). However, measurements of the elastic differential cross sections for Eγ = 22.5 to 52.0 MeV (θ = 45°, 90°, 135°) reported by (1984WR01, 1985WR02) were inconsistent with the results of (1980DO04, 1983DO05). The difference between the measured energy-integrated values of σ(γ) and the E1 part of the photo-absorption cross section σE1(γ) was small and not sufficient to verify E2 strength (1985WR02).
The scattering cross section has been measured for Eγ = 150 to 400 MeV by (1984HA08). Angular distributions for elastic and inelastic scattering are measured at Ebrem = 158.8, 195.2, 197.2, 247.2 and 290.2 MeV (1995IG01). Measurements of elastic and inelastic scattering to 12C*(4.4) at Eγ = 200 to 500 MeV, including the Δ-resonance region, are given in (1993AH01, 1994WI13). A measurement of the total photoabsorption cross section for Eγ = 600 to 1500 MeV is given in (2010RU16). See theoretical analyses in (1996PA06, 1998HU01, 2002SC15, 2002VA01). For pair-production measurements at Ebrem = 4.2 to 31.1 MeV see (1983NO06).
The polarizabilities of bound nucleons in 12C and 16O were measured at Eγ = 61 and 77 MeV (1992LU01). The deduced values, α̃N = (11.5 ± 0.8 (stat.) ± 2.1 (sys.)) × 10-4 fm3 and β̃N = (2.5 ∓ 0.8 (stat.) ± 2.1 (sys.)) × 10-4 fm3, are in close agreement with the values for free nucleons. However, see the analysis of (2001WA24: Eγ = 84 to 105 MeV), which suggests that definite conclusions are severely hampered by model dependencies. See also (1995HA23: Eγ = 58 and 75 MeV, 2014MY01: Eγ = 65 to 115 MeV).
Elastic scattering has been studied up to several GeV. The form factor is well accounted for by a harmonic-well model. Measurements of the elastic scattering form factor indicate the nuclear charge radius is < r2 >1/2 = 2.471 ± 0.009 fm [2.478 fm with dispersion corrections] (1991OF01), 2.464 ± 0.012 fm [2.468 fm with dispersion corrections] (1982RE12) and 2.472 ± 0.015 fm (1980CA07). This compares with < r2 >1/2 = 2.4829 ± 0.0019 fm from muonic X-ray studies (1984RU12). Other values are reported in (1968AJ02, 1975AJ02). See also (1995AN02, 1995AN13, 2010HA14). (1991OF01) reports evidence for an energy dependence of the elastic form factors.
The isoscalar vector hadronic coupling constant, γ = 0.136 ± 0.032 (stat.) ± 0.009 (sys.) (1990KO47, 1990SO03, 1991SO08), is determined from analysis of parity violating electro-weak asymmetry in elastic scattering. Use of the parity violating elastic scattering asymmetries to obtain neutron densities is discussed in (2011MO35, 2012AB04, 2014MO03). See also (1990SU15, 1992MI09, 1993AL07, 1993AL20, 1993HO03, 1995KA14, 1998HO12, 2005ME10, 2009MO35).
A study of the (e, e'γ) reaction by (1985PA01) shows that the relative phase of the longitudinal and transverse form factors of 12C*(4.4) is negative.
Inelastic scattering data for the 12C*(7.65) Hoyle state at Ee = 73 MeV was collected and analyzed along with the world data resulting in the value Γπ = 62.3 ± 2.0 μeV for radiative decay (2009CHZX, 2010CH17, 2011VO16). This value is compared with prior measurements and other analyses; see (2005CR03) and (2014FR09) for references. Analysis of data in (2007CH04) suggests that the Hoyle state is dilute with a radius about 1.5 times larger than that of the ground state.
The longitudinal form factor for the Jπ; T = 1-; 0 isospin forbidden transition to 12C*(10.84), which is sensitive to isospin mixing, was analyzed and indicates a transition strength B(E1) = 0.39 ± 0.20 × 10-5 e2 ⋅ fm2 (1995CA14).
The isospin mixing between 12C*(12.71) and 12C*(15.11) [both Jπ = 1+; T = 0 and 1, respectively] has been measured by (1974CE01): β = 0.19 ± 0.01 or 0.05 ± 0.01. The inelastic scattering to 12C*(12.71, 15.11) was analyzed at q < 0.5 fm-1, Γγ0 = 0.32 ± 0.02 eV and 35.0 ± 1.1 eV were deduced, respectively (2000VO04). The results were combined with (1972SP1C) and (1973CH16) (other low q results) and produced an average of 35.9 ± 0.06 eV for the later transition. These compare with 38.5 ± 0.8 eV from (1983DE53). The Coulomb matrix element was also analyzed in (2000VO04); ME = +118 ± 8 keV was deduced.
The longitudinal form factors show 12C*(16.1, 18.6, 20.0, 21.6, 22.0, 23.8, 25.5) while the transverse form factors show 12C*(15.1, 16.1, 16.6, 18.1, 19.3, 19.6, 20.6, 22.7, (25.5)). At Ee = 150.6 MeV (θ = 180°) two peaks are observed at 16.1 and at 19.6 MeV corresponding to E2 and M2-M4 excitations (1984RY01).
There appears to be evidence for structures at 18.1 ± 0.05, 19.5 ± 0.05 (Γ = 0.5 ± 0.1), ≈ 24 and ≈ 34 MeV (1964GO14). The variation of F(q2) with q2 in the range 0-0.6 fm-2 shows good agreement with the calculations of (1964LE1D) which assumes four 1- particle-hole states at Ex = 19.6, 23.3, 25.0 and 35.8 MeV (see also (1967CR02)). The behavior of the 19.2 MeV level suggests ascription to the expected giant magnetic quadrupole state Jπ = 2-; this state is not likely to have been seen in 11B(p, γ)12C (1965DE1C, 1965DE1K, 1967BI1K, 1967CR02). A positive parity state with a large longitudinal matrix element may also be present (1967BI1K).
No ΔT = 2 excitations were observed in a search for isotensor components of the electromagnetic interaction (1993LO13).
Results and general analysis on scattering at medium to high energies are given in (1990DA14, 1991BR13, 1991BU04, 1991DE32, 1991ER06, 1991TA23, 1992PR01, 1992WA19, 1993AM11, 1993AR06, 1993DE33, 1994AM06, 1994JE04, 1995AV01, 1995DO23, 1995JO21, 1995MO11, 1995VA12, 1995VA33, 1997GI12, 1998RI01, 1999GU20, 2001CA04, 2001GU16, 2002CA26, 2003KI06, 2003KI09, 2003ME09, 2004KI21, 2005KI26, 2006KU01, 2006MA62, 2008CE01, 2009LI04, 2010AM01, 2010HA14, 2014KI06, 2015LO05, 2015MO24, 2015PA35, 2016RO32).
Reviews on the scaling and superscaling behavior of quasielastic electron scattering reaction cross sections are found in (2009MA57, 2010CA14). See other detailed discussion on scaling approaches in (1999DO05, 2003HA44, 2005AM03, 2005NA03, 2006BA62, 2006CA22, 2006CO15, 2007AM01, 2007KI16, 2007MA18, 2009AN06, 2009CI01, 2009MA57, 2009ME07, 2010AM01, 2011AN09, 2015AM02, 2015BE26, 2015KI01, 2016IV03).
In (1984CA34) evidence for a monopole, Jπ = 0+, state near Ex ≈ 20.5 MeV which exhausts at least 1% of the energy weighted sum rule is found in (e, e'p0). The decay of states in the giant resonance region via α-particles has been studied by (1993DE10, 1995DE23): the E2 decay is primarily to 8Be*(2.9[Jπ = 2+]) and reveals a peak with Ex = 21.6 and Γ ≈ 1.5 MeV; see also (1991PO06, 1994CA08, 1999SA27).
Electron spectra in the region of large energy loss show a broad peak which is attributed to quasi-elastic processes involving ejection of single nucleons from bound shells; studies of e'-p coincidences reveal peaks corresponding to ejection of 1p and 1s protons (at 700 MeV the energies of the peaks are 15.5 ± 0.1 and 36.9 ± 0.3 MeV with Γ = 6.9 ± 0.1 and 19.8 ± 0.5 MeV, respectively [1976NA17: DWIA]). Spectroscopic factors for 1s [ = 1.50 ± 0.08 (2000LA23)] and 1p [= 3.56 ± 0.12 (2000LA23)] shell single-particle knockout reactions are discussed in (1990CA14, 1990DE16, 1990WE06, 1991WE10, 1991WE16, 1994IR01, 1994IR02, 1995BL10, 1995KE03, 1998WO01, 1999DO30, 1999RY06, 2000DU12, 2000LA23, 2002MA12).
At 500 MeV the quasi-elastic scattering cross section has been analyzed and indicates the Fermi momentum is 221 ± 5 MeV/c (1971MO06).
Studies of the quasielastic longitudinal and transverse response functions versus missing energy have been carried out. (1987UL03) find in the longitudinal response a broad bump at missing energies between 28 and 48 MeV, attributed to knockout from the s-shell. In the transverse response they find this bump on top of a broader feature with a threshold at 28 MeV extending beyond 65 MeV. This broad feature is attributed to two-particle knockout, a non-quasielastic reaction mechanism; it may account for the observed (e, e') transverse-longitudinal difference. This feature is also observed in unseparated data at larger momentum transfers: it appears to grow with momentum transfer (1988WE1E). See also (1992BO10, 1992WA19, 1994MA26, 1995JO21, 2003AN15, 2003DE10, 2005MO04).
Multi-nucleon correlations and few-body interactions are discussed in (1993KE02, 1995KE03, 1995KE06, 1996KE03, 1996RY04, 1997RY01, 1998AL03, 1998BL06, 1998RY05, 2000DE58, 2000RO17, 2004MU29, 2005HO18, 2005KE06, 2006EG02, 2007PI05, 2009CI01, 2014CO05). Nucleon excitation studies are discussed in (1993RO13, 1995NI01, 1995ZO01, 1997GI02, 1997GI12, 1998GA25, 1999BA31, 2004BO47, 2008BO24, 2011VA11).
Effects such as transparency of the nuclear medium have been studied by (1990FR11, 1992BE23, 1992FR17, 1992GA02, 1992JE03, 1992PA03, 1993LO01, 1993NI11, 1994FR12, 1994FR16, 1994GR05, 1994IR02, 1994KO21, 1994MA23, 1994NI05, 1995FR04, 1996KE14, 1996NI13, 1997AL20, 1997IW03, 1999RY06, 2000DU12, 2000LA23, 2001FR06, 2002DE11, 2002GA43, 2002ME11, 2002ME17, 2003DU23, 2003RY02, 2004BA99, 2004BO47, 2004HA63, 2004LA13, 2005RO38, 2006RO37, 2007CL04, 2009KA02, 2010QI02, 2013RO06). Discussion on other final state effects is given in (1991CA09, 1994IR02, 1994JE04, 1994RY04, 1995BI07, 1995BI19, 1995NI02, 1996BI01, 1996BI21, 1996JE04, 1999KE04, 2002DE07, 2004BA99, 2004BB15, 2005BA07, 2005BA23, 2005PR02, 2007AL14, 2007PI05), and discussion on the reaction mechanism is found in (1990LO09, 1991VA05, 1992DR02, 1993CI05, 1993OF01, 1994IR01, 1994RY03, 1994TA11, 1994WE06, 1999MO02, 2002ME17, 2004FR27, 2004MU29, 2004RO35, 2004TA18, 2011RY03). See also (1993KE02, 1993KO12, 1994BI05, 1994VE08, 1994WA19, 1995RY02, 1996JO15, 1997BI06, 1997GI13, 1998HO20, 1999JO06, 2000DE38, 2000UD01, 2005KE04, 2009TA34, 2014MO25, 2014TO14).
Parity violating muon scattering is discussed in (1993MI03). A review of μ--e- conversion reactions is given in (2006DE31). Cosmogenic production of nuclides, such as 11C, is discussed in (2005GA19, 2006BA66, 2000HA33).
Angular distributions of the elastic and inelastically scattered pions have been measured at many energies: see 12.27 (in PDF or PS). See theoretical analysis in (1990BE53, 1990ER06, 1990FR02, 1990LI10, 1990MI08, 1990TA13, 1991AL01, 1991AR12, 1991OS01, 1991TA01, 1992BI06, 1993CH04, 1993CH16, 1993CH25, 1993MO27, 1993NI02, 1993PE09, 1994CH30, 1995AR02, 1995BA92, 1995KA49, 1996BI12, 1996CH16, 1996EB02, 1997SC09, 1998AH06, 1998CH42, 1998NU02, 1998PE09, 1998RO15, 1999HO13, 1999TA33, 2000EB05, 2000KH17, 2002NO13, 2004SA28, 2005EB03, 2005HA26, 2006AH02, 2006KA47, 2009FA02, 2010IO02, 2011EB03, 2013EB02, 2013KH17).
Angular correlations for π'-γ4.4 and π'-γ15.1 reactions have been studied by (1984SO12, 1984VO04, 1986OL07, 1988OL02) and (1988BA27), respectively. A detailed analysis of the sum rules for population of the Jπ = 1-; T = 0 12C*(10.84) state is given in (1993KO17). The possible group to 12C*(15.4) has a width of ≈ 2 MeV (1981MO07); 12C*(14.1, 16.1) were also populated. Jπ = 2- for 12C*(18.25, 19.4) and J = 4 for 12C*(19.25) are suggested in (1987CO17); 12C*(19.65) is also populated. Study of the giant resonance region suggests states at Ex = 19.85, 22.10, 22.94, 23.70 and 25.40 MeV with Γ ≈ 330, 198, 192, 79 and 232 keV, respectively (1993KO17). See also Ex = 20.0 ± 0.2 and 22.7 ± 0.4 MeV, with Γ = 3.2 ± 0.3 and 1.0 ± 0.2 MeV (1984BL12) and Ex ≈ 18.3, 19.3, 22.1, 23.7 and 25.6 MeV (1982MO25).
A strong energy-dependent enhancement in the pion scattering to 12C*(15.1) but not to 12C*(12.7) is observed at Eπ± = 100, 180 and 230 MeV: this is interpreted as possible evidence for direct (Δ-h) components in the wave function of the T = 1 state (1982MO01). The charge-dependent matrix element between the Jπ = 1+; T = 0 and 1+; T = 1 states, 12C*(12.71, 15.11), was studied by (1990JA05); ME = 157 ± 35 keV was deduced. See the results of (1981MO07) along with other values in 12.18 (in PDF or PS). The ratio of the cross sections to, 12C*(12.7, 15.1) at Eπ± = 50 MeV is 7.1 ± 1 [isospin averaged] (1988RI03). The excitation of these two states has also been studied for Eπ± = 80 to 295 MeV by (1988OA03). A preliminary value for the isospin mixing matrix element between 12C*(18.4, 19.4), 250 ± 50 keV, was given in (1979BO2D, 1979MO1W: Eπ = 116, 180 MeV).
The emission of 2 photons in the capture of stopped pions, i.e. (π-, γγ), occurs at a rate of (1.3 ± 0.3) × 10-5/capture (1979DE06).
Strong energy dependence is observed in the π+ absorption (1981AS07, 1983NA18). At Eπ± = 50 MeV the absorption of π- is about twice that of π+ (1983NA18). Analysis of 4.4 MeV γ-rays produced at Eπ = 73 MeV yields σ(π+) = 14.5 ± 3.0 mb and a cross section ratio, σ(π-)/σ(π+), of 1.23 ± 0.22 (1970HI10).
The Fermi-momentum distribution of protons was measured using reaction (b) at Eπ- = 0.7, 0.9 and 1.25 GeV (2000AB25).
Angular distributions and differential cross sections of elastically and inelastically scattered neutrons have been measured at many energies up to 350 MeV [see 12.28 (in PDF or PS)]. See other results in (1995TI10, 1995ZH49, 2013NE11). Discussion on polarization measurements is given in (1995CH12, 1995CH44, 2005CH58, 2006SV01, 2010WE06). For Optical Potential analyses see (1990NI02, 1991SH08, 1997EL13, 2001KA58, 2009WE04, 2011JA09, 2011RA34, 2012JA03, 2012PA09, 2015GH04, 2016AL14, 2016XU07); for Coupled Channels analyses see (2003AM08, 2005CA16, 2006SV01); for other analyses see (1990BE54, 1991BA39, 1992GA26, 1992KA14, 1992KA21, 1994IS08, 1994XI04, 1996CH33, 1996CH49, 1996GO48, 1997HA21, 1998SU23, 1999SU01, 2000CH31, 2000KE13, 2005PI16, 2008FR02, 2008FR11, 2008GE04, 2009AL05, 2009AL10, 2010NA18, 2016AR13, 2016FR09).
Angular correlations of (n, n'γ4.4) have been studied at En = 13.9 MeV (1973DE45) and 15.0 MeV (1971SP01), and at 14 to 14.7 MeV [see (1968AJ02)]. The spin-flip probability for the transition to 12C*(4.4) has been studied at En = 7.48 MeV (1971MC1K, 1972MC20) and at 15.0 and 16.9 MeV (1973TH08, 1974ME29). Its shape at En = 7.48 MeV is similar to that measured by (1964SC07) in the (p, p') reaction at Ep = 10 MeV (1972MC20); while that at En = 16.9 MeV the shape is similar to that measured by (1969KO07) at Ep = 20 MeV (1974ME29). The quadrupole deformation parameter β2 = -0.67 ± 0.04 (1983WO02).
For reaction (b), complete kinematics involving 12C*(7.65, 9.64, 10.84, 11.8, 12.7, 14.0, 15.1, 16.1) were studied at energies between En = 11.5 to 19 MeV (1991AN06). At En = 14.4 MeV 12C*(9.6, 10.8, 11.8, 12.7) have been reported: see (1975AJ02). A detailed study on the population of 12C*(9.6) at En = 11 to 35 MeV is given in (1983AN02): the decay is dominated by sequential feeding of 8Beg.s. at the higher energies; see also (1953JA1C). The α-decay of the 10.8 and 11.8 MeV states, together with stripping results, suggest Jπ = 1- and 2- for these states (1964BR25, 1971DO1K, 1975AN01, 1975AN02; see also (1966MO05)).
Angular distributions of elastically and inelastically scattered protons have been measured at many energies up to Ep = 1040 MeV: see 12.29 (in PDF or PS). 12.30 (in PDF or PS) displays the information on excited states of 12C. A summary of the decay of some excited states is shown in 12.14 (in PDF or PS).
The angular distributions have been analyzed by DWBA (and CCBA), DWIA (including microscopic calculations) and DWTA (DW t-matrix approximation with density-dependent interactions). Microscopic DWIA calculations give good results for transitions which proceed through the S = T = 1 part of the effective interaction and also give a reasonable description of the S = T = 0 transition. However the mechanism for the excitation of 12C*(12.71) (S = 1, T = 0) remains a puzzle (1980CO05: Ep = 122 MeV). The angular distributions of the inelastically scattered protons to 12C*(12.71) are usually poorly fitted: see e.g. (1990IE01). In (1995SA28) the 0° cross sections were measured for 12C*(12.71, 15.11) at Ep = 65 to 400 MeV; the cross sections, which maintained a nearly consistent ratio at all energies, were evaluated via microscopic DWIA analysis that reproduced the data best by reducing the isovector tensor terms of the effective interactions. Also see the analysis of spin observables at Ep = 198 MeV, for 12C*(12.71, 15.11) up to q ≈ 200 MeV/c (2001OP01).
At Ep = 402 MeV the differential cross sections for 12C*(12.7, 15.1) (Jπ = 1+) are very similar for large q. This may be due to the smallness of precursor effects [precursor to a pion condensate] (1981ES04).
The spin-flip probability (SFP) for the transition to 12C*(4.4) has been measured for Ep = 15.9 to 41.1 MeV: two bumps appear at Ex ≈ 20 and ≈ 29 MeV. It is suggested that the lower one is due to a substructure of the E1 giant dipole resonance while the upper one results from the E2 giant quadrupole resonance (1975DE32, 1982DE02). The SFP has also been studied at Epol. p = 24.1, 26.2, 28.7 MeV (1981FU12: to 12C*(4.4)), at Ep = 42 MeV (1981CO08: to 12C*(12.7)), at Epol. p = 397 MeV (1982SE12: to 12C*(9.6, 12.7, 15.1, 16.1)) [the SFP to 12C*(9.6) is consistent with zero; the others exhibit large SFP at forward angles] and at Ep = 398, 597 and 698 MeV (1983JO08: to 12C*(18.3, 19.4)). The SFP has also been measured for 12C*(12.71) at Ep = 42 MeV (1977MO18) and for 12C*(12.7, 15.1) at Ep = 23.5 to 27 MeV (1978HOZJ) and Ep = 500 MeV (1991CH31). The SFP was measured in the region of 5 < Ex < 30 MeV (1999TA22) and 10 < Ex < 40 MeV (1993BA37); see also (1990BA14, 1990BA61).
(1980HO07) have measured the angular distribution of γ-rays from the decay of 12C*(12.7, 15.1) at Ep = 21.5 to 27 MeV. Microscopic DW calculations were performed for the A0 and a2 coefficients from these and earlier data. The theoretical calculations underestimate A0 for energies below 35 MeV and are in agreement with the experimental A0 for higher energies. The calculations also predict significant differences in the a2 values for the transitions from 12C*(12.7, 15.1), and these are observed (1980HO07).
Angular distributions show that a large deformation exists: β2 = -0.72 (1972DE13) and 0.6 (1967SA13); β2 = -0.663 and β4 ≈ 0 (1983DE36); β2 = 55 ± 11, β0 = 0.15 ± 3 and β3 = 0.39 ± 8 (2010OK01). A DWBA analysis in (2010OK01) suggests 12C*(7.65) has a structure that is consistent with the assumption of a dilute α-cluster condensed state as suggested by (2001TO23).
The p-γ4.4 angular distributions have been studied at Ep = 7.5 MeV (2006LE45). The p-γ15.1 angular correlations have been studied at Epol. p = 100 to 180 (1990PI06) and Ep = 200 MeV (1995WE10), 318 MeV (1992LY01) and 400 MeV by (1988HI12). See also (1990PI06, 1995SU30).
A study at Ep = 66 MeV measured Γ(9.64) = 48 ± 2 keV (2013KO14). Evidence for the Jπ = 2+ excitation of the Ex = 7.65 MeV "Hoyle state" has been reported in (2009FR07, 2010FR03, 2012FR05: Ex = 9.75 ± 0.15 MeV with Γ = 0.75 ± 0.15 MeV) and (2011ZI01: Ex ≈ 9.6 MeV). In these different experiments, the known states at (7.65, 9.6, 9.64, 10.83, 11.80, 12.71) were also observed. The Γ ≈ 600 keV width initially reported in the (p, p') work of (2009FR07) was reanalyzed in (2012FR05) along with the (α, α') data of (2011IT08) yielding the slightly higher Γ = 0.75 ± 0.15 MeV value. In (2009FRZV), the authors question the validity of the Ex = 11.16 MeV state reported previously in 11B(3He, d) reactions and they reiterate the likely 12C*(13.35) Jπ = 4- spin assignment previously suggested in (2007FR17). In (1997TE14), inclusive (p, p') and exclusive (p, p'p) and (p, p'α) reactions populated levels between 0 < Ex < 24.4 MeV.
The GT+ strength distribution in 12B was analyzed in (2001WO07) by comparing the 12C*(15.1, 16.1, 18.35, 19.4, 21.6) excitations with the corresponding Jπ = 1+, 2+, 2-, 2- and 2- excitations from 12C(d, 2He)12B.
For theoretical analysis of elastic and inelastic scattering see (1990TA13, 1990TA16, 1991LI07, 1991TA01, 1992WA19, 1993BY02, 1993DE33, 1995MA23, 1996BE25, 1997DO02, 1997TE14, 1998GI01, 1998GU13, 1998KI17, 1998SU23, 1999GU17, 1999NA43, 2000CH31, 2000DE37, 2000LO20, 2004YA24, 2005PI16, 2006GU23, 2008FR02, 2013WE05, 2015TO11). Analyses of spin observables and polarized beam results are found in (1990BA14, 1990HA45, 1990ST32, 1990TA17, 1991BE45, 1992BE03, 1992BE24, 1992SH01, 1993CH14, 1993CO02, 1993KA45, 1993LA27, 1994DO03, 1994HI02, 1994PH02, 1994WI09, 1995BU37, 1995CH12, 1995CH44, 1995DE32, 1995DO31, 1995KA24, 1996DE31, 1996KA65, 1997BB17, 1997DO01, 1998DO16, 1998HI02, 1999AN32, 2000WE01, 2001HI10, 2001RA06, 2004CU02, 2005DE32, 2006ON03, 2007KH12, 2007YA13, 2008FU13, 2008KI13, 2009CO17, 2010NA18, 2011FU16, 2013PL02, 2014PL05). Global studies evaluating protons on a variety of targets are given in (1990BA14, 1990BA61, 1990HU09, 1990KA05, 1990PH02, 1990ST32, 1992KO04, 1993BE10, 1993CH14, 1993CO02, 1993KA45, 1994HA48, 1994WI09, 1995CH12, 1995CH44, 1995ER10, 1996GO48, 1997DO01, 1998DO16, 1999KU07, 2000DE43, 2000KE13, 2001KA58, 2002DI04, 2002FA14, 2002SA49, 2002TR12, 2005DE32, 2005KI04, 2005KO28, 2007KH12, 2007TA27, 2008FU13, 2008HA03, 2008KI13, 2009CO17, 2009WE04, 2010NA18, 2012DY01, 2012PA09, 2013ZU04, 2014HL01, 2015AR01, 2015BE12, 2016AR13). See also (1997IL02, 1998BA59, 1998KI15, 2001KI25, 2001WO07, 2010AZ01, 2011DU06: astrophysics).
The (p, 2p) reaction has been studied up to energies above 1 GeV. At Ep = 56.5 MeV, p0-decay from a state at 12C*(20.3 ± 0.5) was reported (1969EP01). 12.31 (in PDF or PS) shows states populated in reactions with 156 MeV protons. The analysis suggests the region above Ex = 21 MeV is dominated by Jπ = 1-; T = 1 resonances that mainly de-excite via single-nucleon emission. States in 11B are studied in (2004YA20, 2004YO06). At higher energies, quasifree knockout reactions from distinct shells are observed; see experimental results reported in (1997HA15, 1998MA67, 1998NO04, 1999AC03, 1999CA11, 1999CA15, 2000NO03, 2003TA03, 2004AC08, 2004AN01, 2007RY02, 2008NO01). Discussions include p-p correlations, initial and final state effects, such as color transparency and nuclear modifications to the NN interaction; see (1992LE03, 1994FR12, 1994FR16, 1994KO21, 1995GA46, 1997GA16, 2000ST17, 2006DA15, 2006HI15, 2006VA08, 2007DA19, 2009CO10, 2011RY03, 2014CR05, 2015MO21, 2015OG03).
Although the shapes of the momentum distributions in the (p, pn) reaction (reaction (b)) at 400 MeV are consistent with quasifree knockout, the magnitude of the cross section relative to that for the (p, 2p) process is inconsistent with the PWIA model (1979JA20). However, a study of inclusive (p, p') reactions along with exclusive (p, p'n) and (p, 2p) reactions at Ep = 200 MeV (1999CA11, 1999CA15) found that a comprehensive accounting of p-shell knockout and s-shell knockout to excited states in the residuals was consistent with DWIA calculations, and apparently validated the impulse approach at this energy regime and lower. See also (2015MO21: theory) and 11C yield measurements in (1993KO48).
The 12C(p, pd) missing energy spectrum at Ep = 670 MeV (reaction (c)) shows a strong bump at Emiss = 25 MeV and a weaker one at Emiss = 45 MeV, corresponding to the 10B ground-state and 10B*(20) regions, respectively (1981ER10). See also (1990LO18).
For reaction (d), at Ep = 56.5 MeV (1969EP01) T = 0 states at 12C*(22.2 ± 0.5, 26.3 ± 0.5) were reported to α0-decay (natural parity) while states at 12C*(19.7, 21.1, 26.3) were found to α1-decay. It is suggested that 12C*(21.1) has unnatural parity. At Ep = 44.2 MeV 12C*(12.7, 14.1, 21.6, 26.6) are observed in the angular correlations involving α0; states at 12C*(21.6, 24.1, 26.6) decay via α1 to 8Be*(3.0) [suggesting 2+ for these states, assuming that only resolved states are involved (1981DE08)]. A detailed analysis of the 12C(p, p3α) reaction at Ep = 14, 18 and 26 MeV (1999HA27) indicates the involvement of 12C(p, p'α)8Be and 12C(p, α)9B reaction channels. Other measurements at Ep = 101 MeV (2009CO01, 2009MA21) and Ep = 296 MeV (1998YO09) probed the cluster nature of 12C by evaluating alpha cluster spectroscopic factors and quasifree scattering; consistency with free scattering was found. See also (1994NE05, 1995GA39, 1995NE11, 1995TC01, 1997NE05, 1997SA04).
The angular distribution of elastically and inelastically scattered deuterons has been studied at many energies: see 12.32 (in PDF or PS). Measurements aimed at refining global model parameters are found in (1993BE43, 2001BA18); see also (1990GO28, 1990HU09, 1990ST32, 1992RA31, 2003EL08, 2004KE08, 2006AN14, 2006HA42, 2006PR13, 2008CHZT, 2010GU03, 2011MI20, 2012PA22, 2012UP01, 2016ZH26). Few-body and cluster model analyses are given in (1997MI29, 1999BR09, 2000MI36, 2007AL28, 2008FO06, 2009DE08, 2013BE27, 2014BE17). In (2009DA22, 2010OG03) a method is suggested for determining nuclear radii of unstable states by analysis of diffractive scattering; root-mean-square radii are estimated for 12C*(7.65. 9.64, 9.9, 10.3, 10.84).
In addition to well-known states in 12C such as 12C*(4.4) [Ex = 4440.5 ± 1.1 keV (1974JO14)] and 12C*(12.7, 15.1) [see 12.18 (in PDF or PS) for charge-dependent matrix element results], the population of 12C*((10.8 ± 0.2), (11.8 ± 0.2), 18.3 ± 0.3, 20.6 ± 0.3, 21.9 ± 0.3 (broad), ≈ 27 (broad)) is also reported (1975AS06). The Jπ = 2- state here at 18.3 MeV is different from the 18.4 ± 0.2 MeV Jπ = 2+ state observed in α inelastic scattering (1995JO06). DWIA analysis indicates Jπ = (1+) for Ex = 20.4 MeV and L = (1) for Ex ≈ 30 MeV (1994MO21). The GDR region was studied in (2008GR22). A preliminary report (1977CH1L) suggested two structures at Ex = 26 ± 1 and 29 ± 1 MeV, with Γ = 2 ± 1 and 4 ± 1 MeV, respectively, and determine L = 3 in the excitation of 12C*(18.4).
Isoscalar spin strengths and spin-flip probabilities are reported at Epol. d = 53 MeV (1993IS04), Epol. d = 270 MeV (2001SA68) and Epol. d = 400 MeV (1995JO06); S1 shows peaks for Ex = 12.71 and 18.35 MeV and suggestions of peaks above 20 MeV while S2 is consistent with zero up to Ex = 24 MeV range (2001SA68). Polarization observables are reported at, for example, Ed = 200 MeV (2004KA53), Ed = 393 MeV (1995FU03: Ex = 12.7 MeV) and Ed = 1.8 GeV (1995TO15). See also theoretical analysis in (1990SA45, 2001HI10, 2009DE02, 2009DE13).
The quadrupole deformation parameter is calculated to be β2 = -0.48 ± 0.02 independent of incident energy [Ed = 60.6, 77.3, 90.0 MeV] (1975AS06: coupled channels analysis). (1971DU09: Ed = 80 MeV) report β2 = 0.47 ± 0.05 and β3 = 0.35 ± 0.06 for 12C*(4.4, 9.6), respectively. See also β2 = -0.5 (2007GA07).
Reaction (b) was measured at Ed = 56, 140 and 270 MeV (1994OK01, 1998OK04); the results indicate sensitivity to Coulomb-dissociation and dissociation-diffraction mechanisms (1990SA45, 1991EV03, 1995SA39, 1996SA10, 1998NA42, 1998TO08, 1998TO10, 2002ZA10, 2006EV05, 2012UP01). See also (2002EV01, 2003EV01, 2009DE08, 2014YE03, 2016OG02). Earlier results are reported at Ed = 5.00 to 5.50, 9.20 and 9.85 MeV (1973SA03), 5.1 to 6.25 MeV (1973SH04), 5.4 and 6.0 MeV (1968BO02), 5.5 to 6.5 MeV (1972VA10), 56 MeV (1983BA37) and 2.1 GeV (1989PU01).
For reaction (c) see 8Be in (1979HE06).
Angular distributions of elastically scattered tritons have been measured at Et = 1 to 20 MeV. See (1968AJ02: Et = 1 to 12 MeV), (1975AJ02: Et = 1.11 to 20 MeV), (1980AJ01: Et = 9.0 to 17 MeV) and (1990AJ01: Et = 33, 36 MeV). See also the optical model analyses for Et < 40 MeV in (2007LI55, 2009PA07, 2015PA10).
Angular distributions of 3He ions have been measured for E(3He) = 2 to 217 MeV: see 12.33 (in PDF or PS). Parameters of observed 3He groups are displayed in 12.34 (in PDF or PS). See analysis on angular distributions in (1995GA22, 1997KH07, 2000MO34, 2001KU20, 2003BE70, 2003KH01, 2004BE42, 2007LU04, 2007OH01, 2008DE35, 2009GU16, 2009PA07, 2010HA19, 2015PA10). In (2003KH01), E(3He) = 72 MeV data are analyzed and the deformation length δ2 = 1.05 fm is deduced for 12C*(4.44). The 3He-γ4.44 angular correlations were measured in (1994IG01). See (2003KA24: E = 443 MeV) for polarization observables.
Rainbow effects and Airy patterns are discussed in (1990DE31, 1990KU25, 1991GO25, 1991KU29, 1992AD06, 1992DE18, 1995DA08, 1995DA21, 1995GA22, 2010OG03). The radius of the 12C*(7.65) Hoyle state is reported as 2.94 fm or 1.2-1.3 times larger than the g.s. radius (2008DE35); see additional comments on the dilute nature of the Hoyle state structure in (2006OG04, 2007OH01, 2008DE35, 2009DA22, 2010OG03, 2013HA01).
Angular distributions of the 3He groups to 12C*(15.11, 16.11, 16.58, 19.56) have been compared with those for the tritons to 12N*(0, 0.96, 1.19, 4.25) in the analog (3He, t) reaction: the correspondence is excellent and suggests strongly that these are T = 1 isobaric analog states (1969BA06: E(3He) = 49.8 MeV). See also 12.12 (in PDF or PS) in (1980AJ01) and 12.34 (in PDF or PS). At E(3He) = 46 MeV, the inelastically scattered 3He projectiles were detected along with the 3α particles from the breakup of α-unbound states (2014WH02); levels up to Ex = 25.1 MeV are observed.
The states reported by (1977BU03) at E(3He) = 130 MeV [see 12.34 (in PDF or PS)]: 12C*(4.4, 15.2, 18.4, 18.9, 21.3, 23.5, 25.9, 28.8) are all suggested to correspond to E2 transitions: their strengths add up to 46% of the EWSR (energy-weighted sum rule). The quadrupole deformation parameter β2 = 0.30 can account for both the elastic and inelastic data providing that the ratio of the spin orbit and central deformation βs.o./βcent. is energy dependent (E(3He) = 20.5 to 33 MeV) (1977KA25).
In (1980LE25) states were reported at Ex = 9.15 ± 0.2 and 20.3 ± 0.2 MeV [Γ = 1.8 ± 0.2 and 1.1 ± 0.2 MeV, respectively]: it was suggested that both are E0 states whose intensities are (2.1 ± 0.4)% and (2.6 ± 0.2)% of the EWSR: however these states are not confirmed, see (1981EY02, 1981YO04) in reaction 46 of (1985AJ01).
For discussion on Δ-resonance excitation and coherent π+ production see (1990UD01, 1991DE31, 1992HE08, 1993DM01, 1993FE10, 1993HE03, 1993OL06, 1993RO09, 1993RO30, 1994DM03, 1994JA12, 1994KO23, 1994OS02, 1994OS03, 1994SN01, 1994UD01, 1995KE13, 1995ST29, 1996GA20, 1996OS02, 1997KA52, 1998DA25, 2000BO47, 2002DA20, 2005AL37, 2005BO22).
Angular distributions have been measured at many energies up to 1.37 GeV: see 12.35 (in PDF or PS). Parameters of observed states of 12C are displayed in 12.34 (in PDF or PS). See general theoretical analyses of the angular distributions in (1990AB10, 1990AL05, 1990BO23, 1990CO29, 1990HU09, 1990LE18, 1991AN21, 1991BA23, 1991KU30, 1991LI25, 1991OK02, 1991ZH27, 1992ZH06, 1992ZH40, 1993AL10, 1993TA30, 1994AH05, 1994IN01, 1994RU12, 1994RU15, 1995AI03, 1995KH07, 1996ZH36, 1997CH48, 1998EL14, 1998GA46, 1999GA43, 1999IG02, 2000AB16, 2000EB02, 2000EL03, 2000GU07, 2001EL05, 2001KH02, 2001KI25, 2002HI07, 2002KH01, 2003MO11, 2003ZE06, 2004YA03, 2005AL18, 2005GR40, 2005KU23, 2006FA09, 2006FU11, 2006KU16, 2008KH14, 2008ZO03, 2010IZ01, 2010KA21, 2011AL23, 2011BE20, 2011BE42, 2011GU15, 2012DY01, 2012GI01, 2012PA22, 2013LA28, 2015SU14, 2016AN08, 2016HU08, 2016MI13, 2017BE01). Structures in large angle scattering are discussed in (1990DA23, 1991GO25, 1994DA32, 1995DA08, 2004OH13, 2008DE35, 2011BE42) and studies of backward angles scattering are emphasized in (1990TO09, 1994DA16, 1994YO06, 1995EN09, 1996SO20, 1998BE56, 2002AN26, 2002AR16, 2004JI10, 2012MA26). The large radii deduced for 12C*(7.65), Rrms = 2.89 ± 0.04 fm and 12C*(9.9: Jπ = 2+), Rrms(2+2) = 3.07 ± 0.13 fm, are significantly larger than for 12C*(4.44) and have been suggested as evidence for Bose-Einstein condensate structures (2008DE35, 2009DA22, 2010OG03, 2011OG10, 2013OG05); see also (2004IT09, 2006OG04, 2006TA27, 2008KH02, 2008OHZX, 2008TA21, 2010BE32, 2010OG03, 2011IT08, 2016NA22).
In (2004IT09), an L = 2 component of the reaction was identified near Ex = 9.9 MeV with Γ ≈ 1.0 MeV; the strength is associated with a rotational excitation of the Hoyle state. In (2011IT08), the state is identified at Ex = 9.84 ± 0.06 MeV with Γ = 1.01 ± 0.15 MeV. In (2012FR05) the (p, p') data from (2009FR07) and the (α, α') data from (2011IT08) are simultaneously analyzed via R-matrix analysis, and the Jπ = 2+2 state is identified at Ex = 9.75 ± 0.15 MeV with Γ = 0.75 ± 0.15 MeV. The large α width associated with this Jπ = 2+2 state suggests a highly clustered structure.
In addition to the discovery of the Jπ = 2+2 state, evidence is observed for other previously unreported states in the Ex = 9-12 MeV region. A group at Ex = 9.93 ± 0.03 MeV with Γ = 2.71 ± 0.08 MeV is identified with Jπ = 0+ strength; it is suggested as a Jπ = 0+3 + 0+4 doublet (2011IT08); this state is seen at Ex = 9.8+0.2-0.4 MeV with Γ = 2.7 ± 0.3 MeV in (2003JO07). Analysis in (2011IT08) suggests Ex = 9.04 ± 0.09 MeV and Γ = 1.45 ± 0.18 MeV for 0+3 and Ex = 10.56 ± 0.06 MeV and Γ = 1.42 ± 0.08 MeV for 0+4 states. Additional support for the interpretation of doublet Jπ = 0+ states is found in the GCM calculations of (2016ZH43) and in the cluster model analyses of (2016FU07, 2016IS15). See also (2015FU09, 2016KA19, 2016YO09).
At Eα = 240 MeV (2003JO07), some evidence for Jπ = 2+ strength at Ex is reported at Ex =11.46 ± 0.20, but no evidence was seen for this state in the Eα = 386 MeV data of (2011IT08). In addition, the results of (2011IT08) don't find support for the Jπ = 0+ and 2+ strength at Ex = 11.2 and 11.1 MeV, respectively, deduced in the analysis of the 12B/12N β decay data (2010HY01); however, differences in analysis approaches may explain the different findings. At present it is difficult to suggest a clear picture of the Jπ = 0+ and 2+ strength has emerged. See a review of Eλ transition strengths for Ex ≤ 10.84 MeV in (2013CU05).
Evidence for a Γ = 1.7 ± 0.2 MeV broad Jπ = (4+) state at Ex = 13.3 ± 0.2 MeV is seen in the reconstructed kinematics of 3α ejectiles (2011FR02). It is suggested that this state, along with the Jπ = 0+2 and 2+2 states form a rotational band. Alpha-alpha correlations from 12C*(14.1) to 8Beg.s. lead to an assignment of Jπ = 4+ for that state (1977MC07); see also (1978RI03).
States at Ex = 7.65, 9.64, 10.84 and 14.08 MeV were observed along with a new state at Ex = 22.4 ± 0.2 MeV (2014MA37); the angular correlations of breakup α-particles indicate a Jπ = 5- assignment for the later. A ground state rotational band including 12C*(0[Jπ = 0+], 4.44[2+], 9.64[3-], 14.08[4+] and 22.4[5-]) is suggested.
In the region of the GDR, prominent structures are observed consisting of two ≈ 2 MeV wide peaks at 26.2 and 29.2 MeV (1987KI16: see also for a discussion of deformation parameters). Jπ assignments have been suggested for 12C states with 9.6 ≤ Ex ≤ 39.3 MeV on the basis of their decay into 3α-particles: see (1973JA02: Eα = 90 MeV).
The quadrupole deformation, β2, is -0.29 ± 0.02 (1971SP08), -0.30 ± 0.02 (1976PA05), -0.40 ± 0.02 (1983YA01); β3 = 0.24 (1973SM03), 0.23 (1977BU19) and β4 = +0.16 ± 0.03 (1983YA01: see also for a review of deformation parameters). In (2003JO07) β2 = 0.753 ± 0.049, β0(7.65) = 0.187 ± 0.13, β3 = 0.556 ± 0.066, β0(10.3) = 0.157 ± 0.011, β1 = 0.026 ± 0.005 deformation parameter values are deduced.
In (2003JO07) strength was identified corresponding to (27 ± 5)%, (78 ± 9)%, and (51 ± 7)% of the isoscalar E0, E1, and E2 energy weighted sum rule (EWSR), respectively, with centroids of 21.9 ± 0.3, 27.5 ± 0.4, and 22.6 ± 0.5 MeV and rms widths of 4.8 ± 0.5, 7.6 ± 0.6, and 6.8 ± 0.6 MeV. Less than 7% of the E3 EWSR strength was identified. See also (1998YO02, 2008KH02) and earlier work in (1976KN05, 1978RI03, 1981EY02).
Angular correlation measurements α1-γ4.4 have been carried out for Eα = 10.2 to 104 MeV (see 1980AJ01, 1985AJ01, 1990AJ01). Measurements of the radiative widths for 12C*(7.7, 9.6) are reported in (1974CH32, 1976MA46) and 12.14 (in PDF or PS). The value for Γrad for 12C*(7.65) implies a 45% faster rate for the (3α) astrophysical process (1974CH32). A detailed study of the 12C*(7.65) de-excitation finds the decay is 99.1% via sequential α-decay to 8Beg.s. and < 0.9% via direct decay into 3α-particles (2013RA20).
For cross sections analyses relevant to 16O see (1990AR24, 1991DE15, 1992SA26, 1993DE03, 1996VO18, 1997AB52, 1997GO10, 1999AN35, 2000AN17, 2001BU20, 2001HU14, 2002TI03, 2004SP02, 2004SP04, 2005PA58, 2005SP06, 2006BU32, 2007FR22, 2007ST21, 2009AS01, 2009TI02, 2010KA21, 2011DU06, 2011IR01, 2011SP03, 2012CU04, 2012DE08, 2012SO20, 2013CU04, 2013DE03, 2013GA05, 2013KA03, 2014CH06, 2015IR01, 2015SH22). For reaction (b) and α-cluster knockout studies see (1999NA05, 1999ST06, 2007FR22, 2012CU04, 2012SO20, 2013CU04: exp.) and (2008JA02, 2009JA07, 2011CO10, 2014JA07: theory).
Angular distributions of elastic scattering have been measured at E(6He) = 5.9 to 492 MeV; see 12.36 (in PDF or PS). At E(6He) = 10 MeV (1995WA01) the elastic angular distribution was found to fall off more quickly than expected when compared with the Rutherford cross section; on the other hand, measurements at E(6He) = 38.3 and 82 MeV/A found an enhancement of cross section at angles larger than about 15° (2002LA20, 2011LO07). At E(6He) = 30 MeV, scattering to 12C*(0, 4.4) was measured and analyzed for θcm ≈ 20° - 100° using a coupled-channels approach (2014SM01). The nuclear forward glory effect was studied at E(6He) = 5.9 MeV in (1998OS02, 1999OS04, 2002OS04), and the analysis indicated the low 6He binding energy leads to a loss of flux from the elastic channel, even at very forward scattering angles.
See theoretical analyses in (1993GO06, 1995GA24, 1998TO05, 2000BO45, 2000KR13, 2000MI36, 2002AB16, 2002SU18, 2003AB26, 2003LE25, 2003ZA15, 2004AB12, 2004AB13, 2004MA57, 2005AL18, 2005MI29, 2007RO29, 2008BO19, 2008DE38, 2008EL03, 2008KE06, 2008RO16, 2009DO20, 2009KU25, 2010AY08, 2010DEZW, 2010LA09, 2010LU08, 2010MA61, 2011BA03, 2011LU14, 2012AL24, 2012GI01, 2014KU09, 2015IS03, 2016IB01, 2016SU13).
See 12.37 (in PDF or PS) for a summary of reported measurements on 12C(6Li, 6Li) and 12C(6Li, dα). The inelastic angular distributions to 12C*(4.4, 7.7, 9.6) have been used to obtain deformation parameters (1996KE09); see earlier work in (1994RE15, 1974BI04). Measurements of large angle scattering are reported in (1996GA29, 2004CA46) and analyzed in (1990DA23, 1990SA05, 1993GO06, 1995GA22, 2003LE25, 2005MI29, 2012CA21). A method for determining nuclear radii of excited states, such as 12C*(7.65. 9.64, 9.9, 10.3, 10.84), is suggested in (2009DA22). A study of the E0 strength distribution determines 10%, (5 ± 1)% and (5 ± 2)% of the EWSR, respectively for 12C*(7.7, 10.3) and for 19 < Ex < 21.5 MeV (1987EY01). See general theoretical analyses in (1990KA14, 1991BO48, 1991EV04, 1991SA26, 1992GA17, 1994NA03, 1994SA10, 1994SA33, 1994SK04, 1995BE60, 1995EM03, 1995GA24, 1995KH03, 1995MO28, 1996CA01, 1997SA57, 1997ZE04, 1998PI02, 1999BE59, 2000BE49, 2000EL11, 2000MI36, 2002EL01, 2002EL10, 2003ZA15, 2004EL02, 2005AL18, 2006DA05, 2008KE06, 2009DA22, 2011PA37, 2013BA13, 2015AY05, 2016CA36).
At E(pol. 6Li) = 30 MeV the angular distributions and polarization observables corresponding to 12C*(0, 4.4, 9.64) have been studied (1994RE01, 1994RE15); see also E(pol. 6Li) = 50 MeV measurements to 12C*(0, 4.4, 7.65, 9.64) reported in (1995KE10, 1996KE09) and theoretical analyses given in (1990FI12, 2011BA23, 2011PA37).
At E(6Li) = 60 MeV reaction (b) takes place via 12C*(0, 4.4, 7.7) (1982AR20) and can involve structures in 16O. See other measurements and analysis of the 6Li breakup mechanism in (2000SC11, 2004SO23: exp.) and (1991EV04, 1991EV05).
See 12.37 (in PDF or PS) for a summary of reported measurements on 12C(7Li, 7Li). Analyses of elastic scattering distributions are given in (1991BO48, 1994SK04, 1997BE05, 2000EL11, 2002EL01, 2004EL02, 2005AL18, 2011BA23, 2014PI02) At E(pol. 7Li) = 34 MeV the angular distributions and polarization observables corresponding to 12C*(0, 4.4, 7.65, 9.64) and 12C*(0, 4.4) + 7Li*(0.48) have been studied (2000BA75, 2002KE04); see other results in (2001BA29, 2001BA57, 2006MO24) and (2011BA23: theory). For fusion and yield measurements see (2007PA33).
For the 6Li and 7Li + C interaction cross sections at 790 MeV/A see (1985TA18).
Angular distributions for elastic and inelastic scattering have been measured at E(7Be) = 8 to 280 MeV; see 12.36 (in PDF or PS). See theoretical analyses and discussion in (1995FA17, 1996KN05, 1997KN07, 2006DA05, 2010HO08).
Reaction cross sections and interaction cross sections are reported at E(8B) = 30 to 110 MeV (2014FA18, 2015FA03). See also (2000AB31, 2000BH09, 2001BH02, 2002AB16, 2002WA08, 2003WE07, 2004KH06, 2006SH20).
Angular distributions for elastic and inelastic scattering have been measured at E(8B) = 25.8 to 320 MeV; see 12.36 (in PDF or PS). See theoretical analyses and discussions in (1995FA17, 1996AL13, 1996KN05, 1997KN07, 2000BO45, 2006DA05, 2006DA27, 2010HO08).
Reaction cross sections and interaction cross sections are reported at E(8B) = 206.4 MeV (2011BA25), 280 and 480 MeV (1999FU08), 288 MeV (2015JI07), 320 MeV (1995PE09) and 616 MeV (2003EN05). See also (1998KN03, 2000AB31, 2001LE21, 2002AB16, 2002PA51, 2004EV02, 2006HU12, 2006TR07, 2011HA38).
Angular distributions for elastic scattering have been obtained at E(9Be) = 3 to 158.3 MeV; see recent studies listed in 12.36 (in PDF or PS). At E(9Be) = 158.3 MeV angular distributions to 12C*(0, 4.4) were measured by (1984FU10), and at E(12C) = 65 MeV angular distributions to 12C*(0, 4.4, 7.7, 9.6) were measured by (1985GO1H).
Excitation functions were measured for elastic scattering at Elab = 13 to 21 MeV (2011OL01) and for elastic and inelastic scattering to 9Be*(2.43) or 12C*(4.44) at Ecm = 2 to 16 MeV (1995CA26); analysis indicated significant components of 3He transfer in the reactions (1995CA26); see also (1998GR21).
The interaction cross section of 9Be ions on 12C at 790 MeV/A is reported in (1985TA18). See estimates of the total reaction cross sections for E(9Be) = 3 to 26 MeV (2011ZA05); also see (1993FE12, 2000BH09, 2002AB16, 2002BR01, 2003CA07, 2006SH20, 2008KO29, 2013YA01, 2016TR10). For fusion and yield measurements see (1978CH02, 1981JA09, 1982DEZL, 1982HU06, 1983JA09, 1985DE22, 1992FI04, 1998CA27).
Angular distributions of 10Be and 11Be elastic scattering are summarized in 12.36 (in PDF or PS). For theoretical analyses, see (10Be: 1999BR09, 2000AB31, 2009RO31) and (11Be: 1995EV01, 1996EV01, 1996VO04, 1997AL05, 1997JO16, 1998TO05, 1999BR09, 1999FO13, 2000BO45, 2000JO21, 2002AL25, 2002BO25, 2002SU18, 2002TA31, 2003TA04, 2005BA72, 2005TA34, 2009HA18, 2010LA09, 2011OG09, 2011OG10, 2015IS03, 2015LU04).
The interaction cross section of 10Be ions on 12C at 790 MeV/A is reported in (1985TA18). See estimates of the total reaction cross sections for Ecm = 12.7 MeV (2011ZA05); see also (1993FE12, 1996AL24, 2000BH09, 2002AB16, 2002BR01, 2006SH20). For 11Be (reaction (b)), see measurements on the reaction cross sections in (1991FU10) and see other theoretical analyses in (1993FE02, 1993MA25, 1994SA30, 1996AL13, 1997FO04, 2000BH09, 2002BR01, 2003CA07, 2006GO05, 2006SH20, 2007SH33, 2008AL06, 2013SH17).
The 11B + 12C reaction has been studied for E(11B) = 10 to 100 MeV and for E(12C) = 15 to 87 MeV; see 12.36 (in PDF or PS), 12.20 (in PDF or PS) in (1985AJ01), 12.20 (in PDF or PS) in (1990AJ01) and discussion in (1980AJ01). Proton spectroscopic factors for elastic transfer reactions ranging from C2S = 2 - 5.6 have been deduced from measurements at Ecm = 15 to 40 MeV (1991AL12), and 2.15 ± 0.23 was deduced at E(11B) = 50 MeV (2014LI49). Spectroscopic factors for 12C*(0, 4.4, 9.64) from analysis of measurements at E(12C) = 18 MeV (2014HA34) and E(12C) = 344.5 MeV (1990JA12, 1992JA12) are given in 12.38 (in PDF or PS). See other analyses in (1990KA17, 1998KH16, 2001RU14, 2003ME36). For fusion and yield studies see references in (1985AJ01, 1990AJ01) and (1993HA14, 1994BA41, 1996JA12, 1996KI17, 1999CA50, 2000TAZK, 2006JI01, 2009JI04).
Angular distributions for elastic and inelastic scattering have been measured at E(11Li) = 550 to 660 MeV; see 12.36 (in PDF or PS). See theoretical analyses and discussion in (1991CA14, 1992TA16, 1992YA04, 1993DA09, 1993ME02, 1993TH01, 1994AL02, 1994CA07, 1994HU04, 1994SA16, 1995AL01, 1995AL02, 1995CO01, 1995DA04, 1995EV03, 1995FA17, 1995FO08, 1995GA24, 1995HU08, 1995KH11, 1996CA01, 1996KH03, 1996KN05, 1996RA18, 1996UE01, 1996UE07, 1997CH32, 1997KN07, 1997MO42, 1998CH18, 1998MO27, 1999MO37, 2000MO34, 2000PA14).
Reaction cross sections are reported at E(11Li) = 341 and 451 MeV (2013MO21). See other theoretical analyses mainly related to the 11Li density distribution and structure in (1992OG02, 1992YA02, 1993FE02, 1993MA17, 1993MA25, 1996AL13, 1996AL24, 1996BU09, 1997FO04, 1997ZA08, 1998BE09, 1998GA37, 1998KN03, 2000BO45, 2001BH02, 2001OG10, 2002WA08, 2004CA18, 2004LO12, 2007AL07, 2007SH33, 2008CA08, 2009SH25, 2011IB02).
See analyses of elastic and inelastic scattering at E < 100 MeV (1990DE13, 1991AL03, 1991TR03, 1991VE02, 1992AP01, 1994AP01, 1995AP01, 1995LI27, 1997AP06, 1997BR05, 1998AP03, 2000EB03, 2001BO18, 2001BO41, 2001EL08, 2002BO17, 2003AL17, 2005ER05, 2006KU06, 2011HA36), at E = 100 MeV to 1 GeV (1990JA12, 1990WA01, 1991AL16, 1992AY03, 1992GA08, 1992KA36, 1992LE02, 1993LI13, 1993MC01, 1994KH02, 1995FA17, 1996BE25, 1996EL05, 1997BR04, 1997BR30, 1997CH48, 1997IN02, 1997KH04, 1997KN07, 1997SI21, 1997ZE04, 2000KH06, 2000KI05, 2001FA24, 2002AH05, 2002BO58, 2002YA15, 2004AH11, 2005AL18, 2005CH48, 2007KI19, 2010BA45, 2012FU04, 2012FU09, 2013FU01, 2013WE05, 2016MI03), and at E > 1 GeV (1990AL10, 1990AM02, 1990DA12, 1990DA23, 1991CE09, 1991ZH20, 1992CH30, 1993CE01, 1994CH35, 1994GU20, 1995BE26, 1995GA24, 1996FA08, 1998CH18, 1998EL14, 1999MA18, 2000AB31, 2000EL03, 2001LU09, 2002AB16, 2002AH02, 2002FA10, 2002VA17, 2003BE31, 2004FA08, 2004GH02, 2006CH45, 2007CH42, 2009FU11, 2012GI01, 2013WE05, 2014MI22, 2016FU13). See also (1991PU01, 1991SA29, 1996AD04, 1996RA25, 1997AB50, 2007CH62, 2011FU16, 2012FU04). For comments on "rainbow" scattering and Airy minima see (1991BR04, 1992MC07, 1995GA22, 2000ME04, 2000ME05, 2002KI15, 2003SZ12, 2004KI13, 2004MI12, 2010DE32, 2010FU12, 2016KH09).
The nuclear sizes of 12C*(0, 4.4, 7.65) were determined by a Frauenhofer analysis of the small angle diffraction pattern at E(12C) = 121.5 MeV; results indicate Rdiffraction = 6.35 ± 0.09, 6.26 ± 0.10 and 6.86 ± 0.11 fm, respectively (2011MA04). See also (2009DA22), who evaluated 3He, α, 6Li and 12C scattering data, deduced the diffractive radii for 12C*(0, 4.4, 7.65, 9.64) and deduced Rrms = 2.34, 2.36 ± 0.04, 2.89 ± 0.04, 2.88 ± 0.11 fm for those states, respectively.
The relative population of elastic and inelastic channels is very energy dependent, for example, because of structure effects and molecular-like states in 24Mg; see references listed in (1975AJ02, 1980AJ01, 1985AJ01, 1990AJ01), and see footnote a in 12.40 (in PDF or PS). The spin alignment of 12C*(9.64) was studied in (1993DA22, 1995DA05) and shows little energy dependence. See also (1990SA07, 1990SA48, 1992GR15, 1992RA25, 1993AB05, 1993ME04, 1994AD13, 1994ME18, 1994SA07, 1995BE33, 1995HI21, 1996AD04, 1996SC02, 1998KO29, 1999IT02, 2000SA57, 2001BO18, 2002IT05, 2003SA36, 2003SA39, 2003SZ12, 2005GA33, 2006PE23, 2007FR22).
For reaction (b), several states are observed by reconstructing the complete kinematics of decay α particles, see 12.40 (in PDF or PS). In (2007FR17), the three-α breakup systematics are analyzed to determine spin values for states with Ex ≥ 7.65 MeV; the analysis found no evidence for the Jπ = 2+ excitation of the Hoyle state that is expected near 10 MeV. Contradictory results for previous Jπ value assignments for states such as 12C*(11.83, 13.35) were also found along with suggestive evidence for new broad states nears Ex = 11.8 and 12.5 MeV. In (2007FR17) analysis of the Ex = 11.16 MeV region is given that showed limited evidence for a previously accepted state; however, in light of the findings in (2012SM06), the result of (2007FR17) does not provide sufficient evidence for the state's existence (private communication, M. Freer, June 2017). In (2010MU05) analysis of the α-particle angular correlations found no evidence for excess Jπ = 2+ strength in the Ex ≈ 9 to 10 MeV excitation region.
In (1991CA01) no evidence for direct 3α-decay was observed from any state. Detailed measurements of the 12C*(7.65) decay systematics, which are relevant for astrophysical 12C formation, are given in (1994FR05, 2014IT01); see also (1996RA08). In (2014IT01) the decay kinematics of 12C*(7.65) are analyzed, and the results are consistent with 100% sequential decay via 8Beg.s., with limits of < 0.2% decay via 3-body phase space and < 0.08% decay into 3 equal energy α particles. The α-α correlation data is analyzed in (2007FR05), and discussion relating the correlations to the nuclear radii of excited states is given.
Elastic and inelastic angular distributions are reported at E(12C) = 127.2 MeV (2010AL10) and E(13C) = 16.3, 20, 29.5 MeV (1995LI23) and 240 MeV (2010DE32). See previous measurements reported at E(12C) = 15 to 36 MeV and 87 MeV (1975AJ02), at E(12C) = 20 to 35 MeV and E(13C) = 12 and 36 MeV (1980AJ01), at E(12C) = 15 MeV and E(13C) = 87 MeV (1985AJ01), and at E(12C) = 94.5 MeV and E(13C) = 16.3 to 26.5 MeV, 36 MeV and 260 MeV (1990AJ01).
The spin-flip probability to 12C*(4.4) has been studied at E(13C) = 36 and 56 MeV by (1985BY01); also see (1981TA21). The mirror scattering reactions of 12C + 13C and 12C + 13N are compared in (1995LI10, 1995LI23, 1997IM01). Rainbow scattering and Airy minima are discussed in (2003BE70, 2004BE42, 2010DE32, 2015OH02). See also (1990BA03, 1993IM02, 1999RA24, 2010AL10).
For reaction (b) elastic angular distributions are reported at E(12C) = 12 to 20 MeV (1972BO68) and E(14C) = 31.0 to 56 MeV (1985KO04). Excitation functions to 26Mg resonances are studied for 12C(14C, 14C) at Ecm = 22 to 30 MeV (1992FR13) and Ecm = 6 to 35 MeV (2003SZ11).
Elastic and inelastic scattering has been measured at E(13N) = 16.3, 20 and 29.5 MeV (1995LI10, 1995LI23) and at 153.4 MeV (2004TA15). The 12C + 13C and 12C + 13N systems appear to comply with charge symmetry, see (1995LI10, 1995LI23, 1997IM01).
This reaction has been used to populate 12C-12C quasi-molecular states in 24Mg, see for example measurements at E(14N) = 30 to 45 MeV (1994ZU03) and analyses in (1994BE55, 1999SA54, 2002BE71, 2002BE73).
Elastic and inelastic angular distributions are reported at E(14N) = 80.73, 100.3 MeV (1990DE13), 116 MeV (1997ZI05) and 280 MeV (1990BR21). See previous measurements reported at E(14N) = 21.5 to 27.3 and 62.5 MeV (1968AJ02), E(14N) = 21 to 155 MeV (1975AJ02), E(14N) = 37 to 155 MeV (1980AJ01), E(14N) = 48 to 78 MeV (1985AJ01) and E(14N) = 150 MeV (1990AJ01). At E(14N) = 155 MeV 12C*(0, 4.4, 7.7, 9.6, 10.8, 11.8, 12.7, 13.4, 14.1) are reported; see (1975AJ02). High-energy γ-ray emission has been studied at E(14N) = 280 to 560 MeV (1986ST07). See also (1994AD08, 1997IN02, 2003AU04).
The angular distribution for quasielastic scattering at E(16C) = 47.5 MeV/A is reported for θcm = 5 ° - 40° (2009FA07).
Angular distributions involving 12C and 16O states have been measured at E(16O) = 17.3 to 1503 MeV and at E(12C) = 65 to 76.8 MeV: see 12.41 (in PDF or PS). See general analyses in (1990DA12, 1991ST07, 1992CH29, 1992CO01, 1993MA09, 1994KH02, 1994SA24, 1996EL05, 1997BR04, 1997CH23, 2000EL03, 2000KI30, 2000ME04, 2002AN35, 2002KU41, 2003BE31, 2005CH48, 2005KO52, 2006HO04, 2007GO35, 2009CH46, 2009FU11, 2011GR11, 2011MO07, 2012FU04, 2012GR16, 2013GR13, 2014FA04, 2014FA11, 2016FU13, 2016MA52).
The reaction dynamics leading to the Airy patterns at large scattering angles are discussed in (1997RI08, 2001AN04, 2001GO46, 2001MI06, 2002MI19, 2002MI39, 2002SZ03, 2003GO34, 2003OG04, 2003SZ12, 2008GR12, 2008GR14, 2008KO16, 2009KO05, 2010BA45, 2010DE10, 2014OH02, 2015MA12, 2016HA01).
In (1979DO01) excitation of the giant quadrupole resonance is observed in groups at 12C*(25.3, 26.7) with Γ ≈ 4 MeV that contain (25+15-10)% of the energy-weighted E2 sum rule strength; states at 12C*(0, 4.4, 9.6, 10.8, 15.8, 21.6) were also populated.
For fusion resonant excitation function studies to states in 28Si see (1992SA21, 1993BE17, 1993ES01, 1994GA06, 1995BU29, 1995FR12, 1995SI13, 1997FU12, 1997GY02, 1998KE02, 2008LE27, 2011LE19, 2011CO05, 2012RU02, 2012LE04, 2013KU04, 2014KU06, 2014GO03) and (1994GR26, 2004KO38, 2007FR22: theory). For studies of other nuclides see (20Ne: 1994RA04, 1995SU06), (24Mg: 1991CO09, 1994CO01, 1994KU18, 1995FR12, 1997FU12, 1998FR03, 2001FR19, 2001TU06, 2001WI18, 2011JO02, 2012DI04 and theory: 2007FR22) and (26Al: 1993BE17, 1997BA51, 1998BA19). See also (1993HA14, 1993WA16, 1994CZ03, 1994DE21, 1995SC30, 2006YA14, 2007GA43, 2009CH35, 2009LO01, 2012UM02, 2015AB01). For discussions on fragmentation reactions see (1990WE15, 1992MA13, 1992ME02, 1999BO46, 2000CH20, 2000FA12, 2001DE50, 2002MO22, 2008KU15, 2011DE09).
Elastic and inelastic angular distributions are reported at E(17O) = 22 to 38 MeV (1993TI05) and E(18O) = 66 to 120 MeV (2001SZ05, 2006SZ06), 84 MeV (2011CA33), 94.5 MeV (2009AD08), 105 MeV (2010RU03, 2010RU13, 2010RU15, 2011RU07) and 216 MeV (2014AL05, 2014AL11). See previous measurements reported at E(17O) = 35 MeV (1975AJ02), 30.5 and 33.8 MeV (1980AJ01), 40 to 70 MeV (1990AJ01), and E(18O) = 35 MeV (1975AJ02), 32.3, 35, 47.5, 55 and 57.5 MeV (1980AJ01) and 32.0 to 140 MeV (1985AJ01). Fusion yields and other reactions to isotopes in, for example, Ne and Si are reported in (1990XE01, 1993BE17, 1993TI05, 1996FO16, 1999BO46, 2000CH20, 2000FA12, 2006FR16, 2006YI01, 2011BA22, 2011GI03, 2014ST22) and (1980AJ01, 1985AJ01, 1990AJ01). See also analyses in (1991TH02, 1991TH04, 1997KI22, 1999MA96, 2002BR01, 2004KH06, 2006BH01, 2008KO29, 2009AB07, 2011KU06, 2011SH26, 2012HO19, 2012RA29, 2014HO02).
Angular distributions for elastic scattering and quasielastic scattering have been measured at E(17F) = 60 MeV (2012ZH21) and 170 MeV (2005BL23). For reaction (b), elastic scattering and fusion angular distributions are reported at E(19F) = 10 to 16 MeV (1990XE01), 19 to 56 MeV (1999CA50), 22 to 24 MeV (2004SU02), 48 to 72 MeV (2002AN11), 57 to 64 MeV (2002SU17), 83.6 MeV (2003WO17, 2004KI07, 2006WO04), 92 MeV (1997AI01, 1997AI06), 96 MeV (1996BH06, 1999BA11, 2001BB02, 2002BA50), 111 to 136.9 MeV (1997PO07, 2001PO01), 121.7 MeV (1995VA05) and 912 MeV (2001ME26). See previous measurements reported at E(19F) = 40, 60 and 68.8 MeV (1975AJ02), E(19F) = 18.0 to 60.1 MeV (1985AJ01) and E(19F) = 29.3 to 60.1 MeV (1990AJ01). The substate population probability for 12C*(4.4) has been studied by (1986IKZZ) at E(19F) = 63.8 MeV.
Elastic angular distributions are reported at E(20Ne) = 390 MeV (1993BO28) and E(22Ne) = 264 MeV (2010AL10). See previous measurements for reaction (a) reported at E(20Ne) = 65.7 MeV (1980AJ01) and at E(12C) = 37 MeV (1975AJ02), 20 to 34.4, 60.7, 72.6 to 75.2 MeV [to 20Ne*(0, 1.6)] and 77.4 MeV (1985AJ01). Fusion to sulfur, reaction cross section, fragmentation yield and evaporation residue studies are also reported in the literature. See also (1990SL01, 1997BR05, 1997FR04, 2004FA08, 2007FR22).
Elastic angular distributions are reported for reaction (a) at E(12C) = 19, 21 and 23 MeV (1993LE08), 32 to 48 MeV (1997SC14), 85 MeV (2000SI36) and 104 MeV (2017JO03), and at E(24Mg) = 130 MeV (2004BE08, 2004BE18, 2009BE34) and 768 MeV (2001CH11, 2001CH56). See previous measurements for reaction (a) at E(12C) = 20 to 36, 20 to 60, 24.8, 27.7 to 34.8 and 40 MeV (1985AJ01) and for reaction (b) at E(12C) = 20 to 56 MeV (1985AJ01). The B(E2) values and deformation parameters for the first Jπ = 2+ states of 24,30,32Mg are measured at E ≈ 32 MeV (2001CH11, 2001CH56). See also analyses of scattering distributions given in (1991LI34, 1992GR15, 1994LI33, 1996FR23, 1997FR04, 1999KU01, 1999LE14, 1999LE38, 1999LI34, 2000LU03, 2001BO41, 2001BO46, 2001KU01, 2002BO17, 2002BO58, 2002KU33, 2004BE31, 2005BO28, 2005BO31, 2006KA23, 2006KA43, 2006MA33, 2007FR22). Reaction induced fission of 24Mg to 12C-12C cluster states is studied at E(24Mg) = 170 and 180 MeV (1991BE27, 1991FU03, 1991FU09, 1994CU05, 1995CU01, 1995LE22, 2000CU02, 2001SH08) and Ecm = 43.3 to 60 MeV (1994GY01). Studies on fusion to 32S and 36Ar, fragmentation yields, and other reaction cross sections can be found in the literature.
Elastic angular distributions have been measured at E(12C) = 21 MeV (2011HA47) and 30.0 to 39.9 MeV (1979RO11), while that of the transition to 12C*(4.4) has been studied at E(12C) = 82 MeV (1977BE42) and E = 344.5 MeV (1990JA12). See also (2004FA08, 2004GA16, 2006ZA10). Results on fusion, fragmentation yield, and other reaction studies are found in the literature.
Elastic scattering for reaction (a) was studied at E(12C) = 60, 65, 75 and 85 MeV (1998YA02) and E(28Si) = 145 and 160 MeV (1991RA05). See previous measurements at E(12C) = 19 to 36, 24, 27, 30, 40.2, 49.3, 70 and 83.5 and 186.4 MeV and at E(28Si) = 58.3 to 116.7 MeV see (1980AJ01), at E(12C) = 19 to 48, 41.3, 56.0 to 69.5 and 131.5 MeV see (1985AJ01), and at E(12C) = 56, 59, 66, 69.5 and 65 MeV see (1990AJ01). The α-γ angular correlations have been studied at E(28Si) = 112.3 and 142.7 MeV: 12C*(4.4) is found to be produced almost entirely in the m = 0 magnetic substate (1986RA08). Elastic and inelastic scattering on 29Si was studied at E(12C) = 36.8 MeV (1968AN21). See theoretical analysis of elastic scattering on 28Si in (1992GR15, 1997CH41, 1999LE14, 1999LE38, 1999RA24, 2001EL08, 2004PA17, 2010BA45) and see specific discussion on "forward glory" scattering in (2000DA15, 2003LE25, 2004DA27, 2011DA04). Results on fusion, fragmentation yield, and other reaction studies on 28,29,30Si targets are found in the literature.
Elastic and inelastic angular distributions and B(E2) values are reported at E(32S) = 65 to 67 MeV (2006SP01). See previous measurements at E(12C) = 35.8 MeV and E(32S) = 73.3 to 128.3 MeV (1980AJ01), E(32S) = 60 to 99 MeV and 160 MeV (1985AJ01), and E(32S) = 194, 239 and 278 MeV (1990AJ01). See also (1990ME07, 1991AR15, 1991BE27, 1991FI04, 2001PI10, 2003BE75), references in (1980AJ01, 1985AJ01, 1990AJ01) and other references in the literature for discussion on fusion, fragmentation yield and other reaction studies.
Elastic angular distributions for reaction (a) have been studied at E(12C) = 54 and 63 MeV (1980GL03). For reaction (b) see measurements in (1989PL02, 1990LE08, 1990LE10, 1991PA08, 1993YO03, 2004MO48).
The elastic scattering in all three reactions has been studied at E(12C) = 51.0, 49.9 and 49.9 MeV, respectively (1979RE03) and for reaction (a) at E(12C) = 180, 300 and 420 MeV (1986SA29). See theoretical analysis of elastic scattering on a 40Ca target in (1994SA37, 2003AL17, 2008KI20, 2013XU06). Results on fusion, fragmentation yield, and other reaction studies are found in the literature.
12N decay to 12C is complex. Most of the decay populates 12Cg.s. with small branches populating 12C*(4.4) and several α-particle unbound states (see 12.42 (in PDF or PS)). The ground state decay branch is determined by subtracting all other observed decay branches from unity. Early studies were motivated by evaluation of the 12B and 12N mirror decays to states in 12C and by parity violation studies. The decay rates to 12C*(4.4) measured in (1981KA31) are most precise and have been used as normalization factors in modern experiments to deduce the relative and absolute branching ratios of weaker decay branches, see 12.23 (in PDF or PS). In most articles, measurements on 12N and 12B were published together; see reaction 32 12B β--decay for detailed discussion on the experiments.
Studies on 12N decay are more complicated than those on 12B decay because the high-energy 17.3 MeV β+ particles can produce Bremsstrahlung photons while interacting in the β-counter, which can be detected in the γ-counter giving rise to a huge background under the discrete photo-peaks. The Q-value for 12B decay is 13.37 MeV, which leads to a significantly lower background radiation. In addition, the β+ annihilation photons can sum with decay γ-rays in the detector causing a distortion away from the expected response function. Discussion on systematic effects is given in (1974MC11, 1978AL01).
A detailed study of the high-energy portion of the γ-ray spectrum identified decay branches populating the 12C*(12.71, 15.11) states (1967AL03). The β-γ spectra were analyzed to determine the ratios I(Eγ = 12.72)/I(Eγ = 4.4) = 2.9 × 10-3 ± (26%) and I(Eγ = 15.11)/I(Eγ = 4.4) = 1.78 × 10-3 ± (20%). Using the known Γγ and γ-decay branching ratios the β-decay intensities to these states can be deduced.
Interest in the higher-lying Jπ = 0+ and 2+ states led to measurements where 12N and 12B ions were produced at rare isotope facilities. Analysis of these data gave precise details on the α breakup channel for 12C states up to Ex = 15.11 MeV populated in the decays, see for example (2004FY03, 2005DI16, 2009DI06, 2014TE01). In (2009HY01, 2009HY02, 2010HY01) it is found that interference of the Jπ = 0+2 state with other Jπ = 0+ strength around Ex ≈ 11.2 MeV leads to "the very broad component from 8.5 to 11 MeV, which has been mistaken for a 10.3-MeV resonance with a 3-MeV width". Rather than attribute their observed strength to a 10.3 MeV group, they provided the β feeding strength for the Ex = 9-12 MeV and 12-16.3 MeV regions [excluding the 12.7 MeV state]. A multi-level many-channel R-matrix analysis of the data (2010HY01) indicated a Jπ = 0+ state at Ex = 11.2 ± 0.3 MeV with Γ = 1.5 ± 0.6 MeV and B(GT) = 0.06 ± 0.02 and a Jπ = 2+ state at Ex = 11.1 ± 0.3 MeV with Γ = 1.4 ± 0.4 MeV and B(GT) = 0.05 ± 0.03.
The β-decay of 13B primarily populates bound states in 13C with an intensity > 99%. However weak decay branches to 13C*(7.54, 8.86, 9.90) and possibly 13C*(9.50) lead to β-delayed neutron emission to 12C*(0.4.4) with Pn = (0.28 ± 0.04)% (1962MA19, 1969JO21, 1974AL12); see Fig. 4 [13B β-n-decay scheme].
The decay of the giant resonance in 13C takes place predominantly to 12C*(15.1, 16.1) [and to their analogs in 12B]. Below Eγ = 21 MeV transitions to 12C*(4.4) are dominant (1975PA09). A review on isospin component splitting in 13C up to Eγ ≈ 30 MeV is given in (1993MC02).
The neutron decay of the pygmy and giant dipole resonances of 13C were studied using Ee = 129 MeV electron scattering (1999SU12). Neutron decay from the pygmy resonance tends to populate 12C*(0, 4.4), while neutron decay from the GDR tends to populate 12C*(12.7, 15.11).
Angular distributions have been measured at Eπ+ = 90 to 170 MeV to 12C*(0, 4.4, 7.7, 9.6, 12.7, 14.1, 15.1, 16.1, 19.1, 20.6, 22.9, 25.3) (1981AN10): an energy dependent ratio for the excitation of 12C*(12.7, 15.1) is reported along with similarities in the population of states seen in this reaction and in the (p, d) reaction. Angular distributions are reported to 12C*(0, 4.4) at Eπ+ = 32 MeV (1982DO01). The population of 12C*(4.4) is more than 10 times that of 12Cg.s..
Angular distributions have been measured at Ep = 8 to 800 MeV; see (1995TO03) for Ep = 35 MeV to 12C*(0, 4.4), see (1982BU03) for Epol. p = 123 MeV† to 12C*(0, 4.4), see (1990AJ01) for Ep = 18.6 MeV† to 12C*(0, 4.4), 41.3 MeV to 12C*(0, 4.4, 12.7, 15.1, 16.1), 800 MeV to 12C*(0, 4.4, 12.7, 14.1, 15.1, 16.1) and Epol. p = 119 MeV† to 12C*(0, 4.4, 7.7, 9.6, 12.7, 14.1, 15.1, 16.1, 16.6, 17.8, 18.16 ± 0.07, 18.8, 19.9, 20.3, 20.6) and 500† MeV to 12Cg.s., see (1985AJ01) for Ep = 800 MeV to 12C*(0, 4.4, 12.7, 14.1, 15.1, 16.1) and Epol. p = 65† MeV to 12C*(0, 12.7, 15.1, 16.1) and 200 and 400 MeV to 12C*(0, 4.4), see (1980AJ01) for Ep = 16.7 and 17.7 MeV to 12C*(0, 4.4) and 200 to 500 MeV to 12C*(0. 4.4), see (1975AJ02) for Ep = 50† and 54.9† to 12C*(0, 4.4, 12.7, 15.1, 16.1), and 62† MeV to 12C*(15.11, 16.1, 17.76, 18.8, 21.5, 22.55), and see (1968AJ02) for Ep = 8, 12 and 17 MeV to 12C*(0, 4.4). Spectroscopic factors are deduced in measurements highlighted with the symbol †. See also (1990GU26, 1990MU19, 1991AB04, 2004LI41, 2005DE33, 2005TS03, 2009DE02, 2009DE07, 2009DE13, 2012KU35).
The population of 12C*(10.3, 15.4) is reported in (1987LE24) along with structures at Ex = 18.2, 18.8, 19.9, 20.3 and 20.6 MeV that have Γcm = 240 ± 50, 120 ± 30, ≈ 400, ≈ 220 and ≈ 210 keV, respectively. (1984SM04) report structures at 20.61 ± 0.04 and 25.4 ± 0.1 MeV, the latter with Γ ≥ 0.5 MeV. At Ep = 62 MeV, (1974PA01) report the excitation of states having widths [Γ (keV)] of Ex = 15112 ± 5, 16110 ± 5 [< 20], 17760 ± 20 [80 ± 20], 18800 ± 40 [80 ± 30], 21500 ± 100 [< 200] and 22550 ± 50 [< 200] keV: ln = 1 for all states except 12C*(21.5) and (22.55) for which lp = (1) and ≠ 1, respectively. 12C*(14.1) is not excited, consistent with Jπ = 4+ (1970SC02, 1974PA01). For d-γ correlations via 12C*(15.1) see (1987CA20).
For reaction (b), cross sections and angular distributions for deuterons and small-relative angle p-n pairs with small relative angles (1S0 state pairs) were measured at Ep = 35 MeV (1995TO03); both angular distributions were reproduced in coupled channels calculations, and the angular distribution for the singlet state pairs was found to fall off more slowly at large angles. Also see (1996GO07). In a kinematically complete experiment at Ep = 7.9 to 12.5 MeV (1971OT02), it was found that sequential decay via states in 13C and 13N is strongly involved in the reaction. Near Ep = 12.5 MeV there is some indication of sequential decay via singlet deuteron formation.
Angular distributions, mainly for t0, t1 and t2, have been measured for Ed = 0.41 to 29 MeV. See (1985AJ01) for Ed = 18 MeV, see (1980AJ01) for Ed = 24.1, 26.2 and 27.5 MeV and Epol. d = 13 and 29 MeV, see (1975AJ02) for Ed = 0.41 to 0.81, 1.0 to 2.7, 2.2, 3.3 8, 12, 12.1, 13.3, 13.6, 14, 14.8, 15 and 28 MeV, see (1968AJ02) for Ed = 2.2, 3.3, 8, 12 and 14.8 MeV. Also see analyses in (1990GU26, 1995GU22, 2007CO01).
The relative yields of triton groups to 12C*(12.7, 15.1, 16.1) [(Jπ; T) = (1+; 0), (1+; 1) and (2+; 1), respectively] and 3He groups to 12B*(0, 0.95) [(Jπ; T) = (1+; 1) and (2+; 1), respectively] give information on a possible short range charge dependent nuclear force. Ratios were measured at Ed = 62 MeV (1972BR27), 24.1 to 27.5 (1977LI02) and 29 MeV (1979CO08) yielding charge-dependent matrix element values of 250 ± 50 keV, 180 ± 80 keV and 120 ± 30 keV, respectively. If the j = 1/2 component is excluded, which appears to be unwarranted, the charge dependent matrix element of (1979CO08) increases to 140 ± 40 keV. For a comparison of reported charge-dependent matrix element values between 12C*(12.7, 15.1) see 12.18 (in PDF or PS).
Angular distributions, mainly involving α0-3 have been measured at many energies up to 60 MeV; see (1990ES01): Ecm = 1.05 and 1.20 MeV, (1994BU01): E(3He) = 37.9 MeV, (1990MU19): E(3He) = 39.6 MeV, (1992AD06): E(3He) = 50 and 60 MeV, (1959AJ76): E(3He) = 2 and 4.5 MeV, (1968AJ02): E(3He) = 1.6 to 3.3, 1.8, 4.5, 8.8, 9.4, 10.3, 12, 15, 18, 40 to 45 MeV, (1975AJ02): E(3He) = 1.5 to 5.3, 19.1, 27.3, 35.7, 36.8 MeV, (1980AJ01): E(3He) = 18, 20, 29.2 MeV, (1985AJ01): E(3He) = 18.3 and 23.1 MeV and (1990AJ01): E(3He) = 22.7 MeV. A DWBA analysis of α0-3 and 12C*(10.84, 11.8, 12.7, 13.3) distributions (1966KE08) finds l = 1 or 0 for all the groups except α3 (to 12C*(9.6)) for which l = 2. Rainbow scattering effects are discussed in (1992AD06, 1994BU01). See also (1968AR12, 1990GU26).
Angular correlations of α-particles and 4.4 MeV γ-rays have been studied at E(3He) = 4.5 MeV (1962HO13) and 29.2 MeV (1976FU1F). For 12C*(15.1), angular correlations have been studied at E = 9.4 and 11.2 MeV (1969TA09) and at E = 24 and 25.5 MeV (1980BA1U): the average ratio between the p1/2 and p3/2 amplitudes is -0.086 ± 0.030 in the later measurement; see also (1999LE48, 2003ZE06). See (1990ES01, 2007GA24) for discussion on neutron stripping and 9Be cluster transfer, and see (1984VA39, 1985VA1E, 1986ZE1C) for a study of the spin tensors for 12C*(4.4). Ion beam analysis of surfaces is discussed in (2017MO06).
For a detailed analysis of the decays of 12C*(12.7, 15.1) see (1970RE09) and 12.14 (in PDF or PS). Attempts have been made to study the T mixing between the 1+ states 12C*(12.71, 15.11). Reported values for Γα/Γ for 12C*(15.11) are (1.2 ± 0.7)% (1970RE09, 1970RE1F), (6.0 ± 2.5)% (1970AR30) and (4.1 ± 0.9)% (1974BA42). The (1974BA42) value was obtained by observing the decay α-particles (only α1) in reaction (b); using the 12C*(15.11) Γγ0 (1983DE53) and γ-decay branching ratios (1972AL03) leads to Γα = Γα1 = 1.8 ± 0.3 eV. If this isospin forbidden Γα is the result of the mixing between the 1+ states 12C*(12.71, 15.11) [T = 0 and 1, respectively] via a charge dependent interaction, the matrix element is 340 ± 60 keV (1974BA42): see, however, 12.18 (in PDF or PS) and (1980AJ01).
For reaction (c), proton unbound states in 13N that decay to 12C*(0, 4.4, 7.65, 12.7, 14.08, 15.1, 16.1) were studied at E(3He) = 450 MeV (2004FU12).
At E(7Li) = 34 MeV angular distributions have been observed for the reactions to 12C*(0, 4.4) + 7Li*(0, 0.48) and 8Li*(0, 0.95) in all combinations. While 12C*(0, 4.4) are dominant in the two spectra, 12C*(7.7, 9.6) and, in reaction (a) at E(6Li) = 36 MeV, 12C*(12.7) are also populated (1973SC26). See also (1987CO16, 2003TR04, 2004CA46).
Angular distributions have been reported at E(13C) = 16.0 to 50.0 MeV by (1983KO15) who have also studied the excitation functions over that energy range. For reaction (b), (2014MC03) deduced spectroscopic factors and asymptotic normalization coefficients at E(14C) = 168 MeV. See (1988BI11) for measurements at E(13C) = 20.0 to 27.5 MeV.
Angular distributions for neutron exchange reactions involving oxygen isotopes are reported at E(16O) = 42 to 65 MeV (1989FR04), 13 and 14 MeV (1976DU04), 14, 17 and 20 MeV (1971BA68) and 41.7 and 46.0 MeV (1973DE21); E(17O) = 29.8 and 32.3 MeV (1977CH22, 1978CH16), and E(18O) = 15, 20 and 24 MeV (1971BA68, 1971KN05) and 31.0 MeV (1978CH16). See also (1990IM01).
The β-decay of 13O populates 13Ng.s. in (88.7 ± 0.2)% of all decays. The levels with Ex ≥ 3.50 MeV decay via proton emission to 12C*(0, 4.4, 7.65) leading to Pp = (11.3 ± 2.3)%. See (2005KN02) and Fig. 5 [13O β+p-decay scheme]. Also see (1965MC09, 1970ES03, 1990AS01, 2014TE01).
Angular distributions have been measured at Ep = 14.5 (1971CU01), 18.5 (1963LE03), 39.8 (1973HO10), 40.3 (1990YA02), 45 (1978RO08), 46 (1979FR04), 50.5 [unpublished in (1975AJ02)] and 54 MeV (1976AS01).
At Ep = 40.3 MeV, the states at 12C*(0, 4.4, 7.65, 9.64, 12.71, 14.08, 15.11, 16.10, 17.76, 18.80) are populated; cross sections for natural parity T = 0 states are enhanced when compared with the T = 1 states (1990YA02). At Ep = 54 MeV the first T = 2 states of 12C are observed at Ex = 27.57 ± 0.03 and 29.63 ± 0.05 MeV [Γcm ≤ 200 keV] (1976AS01): their identification is supported by the similar angular distributions to the first two T = 2 states in 12B, reached in the (p, 3He) reaction [see reaction 14C(p, 3He) in 12B]. The lower T = 2 state is well fitted by L = 0; the angular distribution to 12C*(29.63) is rather featureless. It is suggested that its shape is more consistent with L = 0 than with L = 2. It is not excluded that the group to 12C*(29.63) may be due to unresolved states. The states are observed with Γp/Γ = 0.3 ± 0.1 and Γα1/Γ < 0.1 for the first T = 2 state and Γp/Γ = 0.8 ± 0.2, Γp0/Γ ≈ 0.4 and Γα/Γ ≈ 0.2 for 12C*(29.63). (1976BA24) has suggested that the second T = 2 state in A = 12 may have Jπ = 0+.
At Ep = 45 MeV, (1978RO08) report Ex = 27595.0 ± 2.4 keV, Γ ≤ 30 keV for the first T = 2 state and calculate the decay properties for two values of the total width, narrow and 30 keV. A subsequent measurement at Ep = 46 MeV reported branching ratios for the decay of 12C*(27.6) to 8Beg.s. + α; 11B*(0, 2.12, 4.45, 5.02, 6.74 + 6.79) + p; and 10Bg.s. + d are, respectively, (10.5 ± 3.0)%; (3.0 ± 2.2)%, (8.0 ± 2.3)%, (0 ± 3.3)%, (8.4 ± 3.2)%, (8 ± 5)%; and (2.8 ± 2.0)% (1979FR04). An additional (9.1 ± 3.5)% of the decay feeds into the 8Be* + α continuum. See also (2006FO11).
Angular distributions of 3He, mainly to 12C*(0, 4.4) and also to 12C*(12.7, 14.1, 15.1, 16.1), have been studied at Ep = 7.5 to 52 MeV; see references in (1975AJ02, 1980AJ01). At Ep = 50 MeV, the analysis indicates Jπ = 4+ for 12C*(14.1) (1970SC02). The angular distributions to the first two T = 1 states in 12C are compared with those of the analog states in 12N obtained in the (p, t) reaction (1976YO03). For reaction (b) the transitions to 12C*(0, 4.4) have been studied at Ep = 46 MeV (1970WE1J, 1971WE05) and to 12C*(4.4) at Ep = 58 MeV (1985DE17).
Alpha groups have been observed corresponding to most known 12C states up to 12C*(16.11), see (1965BR08, 1965SC12) and 12.34 (in PDF or PS). The reaction proceeds mainly via α0-3. Angular distributions have been measured at several energies, see (1959AJ76): Ed = 10.8 to 20 MeV, (1968AJ02): Ed = 0.5 to 28.5 MeV, (1975AJ02): Ed = 1.0 to 40 MeV, (1980AJ01): Ed = 2.7 to 40 MeV, (2004PE10): Ed = 0.5 to 2.0 MeV, (2008GU08): Ed = 0.7 to 2.2 MeV and (1999IG03): Ed = 15.4 MeV. The α-γ correlations give J = 2+ for the 4.4 MeV state (1954ST1C). At Ed = 1.8 MeV, the α-particles to the 7.65 MeV state were observed in coincidence with recoiling 12Cg.s. nuclei; if Γrad = (Γγ + Γπ), then the ratio Γrad/Γ = (2.8 ± 0.3) × 10-4 was reported in (1963SE23). The width of the 9.6 MeV state Γcm is reported as 30 ± 8 keV (1953DU23, 1956AH32).
Analysis of the angular distributions at Ed = 40 MeV, with a one-step, ZRDWBA, leads to Jπ = (1, 2, 3)+, (2, 3)+ and (2, 3)+, respectively for 12C*(19.5, 20.6, 22.5) (1976VA07); spectroscopic factors were also deduced for all observed transitions. At Ed = 40 MeV, the upper limits for the ratio of the cross sections to 12C*(15.11) and 12C*(12.71) are ≈ 0.3% for θlab = 6° to 10° and 0.5% at 40° and 50°: these results by (1974VA15) imply a lower isospin mixing between these two 1+ states than suggested by the work of (1965BR08, 1972BR27). See also (1991AP03, 1994IV01, 1996TA29: material profiling) and (1995HU15: meteorite analysis).
The angular distributions of 6Li ions corresponding to transitions to 12C*(0, 4.4) have been measured at Eα = 27.2 (1995FA21) and 42 MeV (1964ZA1A). At 27.2 MeV, the contributions of the direct and statistical two-nucleon transfer processes are estimated by studying the (α, 6Li) reaction on several targets.
Properties of 12C states have been deduced from measurements of the angular distributions of α0 and α1 particles for Ep < 18 MeV [see (1968AJ02)], at Ep = 2.99 to 5.14 MeV (1977JA11), Ep = 19.85 to 43.35 MeV (1971GU23) and Ep = 3.5 to 7.5 MeV (2000IG05). Early results on the angular distributions of alpha particles and 4.4 MeV γ-radiation indicated that the 4.4 MeV state has J = 2+ or > 4 (1953KR1B). The alpha particles to 12C*(4.432 ± 0.010 MeV) were observed along with a transition corresponding to Eγ = 4.443 ± 0.020 MeV (1952SC1B). The lifetime of 12C*(4.4) was reported as τm = 65 ± 9 fsec (1970CO09). At Ep = 43.7 MeV the angular distributions to the 0+ states 12C*(0, 7.66, 17.76) are fitted by L = 1, while the distributions to 12C*(14.1, 16.1) are consistent with L = 3 [Jπ = 4+ and 2+, respectively] (1972MA21). The energy of the second excited state of 12C is 7654.2 ± 1.6 keV (1973MC01), see additional discussion therein; such a high value leads to a sharply reduced rate for the (α-α-α) process.
At Ep = 7.5 MeV, the α-γ correlations to 12C*(4.44) were measured and analyzed for θ = 20°-160° to deduce spin tensor components and M = 0, 1 and 2 magnetic sublevel populations (2000IG05). The triton-cluster transfer spectroscopic factor amplitudes to 12C*(0, 4.44, 7.65, 14.08, 16.1, 17.76) are deduced from analysis of angular distributions at Ep = 9 to 43.7 MeV (2006AB20). This reaction, which decreases proton and 15N abundances in the 19F production sequence, was studied in (1994KA02, 1998AD12, 2003HU10, 2008BA42, 2009LA13, 2011AD03, 2012DE06, 2012IM02); complementary analyses of this reaction using the Trojan Horse Method are found in (2006LA18, 2007LA37, 2008MU07, 2008MU15, 2008PIZZ, 2009LA13, 2010MU16).
Parity non-conserving alpha-decay reactions are discussed in (1990DU01, 1991DU04, 1991KN03, 2000MI37). Depth profiling and material composition studies using reactions (a) and (b) are discussed in (1990FU06, 1991DU04, 1991IW05, 1992FA04, 1992MA14, 1992MA22, 1994EN07, 1994JA16, 1994OL08, 1996MI28, 1996MI29, 2005KU36, 2010MA26, 2016RE12).
At Eα = 42 MeV angular distributions have been obtained for all four of the transitions: 12Cg.s. + 7Li*(0, 0.48) and 12C*(4.4) + 7Li*(0, 0.48) (1968MI05). See (1995BO31) for a study of the 15N cluster configurations at Eα = 27.3 MeV.
The β-delayed α-decay of 16N can feed only 12Cg.s. from 16O*(8.871, 9.585, 9.845) states. In early measurements such as (1959AL06, 1984WA07), a (1.0 ± 0.2)% β-decay branch to 16O*(8.871) was deduced that was based on the beta spectrum following 16N decay; a subsequent reanalysis by the authors resulted in a revised branching ratio (1.06 ± 0.07)% that was detailed in (1986AJ04). However, the small fraction of α-decay from these states yields a significantly lower α-particle intensity.
The decay to 16O*(9.585), which α-decays 100% to 12Cg.s. dominates the delayed α spectrum; the branching ratio (1.20 ± 0.05) × 10-5 (1961KA06) has been used extensively in the literature. However the result (1.49 ± 0.05) × 10-5 (2016RE01) is in poor agreement. A third reported value (1.3 ± 0.3) × 10-5 (1993ZH13) does little to resolve the discrepancy. In (1961KA06) a gas carrying radioactive 16N passed sequentially through a proportional counter (α-counting) and a GM-tube counter (β-counting). The delayed α branching ratio was deduced from analysis that considered lifetimes, flow-rates and active volumes. On the other hand, (2016RE01) counted the number of 16N nuclei deposited into a Si detector and the number of subsequent α-decays. At present, we accept the result of (2016RE01), though additional verification of this result would be useful.
The smaller decay branches to the neighboring states have been measured relative to the 16O*(9.585) branching ratio, see 12.43 (in PDF or PS). The α-decay of 16O*(8.871) is parity forbidden, and detailed measurements of this decay branch have set limits on irregular parity amplitudes in the wavefunction (1961KA06, 1969HA42, 1970JO25, 1974NE10). In (1974NE10) Γα = (1.03 ± 0.28) × 10-10 eV is determined for 16O*(8.87) (1974NE10).
It was proposed in, for example, (1971BA99) that the 16N delayed α spectrum gives details on the E1 component of the 12C + α capture cross section in the relevant Ecm ≈ 300 keV region. At astrophysical energies the reaction is dominated by the tails of subthreshold states; the interference of these states gives rise to a, so called, "ghost peak" in the delayed α-particle energy spectrum that can be used to deduce the E1 component of the capture reaction. Significant efforts focused on determining the shape of the spectrum (1993BU03, 1993BU18, 1993BU21, 1993ZH06, 1994AZ03, 1997FR12, 1998GA20, 2007FR11, 2007TA34, 2009BU12, 2010TA05).
Reactions (a) and (b) have been studied using Bremstrahling beams with Eγ < 42 MeV (1981MA38), < 50 MeV (1997GO16, 2001KI33), < 100 MeV (1981CH28), < 150 MeV (2012AF07), < 300 MeV (1995GO10, 1995KI04), and with polarized quasi-monoenergetic beams at Eγ = 9 to 11 MeV (2013ZI03). There is evidence for the involvement of many 12C states: see (1965RO05) and references therein. A test of time reversal invariance, via comparison of the 12C(α, γ) vs. the 16O(γ, α) rate found no evidence of T-invariance (1970VO13). Astrophysical implications of the photo-breakup reactions are discussed in (1953HO81).
These reactions proceed mainly through 12C*(0, 4.4). See references in (1968AJ02, 1975AJ02, 1980AJ01, 1985AJ01, 1990AJ01). 12C*(14.1) is populated at Ep = 101.5 MeV (1984CA09). See analysis of the Eγ = 4.44 MeV lineshape in (2001KI25). See also (2016OL04).
Angular distributions, mainly to 12C*(0, 4,4), have been measured at Ed = 13 to 55 MeV (1975AJ02), Ed = 12.7 to 80 MeV (1980AJ01), Ed = 50 to 80 MeV (1985AJ01) and Ed = 18 to 55 MeV (1990AJ01). Spectroscopic factors are reported in (1984UM04: Ed = 54.2 MeV to 12C*(0, 4.4, 7.7, 9.6, 14.1)), (1978BE1T: Ed = 50, 65 and 80 MeV to 12C*(0, 4.4, 14.1)), (1978OE02, 1979OE04: Ed = 80 MeV to 12C*(0, 4.4, 7.7, 9.6, 14.1, and broad (or unresolved) structures at 14.1 ± 2.6, 19.5 ± 1.5 MeV)), (1980YA02, 1984UM04: Ed = 54.25 MeV to 12C*(0, 4.4, 7.7, 9.6, 14.1)).
Reactions involving 12C*(0, 4.4, 9.6) + 7Be*(0, 0.4) and 12C*(7.6) + 7Beg.s. are reported at E(3He) = 25.5 to 30 MeV (1970DE12, 1972PI1A). The α-particle pickup spectroscopic factors are deduced at E(3He) = 26 MeV (1975AU01), 60 MeV (1995MA57) and 70 MeV (1976ST11). See also measurements at E(3He) = 41 MeV (1981LE01).
At Eα = 25 MeV reaction (a) proceeds in part by sequential decay via states in 16O and 20Ne (1968PA12). Angular distributions involving 12C*(0, 4.4) at Eα = 90 MeV have been analyzed by PWIA and DWBA by (1976SH02): Sα = 2.9 ± 0.5 and 0.70 ± 0.23, respectively. In reaction (b), the angular distributions and integrated cross sections of 8Be nuclei (identified through the α-decay) leading to the ground and 4.4 MeV states of 12C have been determined for Eα = 35.5 to 41.9 MeV (1965BR13). The α pickup spectroscopic factors have been measured at Eα = 55 to 72.5 MeV (1973WO06, 1974WO1D, 1976WO11): Sα = 0.25, 1.07, 0.05, 1.40 for 12C*(0, 4.4, 7.7, 14.1) respectively; the excitation of 12C*(9.6) is also reported. See also (1990JA09, 1992JA04, 2008JA02, 2009JA07, 2014JA07).
Reaction (a) was measured at Ecm = 7.2 to 10.2 MeV (1988WE17), see analysis in (1994OS08). For reaction (b), see measurements reported in (1974SP06: E(16O) = 24 MeV), (1974RO04: 49 to 64 MeV), (1977PO14, 1979PO14: 68 to 90 MeV), (1979MO14: 65 to 92 MeV), (1983ME13, 1984ME10: 50 to 72 MeV), (1988AU03: 72 MeV), (1996FR09: 51 to 66 MeV) and (1977KA26: Ecm = 17 MeV).
At E(11B) = 41.25 MeV the t20 and t40 polarization tensors of 12C*(2+1) were measured for θcm = 48° - 62° (2000IK02). In addition, analysis of the measured transfer cross sections for reactions leading to 12Cg.s. + 15Ng.s., 12C*(4.44) + 15Ng.s. and 12Cg.s. + 15N*(6.32[Jπ = 3/2-]) appears to indicate significant participation of multistep processes passing through 11B states. See also optical model analysis of measurements at E(11B) = 115 MeV in (1979RA10).
The γ-recoil method was used to extract the t20 and t40 polarization tensors of 12C*(2+1) at E(13C) = 50 MeV for population of 12C*(2+1) + 17Og.s. and 12C*(2+1) + 17O*(870) (2000IK01). An analysis of the spectroscopic amplitudes is also given. See earlier experimental results in (1975SE03, 1976WE21, 1977DU04, 1979BO36, 1979RA10).
The decay of the lowest T = 2 state of 16O to 12C*(0, 4.4) has been studied by (1973KO02).
At Ed = 13.6 MeV angular distributions have been obtained for the 9Be groups to 12C*(0, 4.4) (1981GO16). Angular distributions have also been measured at Ed = 9 to 14.5 MeV: see (1964DA1B, 1967DE03, 1967DE14).
Angular distributions involving 12Cg.s. have been studied at Ep = 7.9 to 18.6 MeV (1987KI26).
Angular distributions for reactions that mainly involve 40Ca resonances have been reported in (1978PA04: E = 47 to 57 MeV), (1979LE02: 17 to 31 MeV), (1980PA08, 1980SA12, 1980SA31, 1985SA11: 24 to 54 MeV), (1981NU02: 32 to 48 MeV), (1982FU06: 32 to 36 MeV) and (1989LE19: 46.5 MeV). See also measurements and analyses of the α transfer reaction reported in (1972MA36, 1975ER02, 1976PE05).