(See the Energy Level Diagram for 12C)
The yields and angular distributions of protons leading to the ground state and several excited states of 11B have been investigated by (AL56B: E(3He) up to 2.7 MeV), by (HO55I, HO56D: E(3He) = 2.0 MeV), by ((WO56, WO56B, JO57B) and E. Wolicki, private communication: 2 to 4.5 MeV) and by (D.R. Sweetman, private communication: 6.05 MeV). The yield rises rapidly to E(3He) = 1.8 MeV and remains approximately constant to 4.5 MeV, with no indication of resonance. Angular distributions show fore and aft asymmetry and vary only slowly with energy. At E(3He) = 2 MeV, it appears that both direct interaction and compound nucleus formation, involving interfering resonances with l ≤ 3, may be taking place. At higher energies the forward peaking suggestive of direct interaction becomes more obvious. See also 11B. For reactions (a), (c) and (d), see 11C, 8Be and 10B.
Neutron groups corresponding to states of 12C*(0, 4.4, 7.6) have been observed with Eα up to 5.3 MeV. At Eα = 5.3 MeV the forward yield of the group leading to the 7.6 MeV state is about 1/8 of that leading to the 4.4 MeV state: see (GU52, ST55B, ME56A, RI57); see also (DI57).
The energy of the γ-ray from the first excited state is 4.425 ± 0.020 (MI54D), 4.48 ± 0.06 MeV (BE55H) (both values corrected for Doppler shift). The internal pair conversion, coefficient indicates an E2 transition (MI54D); the angular correlation of pairs admits M1 or E2, favoring the latter (HA54A, GO56D, GO56G, AR58A). The angular distribution of γ-rays observed at several bombarding energies is consistent with J = 2+ (TA55B, PR56). The n-γ correlation at Eα = 5.3 MeV (thick target) is isotropic within 6.5% (ST56B: see also (TA58D)). The mean lifetime of the 4.4 MeV level is (2.6 ± 0.9) x 10-14 sec, about one-eighth of the single-particle value for an E2 transition (DE56A).
The 7.7 MeV state appears to decay predominantly into 8Be + α (see 12B(β-)12C and 12C(α, α')12C*). A gamma ray of energy 3.1 MeV has been reported by (BE53C, UE54, ST56B, ST56F, ST57G), but (BE55H, GO57D, KR57) find no evidence of the 7.7 MeV nuclear pairs which should accompany the decay to the ground state. (BE55H) estimate that at least 96% of the decays proceed to 8Be + α; (KR57, KR58B) find < 1.6 x 10-5 7-MeV pairs per 4.4 MeV γ-ray; assuming a population ratio of 1 : 8, this result yields Γπ/Γ < 1.3 x 10-4. An upper limit of 1/600 for the ratio of 7.6/4.4 MeV pairs is reported by (GO57D). (DI54) find no n-γ coincidences other than those associated with the 4.4 MeV level. See also (RO57F).
At Eα = 21.7 and 175 MeV, γ-radiation from the 15 MeV, J = 1+ ; T = 1 state (see 12C(p, p')12C*) is reported (RA54A, WA57B). At the higher energy, the ratio of 15 MeV to 4.4 MeV radiation is 1.2 x 10-2 (WA57E). See also (EL54B, BR55, HA55B, GO56J, BR57H) and (MA55I; theor.).
At Ed = 0.95 MeV, the upper limit to the capture cross section is 0.1 μb (SA55F).
The thin-target excitation function in the forward direction in the range Ed = 0.3 to 4.6 MeV shows some indication of a broad resonance 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 (BU54, MA55J). Angular distributions seem to be dominated by the stripping process: see 11C. The yield of 6.5 MeV γ-rays has been measured at four bombarding energies between 0.8 and 2.2 MeV (SA55F). See also 11C.
Absolute yields and angular distributions are reported for various proton groups by (EN52, BU54, PA54A, MA56J, VA56C) for Ed = 0.18 to 3.1 MeV. Although the excitation functions show several broad peaks, no clear resonances can be identified, and it must be assumed that many overlapping resonances are involved (MA56J). Angular distributions indicate both stripping and compound nucleus processes even at low bombarding energies (PA54C). However, the p1 group, leading to 11B*(2.1), shows no stripping even at Ed = 3 MeV; it is suggested that an orbital angular momentum selection rule is operative here (MA56J: see 11B). Absolute cross sections reported by (BU54, PA54A, MA56J) differ rather greatly.
The yields of 6.8 and 7.3 MeV γ-rays have been measured at four bombarding energies between 0.8 and 2.2 MeV (SA55F). At Ed = 1.70 MeV, θ(lab) = 58°, the cross section for protons leading to the 6.76 MeV state is 6.1 (± 15%) mb/sr (KA56).
Excitation curves for ground state α-particles have been measured for Ed = 0.9 to 2.6 MeV at 45°, 90° and 150°. Broad maxima are observed at 1.0, (1.4) and 2.0 MeV. At Ed = 0.91 MeV, the angular distribution of α0 particles shows a peaking in the forward direction (MA56J). See also 8Be.
Proton groups reported by (BI55) and (MO58F) are listed in Table 12.5 (in PDF or PS). A careful search, at E(3He) = 1.25 MeV, reveals no other level in the range Ex = 4.4 to 7.7 MeV (MO58F: region at Ex = 6.4 MeV obscured). At E(3He) = 2.0 MeV, the proton group leading to the 15.11 MeV level was found to be in coincidence with a 15.10 MeV γ-ray: Γγ/Γ for this level is 0.77 ± 0.20. The ratio of the width for γ-emission to the 4.4 MeV level to the ground state Γγ is ~ 0.03. The 12.76 MeV level also emits γ-rays: Γγ/Γ ~ 0.02, suggested Jπ = 1+ ((GO57B) and H.E. Gove, private communication). Coincidence studies by (MO58F) lead to Γγ/Γ < 0.9% for the 7.7 MeV level, Γγ/Γ = 3 ± 1 % for the 12.76 MeV level, and 50 ± 25 % for the 15 MeV level. See also 11B(d, n)12C, (BR58E, SW58A) and 13N.
See also 14N.
In the range Ep = 0 to 3 MeV, five principal resonances occur, at Ep = 0.16, 0.67, 1.4, 2.0 and 2.6 MeV (see Table 12.6 (in PDF or PS)). All except the second and fourth exhibit resonance for α0, α1, γ0 and γ1 (to 8Be*(0, 2.9) and 12C*(0, 4.4)); at Ep = 0.67 MeV, only α1, γ1 are resonant. It follows from angular momentum selection rules that resonances for α0 must have the character Jπ = 0+ , 1- , 2+ , 3- ...; J = 0+ is excluded by observation of γ0.
The Ep = 0.16 MeV resonance (12C*(16.11)) is well established as J = 2+ ; probably the T = 1 analogue of 12B*(0.95). The angular distribution of α0 particle is strongly anisotropic at resonance and shows a (cos θ) term varying with energy near resonance. The assumption J = 2+ , lp = 1, with interference from an s-wave state at higher energy gives a good account of the observed angular distributions from Ep = 0.13 to 0.3 MeV. The channel spin ratio χ = 0.42 ± 0.02; the relative amplitude of the interfering J = 1- state is 0.022 ± 0.002 (TH52C). The angular correlation of α1 and the subsequent breakup of 8Be*(2.9) also requires J = 2+ , with the ratio of reduced matrix elements for outgoing d to s-waves, B = 0.80, phase difference cos β = 0.60 (GE55C). The angular distribution of γ1 and of the following 4.4 MeV radiation is consistent with the scheme 2+(M1)2+(E2)0+ with the channel spin ratio χ = 0.42 (GR54A); (CR56C) obtain χ = 0.51 ± 0.03. Angular distributions of the 16 MeV radiation, γ0, require J = 2+ , with interference from a J = 1- level at Ep = 1.4 MeV (GR54A, CR56C). (γ0 is not resonant at Ep = 0.67 MeV, so this state cannot be involved here.) The resonant energy is 163.1 ± 0.2 keV; Γlab = 6.5 ± 0.6 keV (see (55AJ61)). The very small α-width suggests T = 1 (BE53).
For the Ep = 1.4 MeV state (12C*(17.23)), the possible assignments are 1- (s-wave), 2+ (p-wave), 1- or 3- (d-wave); d-wave formation would seem to be excluded by the observed width. As indicated above, J = 1- appears to be required to account for the interference at lower energies in α0 and γ0; known higher resonances are probably too narrow to produce the observed effects. (DE57A) find that the α0-dsitributions for Ep = 0.6 to 1.4 MeV are well accounted for by the assumption of s-wave formation of J = 1- through channel spin (χ = 0) with a relative d-wave amplitude A = 0.5, and interference by the 2.6 MeV, J = 2+ , state, with relative amplitude C = 0.25. A qualitative fit to the behavior of α1 can be obtained with the same assumptions (DE57A). Angular distributions of γ0 at Ep = 1.4 MeV admit either J = 2+ or 1- ; for the latter, however, formation in channel spin 2 (χ = ∞, d-waves) is required (GO55). The angular correlation of internal pairs indicates E1 for γ0 (GO56G, GO56J, AR58A). The large E1 width suggests T = 1 for this state (BE53).
The Ep = 0.67 MeV state (12C*(16.58)) may be formed by s- or p-waves; d-waves are excluded by the width (BE53). The angular distribution of α1 at Ep = 0.64 and 0.93 MeV indicates s-wave formation: if J = 2- is assumed, the d-wave admixture is < 10%. The correlation of α1 with the subsequent 8Be*(2.9) breakup is consistent with J = 2- and excludes 1- ; an appreciable f-wave admixture in outgoing α1-particles is indicated (DE57A). Correlation results at Ep = 270 keV can be accounted for by J = 2- with interference from the 1- , Ep = 1.4 MeV state (GE55C, DE57A). The angular distribution of γ1 is reported to require J = 2+ , with interference from the 1- , Ep = 1.4 MeV state (GR54): according to (DE57A), however, the distributions observed by (GR54A, GO55) can equally well be ascribed to J = 2- , with interference from a broad, even parity state, possibly at Ep = 2.0 or 2.6 MeV (see, however, (GI54C)). The angular correlation of internal pairs indicates E1 for the γ1 radiation (GO56G, GO56J, AR57). The relatively large E1 width suggest T = 1 for this state (BE53).
The Ep = 2.0 MeV level is reported to be resonant for α0 and α1; the relative weakness of α1 suggests J = 0+ (PA53B). These seems to be no clear indication of resonance for γ0 or γ1 at this energy (GO55: see also (HU53)). At Ep = 2.65 MeV, resonance occurs for α0, α1 (PA53B) and, weakly, for γ0, γ1 (BA55F, GO55). A large P2 coefficient in the angular distribution of γ0 suggests J = 2+ (GO55). (HO55F) find Ep = 1.98 and 2.61 MeV for the resonant energies for α0. Additional resonances for γ0 and γ1, reported by (BA55F) are listed in Table 12.6 (in PDF or PS). (GE59A) have examined the excitation function for ground-state transitions from Ep = 4 to 7.7 MeV. The experiment locates the maximum of the 12C giant resonance at Ex = 22.55 ± 0.1 MeV but does not resolve individual levels. Two additional peaks, at Ex = 21.4 and 22.1 MeV are suggested. The maximum value of σ(γ, p) is calculated to be 29 ± 5 mb.
An upper limit for the total cross section (average value, Ep = 1.7 to 4.0 MeV) for the production of nuclear pairs with Eπ = 6.5 to 9.5 MeV is 0.03 μb (BE55A). See also (55AJ61, MA56R), (SI57B; theor.) and 8Be.
Observed maxima in the (p, n) cross section are listed in Table 12.7 (in PDF or PS) (BL51A, BA55F, KA57A, GI59). The region covered is characterized by considerable overlapping of resonances (GI59). See also (KO56, MA58A, TA58A).
Absolute elastic scattering cross sections are reported for one angle for Ep = 0.6 to 2.0 MeV by (TA56A), for four angles for Ep = 0.3 to 1.0 MeV by (DE57A). A pronounced anomaly is observed near Ep = 0.67 MeV at all angles; the level is therefore formed by s-waves. The 0.3 to 1.0 MeV results are well accounted for by two resonances: Ep = 0.67 MeV, s-wave, J = 2- , Γ = 0.33 MeV, Γp/Γ = 0.5, d-wave < 10%, and Ep = 1.4 MeV, s-wave, J = 1- , Γ = 1.27 MeV, Γp/Γ = 0.05 (DE57A). (The reported Γp/Γ for the 1.4 MeV resonance appears to be inconsistent with the values 0.8 or 0.2 derived by (BE53) from (p, γ) and (p, α) cross sections.) (TA56A) find no rapid variation in cross section near Ep = 2.0 MeV. The absence of a detectable anomaly near Ep = 0.16 MeV confirms the small value of Γp assumed for this resonance; Γp < 200 eV (J.C. Overley, private communication). See also (KI56).
Maxima in the yield of 2.1 MeV γ-radiation from 11B*(2.1) are observed at Ep = 2.664 MeV, Γ = 48 keV: (HU53, BA55F) and at Ep = 3.15, 3.4, 3.78, 4.28, 4.68 and 5.13 MeV (BA55F: see Table 12.7 (in PDF or PS)). (Judging form the width, the 2.66 MeV resonance is not that observed, e.g., in 11B(p, γ)12C.)
Reported neutron groups are listed in Table 12.8 (in PDF or PS). The group corresponding to the 7.6 MeV state is weak, relative to neighboring groups, at all bombarding energies investigated, and the stripping pattern is poorly developed. The relative weakness of the 7.6 MeV state in this reaction and in the 12C(e, e')12C* and 12C(p, p')12C* reactions is attributed to lack of parentage overlap with the ground state of 12C (LA55). At Ed = 0.92 MeV, there is no indication of a state in the range Ex = 5.1 - 6.6 MeV: the upper limit of the intensity of the corresponding neutron group is < / ~ 1% of the intensity of the group corresponding to the 4.4 MeV state (BI57C). For Ed = 1.1 to 2.0 MeV only the groups corresponding to 12C*(4.4, 12.76) are accompanied by γ-radiation; an upper limit for (n, γ) coincidences from 12C*(7.6) is 0.2% of 12C*(4.4) (DA58C, NE58A, NE59).
Angular distributions of the neutrons to the first four states of 12C have been reported for a number of energies in the range Ed = 0.5 to 10 MeV. At the higher energies, the distributions are understood in terms of simple stripping theory (except for the 7.6 MeV state). At the lower energies, Ed = 0.5 to 5 MeV, a good account of the angular distributions of ground-state neutrons is obtained with the theory of (OW57) which includes not only stripping of the deuteron but also the possibility of stripping a neutron from 11B, and the interference between the two processes. The relative probability of the exchange stripping increases with energy until the Coulomb barrier is surmounted. The exchange process seems to involve s-wave deuteron capture by a 10B core with J = 1+ (PR56A, AM57A, OW57: see also (NE59)). Angular distributions at Ed = 9 MeV indicate odd parity for the 9.6 MeV state (MA56P: see also (GR54B) and Table 12.8 (in PDF or PS)). For other work on angular distributions, see (AM57A, AM58: Ed = 0.50 to 1.15 MeV), (WA55E: Ed = 0.6 MeV), (IH55A: Ed = 0.69 MeV), (GR54B: Ed = 0.85 MeV), (BI57C: Ed = 0.92 MeV), (PR56A: Ed = 1.5 to 5 MeV), (GI53: Ed = 8.1 MeV), and (ZE57: Ed = 10 MeV). See also (BU54, BO56L, BO56M, KO56A, RA57A) and (MA55I, ED58; theor.).
In the range Ed = 1.0 to 5.5 MeV, two slow neutron thresholds are observed at 1.627 ± 0.004 MeV (Ex = 15.11 ± 0.01 MeV) and near 4.1 MeV (broad; Ex = 17.23 MeV) (MA55J). Gamma rays are observed with Eγ = 4.44 ± 0.05 (RU51A) and 12.8 ± 0.3 MeV (KA58A). If the latter γ-ray is properly attributed to decay of the 12.8 MeV level, it is not clear why the level should so decay in view of its instability with respect to 8Be and 8Be*(2.9) (KA58A: see also 10B(3He, p)12C). A 15.1 MeV γ-ray is observed with a threshold of Ed = 1633 ± 3 keV, attributed to the first T = 1 state of 12C at 15.11 MeV. The observed width is < 2 keV. A search for α-particles to 8Be and 8Be* gives Γα/Γγ < 1.5. At Ed = 2.96 MeV the cross section for production of the 16.1 MeV T = 1 state is < 1 mb/sr (KA58A). See also (55AJ61) and (WA57B).
At E(3He) = 4.5 MeV, the ground state deuteron group is strongly peaked in the forward direction (HO57B).
The half-life is 20.34 ± 0.5 msec (weighted mean of (55AJ61, NO56B, CO57B, KR58, VE58A), excluding (JE48C)). Eβ(max) = 13.40 ± 0.05 MeV (VE58A). Branches are observed leading to 12C*(0, 4.4, 7.65, 10.1): see Table 12.9 (in PDF or PS). The fact that the transition to the 0+ ground state is allowed establishes J = 1+ for 12B. This assignment is confirmed by the allowed character of the transition to 12C*(4.4), J = 2+ . The 7.7 MeV level decays mainly by α-emission to 8Be(0) with Q = 278 ± 4 keV; Ex = 7.653 ± 0.008 MeV (CO57D). Gamma transitions with Eγ > 6 MeV accompany < 10-4 of all β-decays (KA56, KA58A); an upper limit of 3 x 10-5 is obtained in a search for β-γ (7.6) coincidences (KA58). Upper limits for (3.2 + 4.4) MeV cascades are given as (0.4 ± 2) x 10-3 and 10-5 of all decays by (TA56C) and (KA58) respectively. It follows that the relative partial width of the 7.6 MeV level is < 3 x 10-3 for 7.6 MeV γ-rays and < 10-3 for 3.2 MeV γ-rays (see also 9Be(α, n)12C). Since the β-transition is allowed, the 7.7 MeV state has J = 0+ , 1+ or 2+ ; J = 1+ is ruled out by the α-decay. The preponderance of α-decay over γ-decay speaks for J = 0+ (CO57D).
The 10.1 MeV level decays mainly via α-emission to 8Be(0); transitions to 8Be*(2.9) amount to < 4%. The c.m. width is about 2.5 MeV (after removing the Eβ5 factor): the best account of the observed α-spectrum is obtained with J = 0+ , Eλ = 1 0.4 MeV, θ2α = 1.5, R = 5.21 x 10-13 cm (CO58A).
Excitation of the 15.1 MeV level by bremsstrahlung is reported by (GA57B, HA57E, GA58A). From measurement of the yield of resonance scattered radiation and of the self-absorption coefficient, the integrated scattering cross section ∫ σsdE, and the peak absorption cross section σ0n are deduced. The resulting values for partial widths are given in Table 12.10 (in PDF or PS). It is noted the γ-ray width for the ground state transition is near the single-particle M1 value of 65 eV, and that the very small α-width strongly suggests T = 1 for this level (HA57E). The scattering angular distribution indicates dipole radiation (LE56A, GA57B, GA58A). The strength of the M1 radiation also indicates T = 1: see (MO58). Inelastic scattering in the giant-resonance region has been studied by (GA58A). See also (GO57J, AX58, MC58).
The cross section for production of 11C exhibits a broad peak at Eγ = 22.5 MeV, Γ ~ 4 MeV, σmax = 8.3 mb (BA55E). Other reported values for σmax are summarized by (CO57B: note a 10% correction in this work). See also (CA57F). AT high energies, the cross section exhibits a long tail, falling off approximately as Eγ-3. The integrated cross section to Eγ = 250 MeV is 80 MeV-mb, accounting for about 1/3 of the sum-rule limit for all absorption processes. It is noted that the relative prominence of the high-energy tail is not a general feature of (γ, n) reactions in heavy elements (BA55E, CO57B). Comparison of (γ, n) and (e, n) cross section for 28 to 145 MeV are consistent with the assumption that the transitions are predominantly E1 (BA58L). The angular distribution of photoneutrons at the giant resonance is W(θ) = 1 + (1.35 ± 0.88)sin2θ, indicating considerable emission of neutrons with l > 0 (FA56A). See 12C(γ, p)11B and (TE54C, MO55A, BA57D; theor.).
Discontinuities in the yield function are reported to indicate levels at 19.3, 19.8, 20.1, 20.5, 20.7, 21.1, 21.6, 22.4, and 22.8 MeV (GO54F, KA54A). The first two are given as 19.09 ± 0.05 and 19.55 ± 0.05 MeV by (SP55A). Eighteen discontinuities observed between Eγ = 18.90 and 22.88 MeV are tabulated by (KA58B). A search for resonance absorption near Eγ = 22.8 MeV indicates a width Γ > 580 keV, in apparent contradiction of the activation results (TZ56). (WO58A), using monochromatic gamma rays, find no evidence of fine structure in the total cross section from Eγ = 20.3 to 20.8 MeV. The upper limit is, however, not in conflict with the recent report of (KA58B). See also (JO55F, SA55J, BA58B, SM58A).
The cross section exhibits a giant resonance at Eγ = 21.5 ± 0.5 MeV, Γ = 1.7 ± 0.5 MeV (HA51F). The peak cross section is 22 mb, and the integrated cross section to 24 MeV is 56 MeV-mb (CO56D): compare 11B(p, γ)12C (GE59A). The photoproton spectrum shows the general features of the inverse reaction, 11B(p, γ)12C, and suggests resonances at Eγ = 17.3, (20.8), 22.6, and (23.1) MeV (CO56D: see, however, (WO58A)). (LI57C) finds indications of peaks at Eγ = 21.8, 22.6, 23.3 and 25.8 MeV. An absolute measurement, based on σ(12C*(γ, 3α)) for Eγ = 17.6 MeV yields σ(γ, p) = 1.19 ± 0.21 mb, in good agreement with the value 1.09 ± 0.16 mb calculated from the inverse reaction (MA56R). See also (GO56L, CH58C, PE58, WH58).
Angular distributions of photoprotons show a pronounced 90° peaking, somewhat skewed in the forward direction (HA52G, HE53A, JO55F, KL56A, DO57, LI57C, MI57B). Such distributions are inconsistent with s-wave proton emission from J = 1- ; 12C compound states formed by E1 absorption and suggest a direct interaction involving independent-particle states: L-S coupling seems to be favored (MA55E). The angular distributions of 12C(γ, n) and (γ, p) are evidently quite similar, as expected on the assumption of charge independence; the difference of about a factor of 2 in total cross section is ascribed to a 1% T = 0 admixture in the intermediate state (BA57D). See also (HE53A, CH57B, BA58A, PA58, PE58A, SM58A) and (MO55A, SI57B; theor.).
Maxima in the yield of 3-prong stars are reported at Eγ = 17.3, 18.3, 21.9, 24.3 and 29.4 MeV; some evidence of fine structure is also found. The integrated cross section is 1.21 ± 0.16 MeV-mb for Eγ < 20.5 MeV, 2.8 ± 0.4 MeV-mb for 20.5 ≤ Eγ < 42 MeV, and < 0.2 MeV-mb for 42 ≤ Eγ < 60 MeV (GO53F, GO55B). (CA55B) summarize cross section measurements for the 7Li(p, γ) radiation and find evidence for a resonance near Eγ = 12.3 MeV and possibly others at 15 and 16 MeV. According to (JO55), peaks occur at Eγ = 14.7, 15.8, 16.6, 18.3, 24.3, and > 29 MeV, in fair agreement with (GO53F). Absolute cross sections are reported for Eγ = 13 to 30 MeV, and integrated cross sections agree well with (GO53F, JO55). See also (DA53D, GU53A, MI53C, HA55G). According to (GO55B), the three-body reaction is not involved for Eγ < 40 MeV (see, however, (MI53C, CH54E)). The reaction 12C(γ, α)8Be*(p)7Li is reported by (LI56).
Studies of angular distributions indicate that for Eγ = 12 to 15.6 MeV, the reaction involves mainly E2 absorption (12C*: J = 2+ ; T = 0); from 15.6 to 20 MeV both E1 (J = 1- ; T = 1) and E2 (J = 2+ ; T = 1), and for Eγ > 20 MeV, mainly E1 (J = 1- ; T = 1). Significant E2 absorption (J = 2+ ; T = 0) also occurs for Eγ = 20 to 25 MeV (GO55B: see, however, (TE51B, GE53A)). See also (LI53B, GR54, CO55, SO55, TI55A, MA56R, MU57C).
Both elastic and inelastic scattering angular distributions have been studied at Ee = 80, 150 and 187 MeV by (FR55, FR56D) and at 420 MeV by (EH58A). The elastic data are well accounted for by a modified Gaussian charge distribution of r.m.s. radius 2.50 x 10-13 cm, derived from a harmonic well with a characteristic length parameter of 1.68 x 10-13 cm (FR56D, EH58A). See also (HO53E, FE56D, HO56E, HO57G, EH58, RA58E).
Inelastic peaks corresponding to 12C*(4.4, 7.7, 9.6) are observed, in addition to some unresolved structure near 11 MeV. There is no indication of the 15.1 MeV level. The observed angular distributions agree well with shell-model calculations of (RA55C, MO56C, TA56D, TA57C) with a harmonic well of r.m.s. radius 2.40 x 10-13 cm. Predicted absolute cross sections are low by a factor of 2 in L-S coupling, 6 in j-j coupling; it is presumed that some collective modes of excitation are involved.
Excitation of the 4.4 MeV level is electric; a width of (12.5 ± 2.5) x 10-3 eV, τm = (0.53 ± 0.11) x 10-13 sec, is obtained (HE56E). The 7.7 and 9.6 MeV levels are also electrically excited; the angular distributions indicate either monopole or quadrupole transitions, J = 0+ , 2+ . The matrix element for the 7.7 MeV E0 transition is 50 mb, in good agreement with that observed for the 16O monopole transition (SC55A, FR56D). A shell model calculation in intermediate coupling indicates that configuration mixing is required to give a non-zero matrix element for the 0+-0+ transition and suggests that a semi-collective model is indicated (SC55A, SH56D, TA57C: see also (LA55)). According to (EL56), satisfactory agreement is obtained with a 50% admixture of 1s31p82s and 1s41p72p. (RE56B) also finds reasonable agreement using the 1s-12s configuration and suggests that such a "core" excitation might appear quite generally in the light nuclei (see 16O, 14C and (CH54D)). Calculations using an independent-particle approach to a collective description give a good account of the form factors for both the 4.4 and 7.7 MeV excitations. The form factor for the 9.6 MeV level is consistent with J = 1- (FE56D: see also (PA57C)). See also (EL58; theor.).
A gamma ray of energy 4.42 ± 0.03 MeV is observed at En = 6.58 MeV (DA56D: see also (TH54B, BA55C, BE55I)). Production of 15.1 MeV γ-rays is observed at En = 90 MeV (WA57B, WA57E). At En = 14 MeV, inelastic neutron groups corresponding to 12C*(4.4, 9.6) are reported by (WO56A: see also (WH53, BE56B, CA56, AN58)). The angular distributions for neutrons corresponding to 12C*(4.4) agree well with (p, p') distributions and with direct interaction theory (AN58: En = 14 MeV).
Inelastic excitation leading to α-particle stars has been studied by (FR55I); levels of 12C at 7.7 and 9.6 MeV are involved. (JA53) find that for En < 20 MeV, most events proceed through a level at 10 ± 0.8 MeV, Γobs = 1.6 MeV, to 8Be(0) (See (FR55I) and 12B(β-)12C). See also 13C, (LI53B) and (LA56E; theor.).
Elastic scattering differential cross sections have been determined by (BU53B, GI57, GR57F: Ep = 9.4 to 9.6 MeV), (FI54B: Ep = 10 MeV), (SH56B: Ep = 12 MeV), (PE57A: Ep = 14 to 19.4 MeV), (DA56B: Ep = 17.0 MeV, c.m.), (KI55B, KI56: Ep = 14.5, 20 and 31.5 MeV), (BR52C, WR53A: Ep = 30.6 MeV), (HI57: Ep = 40 MeV) and (GE57: Ep = 96 MeV). Calculations based on the diffuse-surface optical model give a good account of the data at higher energies (GL57, ME57B, GL58). At Ep = 9.5 MeV, some evidence for compound elastic scattering is seen in the marked energy variation at back angles (GI57). See also 13N. Polarization of elastic and inelastic protons has been studied by (BR58F) for Ep = 16 to 18 MeV. Polarization of elastic protons for Ep = 5 - 7 MeV is reported by (WA58A, WA58D). See also (LE57H, KO58A, SQ58; theor.). Polarization studies at high energies are discussed by (ER56A, NI56B, AL57B, HE57C, HI57B, TY57, NI58B, NI58C).
Excitation of the 4.4 MeV level is commonly observed for all energies above Ep ~ 5 MeV: see (55AJ61) and (RE56C: Ep = 5 to 6 MeV), (GI57, HO57C: Ep = 9.5 MeV), (CO57: Ep = 12 MeV), (PE57A: Ep = 14 to 19 MeV), (BR52C: Ep = 31.5 MeV), (CH58: Ep = 40 MeV), (ST56A: Ep = 96 MeV), (DI57A: Ep = 95 and 135 MeV) and (AL57C, MA57B, TY57B, MA58H, TY58B: Ep = 182 MeV). Ex = 4431 ± 8 keV (BU57C). The 7.7 and 9.6 MeV levels are reported by (CO57, HO57C, MA57B, PE57A, CH58). Levels at 12.6, 15.0, and ~ 20 MeV are also reported by (MA57B, TY57B); the last appears strongly in the work of (ST56A) (Ex = 20.8 MeV) and is there associated with the giant resonance seen in 12C(γ, n) and 12C(γ, p).
For Ep < / ~ 30 MeV, the angular distribution of the proton group corresponding to the 4.4 MeV level exhibits a minimum near 90° - 100° (c.m.) and a definite fore-and-aft asymmetry. Neither the compound nucleus model nor the direct interaction theory appears to give a satisfactory account of these distributions (CO57, GI57, PE57A). A direct interaction calculation, using distorted waves, does reproduce the general features of the distributions and also fits the observed (p'-γ) correlation of (SH56) and (LE58A). See also (BE56F, BA57K, BU57A, MA57I, BR58C, CH58, MO58C).
The angular distribution of protons corresponding to the 7.7 MeV state depends strongly on energy in the range Ep = 14 to 19 MeV, but consistently shows a strong forward peak, indicative of l = 0 and hence J = 0+ (PE57A). See also (LA55). An attempt to observe γ-decay of this level yields an upper limit of 3% for Γγ/Γα (HO56C). The angular distribution of protons leading to the 9.6 MeV level is consistent with l = 1, J = 0- , 1- , 2- (PE57A).
The angular distribution of pick-up deuterons at Ep = 95 MeV indicates significant contributions of high momentum components in the bound, 1p neutron wave function, suggesting strong interactions, (~ 200 MeV), for close distances, R ~ 1 x 10-13 cm (SE55C, SE56A). See also (GR56E).
Emission of (15.1 ± 0.2) MeV γ-radiation, ascribed to the first T = 1 level, has been studied in the range Ep = 15 to 340 MeV by (WA57B, WA57E). The general shape of the excitation function indicates direct nucleon-nucleon interaction for the higher energies; near threshold, emission of s-wave protons is indicated. Estimates of the α-particle width, and comparison with isobaric spin forbidden reactions (e.g. 12C(α, α')12C*, 12C(d, d')12C*) indicate a T = 0 admixture a2 ~ 10-3. At 31 MeV, θlab = 80°, γ-rays of energy 15.1, 12.8 and 10.7 MeV are observed, with relative intensities 1/0.090 ± 0.015/0.095 ± 0.014. The 12.8 MeV radiation is ascribed to excitation of a 12C level of that energy, while the 10.7 MeV radiation represents a cascade from 12C*(15.1) to 12C*(4.4) (WA57E: see also 10B(3He, p)12C).
A study of reaction (c) at an energy of 29 MeV shows no indication of direct 4-body decay of 13N*; 1/4 of the events proceed via 8Be(0), and > 1/2 via 8Be*(2.9). Evidence is found for the participation of 12C*(9.6, ~ 12, 16, 20, 25) (NE55C). See also (RE55A), (JA57B) and (CU55A, SA56E, SA56F).
Inelastic groups corresponding to 12C*(4.4, 9.6) are reported by (KE51B, FR54E, GR56B, HA56C: see also (CA56K)). The 7.7 MeV level has not been observed. The angular distribution of the Q = -4.4 MeV group at Ed = 15 MeV has been analyzed in terms of direct nuclear interaction theory and in terms of electric interaction theory by (HA56C); neither appears to give a satisfactory account of the observations.
Elastic scattering has been studied at Eα = 19 MeV by (PR58A), at 31.5 MeV by (WA56F), at 40 MeV by (IG56, WE56, IG57) and at 48 MeV by (VA55B). The angular distributions show strong diffraction effects indicative of a direct interaction. Inelastic groups corresponding to levels at 4.4, 7.64 ± 0.07, 9.6 and possibly, 12.7 MeV are observed. 12C recoils corresponding to the ground and 4.4 MeV states are also reported; the absence of recoils corresponding to the 7.7 MeV state is taken to indicate that this state disintegrates primarily (> 80%) by α-emission (RA55A: see 11B(d, n)12C). From a similar experiment, (EC58) find that the chance is less than 0.1 for Γγ/Γ > 10-3.
Angular distribution of the Q = -4.4 MeV inelastic group at Eα = 31.5 MeV are consistent with the direct surface interaction theory of (AU53). A similar analysis of the Q = -7.7 MeV group gives good agreement for J = 0+ (WA56F). At Eα = 42 MeV, the angular distribution of this group is well matched by the j20(kr) or j22(kr) functions, indicating Jπ = 0+ or 2+ . The former is preferred in view of the small γ-width (EC58). See also (WE56, FI57B, PR58A, SH58A).
The decay is mainly to the ground state via an allowed transition. Transitions to 12C*(4.4, 7.65) also are allowed. Branching ratios are 100/15/3; log ft = 4.17, 4.4 and 4.4, respectively (VE58A). Delayed α-particles with a total energy of ~ 4 MeV are also observed, suggesting that a state of 12C in the region 11 to 12 MeV is involved (AL50G). See 12N.
Angular distributions of the ground state tritons have been measured at Ed = 2.2 and 3.3 MeV (HO54C).
Angular distributions of the α-particle groups to the ground and 4.4 MeV states have been obtained at E(3He) = 2 MeV (HO57) and 4.5 MeV (HO57A). Some direct interaction appears to be involved at both energies. At E(3He) = 2 MeV, a 15.1 MeV γ-ray is observed (BR57, GO57B, BR58E).
For α-groups have been observed corresponding to 12C*(0, 4.4, 7.7, 9.6): see Table 12.11 (in PDF or PS) and (HO57C). Alpha-gamma correlations give J = 2+ for the 4.4 MeV state (ST54F) while γ-γ correlations give J = 0 or > 2 for the 7.7 MeV state (SE55: see, however, 12B(β-)12C). The width of the 7.7 MeV state is < 25 keV (DU53, AH56) and that of the 9.6 MeV state is 30 ± 8 keV (c.m.). The Jπ values for the 9.6 MeV state are limited to 0+ , 1- , 2+ , 3- , 4+ (DO56C). Angular distributions of the α-particles to the ground, 4.4 and 9.6 MeV states have been measured at Ed = 20.9 MeV (FI57B). See also (GI52, BO58A, BO58C). A small yield of 15 MeV γ-radiation is observed at Ed = 10.8 MeV, presumably due to excitation of the 15.1 MeV, T = 1 state (RA54A). See also (GR56B, RA58B) and 16O.
Alpha particles have been observed to a state of 12C at 4.432 ± 0.010 MeV (SC52). The γ-ray energy after Doppler correction of 20 keV is 4.443 ± 0.020 MeV. The necessity for the correction implies a lifetime < 3 x 10-13 sec (TH52); see 12C(γ, γ')12C*. The angular distributions of short-range alpha particles and 4.4 MeV γ-radiation indicate that the 4.4 MeV state has J = 2+ or > 4 (KR53: see also (GO57H)). See also 16O and (RA58A).
There is evidence for the involvement of 12C states at 9.6 and ~ 11 MeV which decay to the ground state of 8Be, a state at 12 - 13 MeV, decaying mainly to the 2.9 MeV state of 8Be, and T = 1 state at ~ 16 and 18 - 19 MeV, again leading mainly to the 2.9 MeV 8Be state. The 4.4 and 7.7 MeV states of 12C seem to occur rarely, if at all (see 16O).