(See Energy Level Diagrams for 4He)
Ground state:Due to non-central forces, the wave function for the Jπ = 0+ ground state of 4He can be a positive-parity mixture of three 1S0, six 3P0, and five 5D0 orthogonal states (1967BE74). Of course, the symmetric S-wave component is the dominant part of the wavefunction, with significant D-wave and almost negligible P-wave contributions. Since the D-state admixture can be inferred from measurements such as the tensor analyzing powers for 2H(d, γ)4He (reaction 1), it has been the subject of much experimental and theoretical attention since the previous compilation (1973FI04), despite confusion stemming from the fact that in some cases the results refer to only part of the full D-state probability as calculated in (1988CA19, 1990CH06, 1991AR01).
Recent variational and Green function Monte Carlo (GFMC) calculations [(1988CA19, 1991CA35)] using realistic nucleon-nucleon potentials have been highly successful in reproducing the ground-state properties of light nuclei. These calculations for 4He give D-state probabilities ranging from 15 - 17.5%, depending on the potential model (including three-body forces) used, and P-wave probabilities that are much smaller (≈ 1%). Other theoretical and experimental estimates of the D-state percentage are considerably lower, but these inferences can be complicated by the presence of more than one multipole and other D-state effects (see the discussion for reaction 1).
The latest GFMC calculation (1991CA35), using a truncated version of the Argonne V14 NN interaction (1984WI05), overbinds 4He by 0.9 MeV, whereas most variational calculations underbind it by more than 1 MeV. In both cases, three-body forces contribute at least 3 MeV to the binding energy. When the GFMC calculation is corrected perturbatively for the terms in the NN interaction (1984WI05) that could not be included, the binding energy decreases by almost exactly enough to agree with the experimental value, 28.296 MeV. This energy results from a cancellation of large kinetic-energy and two-nucleon potential-energy terms, so that the three-body forces, though small in comparison to the two-body forces, make a significant contribution to the binding energy. Since the nuclear forces are assumed to be charge-independent, the small amount of repulsive Coulomb energy (0.75 MeV) implies high isotopic purity of the T = 0 ground state.
Recent calculations (1991CA35) of the charge density give form factors that are in reasonable agreement with electron-scattering experiments. For momentum transfers greater than about 4.5 fm-1, the variational calculation follows the data somewhat better than does the GFMC calculation. The Fourier transforms of the proton-pair distributions have also been calculated and compared with measurements of the Coulomb sum. The comparison is quite good for both variational and GFMC calculations when the experiments are corrected for the finite energy range of the measured sums.
The unbound excited-state level structure presented here is based on the comprehensive, Coulomb-corrected, charge-independent R-matrix analysis of (1989HA2A). This analysis takes its isospin-1 parameters from an analysis of p-3He scattering data (see 4Li, GENERAL section), but with the eigenenergies shifted by the internal Coulomb energy difference ΔEC = -0.64 MeV and the p-3H and n-3He reduced-width amplitudes scaled by the isospin Clebsch-Gordan coefficient √1/2 (square root of 1/2). The isospin-0 parameters are then varied to fit the experimental data for the reactions among the two-body channels p + 3H, n + 3He, and d + 2H, at energies corresponding to excitations in 4He below approximately 29 MeV. In this fit, the T = 0 nucleon-trinucleon reduced-width amplitudes are constrained by the isospin relation
and a small amount of internal Coulomb isospin mixing is introduced by allowing
Although the 4He analysis is not yet complete, the predicted levels are sufficiently stable that we feel it is worthwhile to report them as preliminary results. The BW resonance parameters at channel radii apt = an3He = 4.9 fm and add = 7.0 fm are given in Table 4.3 (PDF or PS) and are shown in Fig. 2. These states have relatively pure isospin, except in the cases noted below. As the previous compilation (1973FI04) pointed out, the general features of the level structure at excitation energies below 30 MeV can be understood in terms of Wigner's supermultiplet theory in which the degenerate  states are lowered and the  states are raised by an attractive particle-hole interaction. The P-wave  levels having T = 1 and T = 0 are much more interspersed in the present scheme than in the previous compilations, however, leading to significant isospin mixing in those states. In addition, several new T = 0 levels that have essentially d + d character appear, some of which were anticipated by a prediction of Sergeyev (1972SE02).
The first three T = 0 excited states (0+, 0-, 2-) of Table 4.3 (PDF or PS) are in reasonable agreement with those of Table 3.0.2 (which were fairly well established) in (1973FI04). Above about 22 MeV excitation energy, differences begin to occur. There is no evidence in the analysis of the 4He-system reactions for a separate 0+ or 1+, T = 0 level at Ex = 25.5 MeV as has been seen in the α + 4He* final states of reactions 28 and 32. It is possible that the anomaly seen in these reactions is due to a shadow pole associated with the 0+ excited state at Ex = 20.21 MeV, or that the true position of the 0+ state is several MeV higher, as is indicated by the position of the S-matrix pole (see discussion below).
Nestled among a series of four negative-parity, T = 1 levels in the range Ex = 23 - 26 MeV (which were at least 3 MeV higher in (1973FI04)) is a new 1-, T = 0 level at Ex = 24.25 MeV that has important effects on the d + d reactions at low energies. Isospin mixing between this state and the 3P1 , T = 1 level at Ex = 23.64 MeV causes significant differences in the p-wave part of the d + d reactions, as have been observed in muon-catalyzed (1984BA1W) and polarized (1981AD07) d + d fusion experiments. The 1-, T = 0 level was seen by (1981GR16) in their 2H(d, p)3H analyzing-power data, but no evidence of their proposed 4+ level at Ex = 24.6 MeV was found by (1989HA2A) in fitting their measurements.
The remaining T = 0 levels at Ex = 27 - 30 MeV are primarily d + d states, except for the 1+ level at Ex = 28.31 MeV. The 5S2 level at Ex = 27.42 MeV is interesting on two accounts: it marks the first appearance of a state from the  representation, and it probably corresponds to a resonance that had been seen by (1966LE1A) in 6Li(d, α)4He* spectra, but was later withdrawn by (1968BA20) when they failed to see it in d + d elastic scattering measurements. The effect of the broad resonance can be seen in d + d elastic scattering excitation functions measured by (1969WI01), however. Because of its width, this state causes the 5S2 transitions of the d + d reactions to be important even near the d + d threshold, in contradiction to the earlier theoretical picture that only the 1S0 transitions were important due to Pauli exclusion of the quintet d + d S-waves.
The series of 3PJ levels concentrated near Ex = 28.5 MeV are clearly the ones from the  representation predicted by (1972SE02). These broad levels are not apparent in the data, but they are required primarily by the cross-section and analyzing-power measurements for d + d elastic scattering. The 1- level in this sequence has been seen in the decay of 4He* in the final states of reactions 25, 28, and 32. The 1D2 resonance that was previously thought to be at 33 MeV is at Ex = 28.67 MeV, and another 2+ resonance, primarily in the 5D2 d + d channel, gives a second  state at Ex = 29.89 MeV.
Estimated uncertainties on the parameters given for 4He in Table 4.3 (PDF or PS) are as follows: At excitation energies below 26 MeV, the positions are uncertain by 20 keV or less, except for the (1-, T = 0) level at 24.25 MeV, which is uncertain by 150 keV. At excitation energies between 26 and 30 MeV, the uncertainties in the positions are generally less than 90 keV, with that of the (1-, T = 0) level at 28.37 MeV less than 10 keV. The widths of the levels (partial and total) are generally known to about 10%.
The uncertainties in the BW resonance parameters are usually far less than the changes that occur when the resonance parameters are derived from the poles of the S-matrix. A significant difference between these parameters and the BW parameters of Table 4.3 (PDF or PS) is in the position of the 0+ state. The S-matrix poles are located at least 3 MeV higher in excitation energy than is the pole of KR, meaning that the 0+ state is no longer the first excited state of 4He. This might explain the great difficulty shell-model calculations (1977BE02, 1988CE05) have in obtaining the excitation energy of the 0+ state as low as the "traditional" position it has occupied between the p-3H and n-3He thresholds. Other differences involve the ordering of the P-wave levels, and the appearance of low-lying, positive-parity, T = 1 levels.
Experimental work not discussed explicitly: (1973AN26, 1973AY02, 1973BR20, 1973DE17, 1973EL04, 1973GA17, 1973GO38, 1973HE06, 1973HE26, 1973JA21, 1973KA08, 1973MI20, 1973NO07, 1973SO08, 1973TO06, 1973TR04, 1974BA94, 1974GE10, 1974GO15, 1974GR02, 1974HE17, 1974LI10, 1974MI10, 1974RU06, 1974TO03, 1975BI08, 1975GE12, 1975GL08, 1975KA05, 1975SC31, 1976AR11, 1976BA57, 1976BO05, 1976BU19, 1976DA24, 1976HA17, 1976JA17, 1976OH02, 1976SC26, 1976SH23, 1976SK02, 1976SU06, 1976TA11, 1976WA12, 1976ZA11, 1977BO22, 1977CA05, 1977GO16, 1977KA02, 1977KA10, 1977LA13, 1977LE02, 1977MI13, 1977NO10, 1977RO18, 1978AR05, 1978AR21, 1978BA75, 1978CO16, 1978FA06, 1978GE12, 1978HA42, 1978LU05, 1978ZA06, 1979AB14, 1979BA27, 1979BA33, 1979BA66, 1979DR10, 1979EG01, 1979HO04, 1979JU02, 1979KA03, 1979SK05, 1979SU14, 1979WA02, 1980BA17, 1980GO21, 1980KA17, 1980MA20, 1980NE11, 1980OR05, 1980RO03, 1980WA10, 1981EG03, 1981FA02, 1981FA07, 1981GO03, 1981LA07, 1981NE08, 1981SM04, 1981VA05, 1981WA15, 1981WI11, 1981YU01, 1982BA16, 1982ER06, 1982IS06, 1982KE10, 1982LA09, 1982LA11, 1982LA20, 1983AN02, 1983AR05, 1983CO09, 1983RI01, 1983WA09, 1983YO01, 1984AR17, 1984FO18, 1984GM01, 1984HO01, 1984KA33, 1984KR12, 1984KR23, 1984LA19, 1984LA32, 1984MA71, 1984TS01, 1984TU02, 1984VO05, 1984WA18, 1985BE63, 1985BL05, 1985CE13, 1985CE16, 1985CH37, 1985TA13, 1985TA18, 1986BA68, 1986BU05, 1986CA29, 1986EN05, 1986FA13, 1986HE16, 1986KE01, 1986KL04, 1986LA26, 1986SM04, 1986SO03, 1986WA11, 1986WH01, 1987AL09, 1987BA69, 1987HU13, 1987LA25, 1987ME01, 1987ME18, 1987QA01, 1987WA25, 1987ZA07, 1988AR20, 1988DY01, 1988LA11, 1988ME11, 1988RA31, 1988SI14, 1988ST06, 1989AB10, 1989AR08, 1989AR16, 1989AR20, 1989BA23, 1989CL01, 1989CO14, 1989CR05, 1989DM02, 1989GL03, 1989SH17, 1989SZ02, 1989TA19, 1989YO03, 1990AB11, 1990BA58, 1990GE12, 1990LU10, 1990NI01, 1990SM04, 1990YA11, 1991DE02, 1991SC05, 1991WE06).
Level calculations not discussed: (1973CA16, 1973GE11, 1973KU02, 1973MA48, 1973NA19, 1973PE05, 1974LE30, 1974NA05, 1974NA18, 1974SA05, 1974SI05, 1974YA11, 1976BE01, 1977HI09, 1977SC18, 1977VE09, 1978AT01, 1978DE16, 1979BE15, 1979BE42, 1979TA23, 1981CE02, 1981SA32, 1981SC09, 1981VA23, 1982AZ01, 1982AZ02, 1982BE39, 1983BE52, 1983GE13, 1983GR24, 1983HO22, 1983KU20, 1983MA44, 1983VA08, 1983ZE06, 1984BA41, 1984KU13, 1984LI01, 1984MA03, 1984SU07, 1984VA06, 1985BE61, 1985CA40, 1985CE06, 1985DO20, 1985DU05, 1985LI09, 1985PO22, 1986AY01, 1986BE51, 1986DA04, 1986DU10, 1986KA02, 1986KN08, 1986RO03, 1986ST13, 1987BL18, 1987CA10, 1987CE01, 1987HO07, 1987KR07, 1987RE04, 1988ZH03, 1988ZH05, 1988ZH07, 1990CE06, 1990KH01, 1990OK03, 1990VA14, 1990WO09, 1990ZH10).
Other theoretical work: (1973AV03, 1973BO34, 1973BU01, 1973DE19, 1973DU10, 1973IO01, 1973KO26, 1973KU03, 1973LE24, 1973LI14, 1973MA10, 1973MA20, 1973NA26, 1973PA17, 1973PA19, 1973RA27, 1973WE14, 1973ZA03, 1973ZA11, 1974BE15, 1974DE41, 1974DH03, 1974DO10, 1974DZ03, 1974FI04, 1974FI13, 1974GR03, 1974KA35, 1974KH02, 1974KO03, 1974MA21, 1974PA11, 1974SA18, 1974SA29, 1974SA30, 1974SA31, 1974SO13, 1974ST14, 1974TE05, 1974TO08, 1974WE09, 1974WO06, 1974ZA01, 1974ZA07, 1974ZA08, 1975BA68, 1975BA76, 1975BO47, 1975CH22, 1975DO04, 1975FL02, 1975GO04, 1975KU01, 1975LA15, 1975LA19, 1975LI05, 1975SO07, 1975TJ01, 1975VI08, 1975WA30, 1976BA51, 1976CE01, 1976CO10, 1976FL09, 1976GA24, 1976GI06, 1976GI09, 1976HE01, 1976KI01, 1976KI16, 1976LA07, 1976LI20, 1976NA10, 1976TO07, 1976UL02, 1976UL04, 1977AV06, 1977BA74, 1977BE61, 1977BH04, 1977BL11, 1977BO24, 1977CR01, 1977DU01, 1977FR16, 1977HA02, 1977HE15, 1977HI11, 1977KI10, 1977KO25, 1977LA06, 1977LE13, 1977LE20, 1977LI11, 1977LI18, 1977LO18, 1977OS06, 1977SO05, 1977SO12, 1977TO03, 1978BE41, 1978BE57, 1978BI14, 1978CA04, 1978FA07, 1978FE08, 1978FR17, 1978FU12, 1978GI10, 1978HO07, 1978KI04, 1978LA08, 1978LI08, 1978LO16, 1978MC04, 1978OS05, 1978SI15, 1978SM02, 1978TJ02, 1978UL02, 1978WA13, 1978ZA05, 1979AY02, 1979BL05, 1979BL06, 1979FI01, 1979GH01, 1979GU16, 1979HE16, 1979HU02, 1979JA09, 1979KA06, 1979KA43, 1979MA07, 1979MO07, 1979OS09, 1979PE06, 1979RA30, 1979RI16, 1979RU09, 1979SA13, 1979SH07, 1979ST02, 1979UE02, 1979WA13, 1979WA14, 1979YA06, 1980BE17, 1980CH37, 1980DE01, 1980DU06, 1980FO14, 1980FU05, 1980GR01, 1980HA54, 1980KA18, 1980KH01, 1980KO04, 1980LA20, 1980LI09, 1980MA30, 1980ME07, 1980SA16, 1980TO11, 1980ZN01, 1981BA41, 1981BE01, 1981BE24, 1981BE39, 1981BE63, 1981BL06, 1981CA14, 1981CH03, 1981DE27, 1981DE34, 1981DO01, 1981DO02, 1981DR11, 1981DU08, 1981DU19, 1981DZ01, 1981FO01, 1981FO11, 1981FR20, 1981GO09, 1981GU10, 1981JA07, 1981JE01, 1981JI05, 1981KA12, 1981KA39, 1981KO37, 1981LE22, 1981LO08, 1981NA04, 1981NI05, 1981NO04, 1981PA16, 1981PL03, 1981SA14, 1981SH07, 1981ST19, 1981ZA01, 1981ZA02, 1981ZA05, 1982AT01, 1982AV08, 1982BA73, 1982BL05, 1982BO08, 1982DA03, 1982DA19, 1982DE12, 1982DE35, 1982DE51, 1982FR11, 1982FR14, 1982GR18, 1982HU11, 1982KA06, 1982KA11, 1982KH01, 1982KH05, 1982LA07, 1982LA16, 1982LA19, 1982MU13, 1982NI02, 1982SH08, 1982SI13, 1982SO07, 1982VA15, 1982VE12, 1982WA07, 1982WE09, 1982ZA01, 1983AR17, 1983BA43, 1983CA10, 1983CH59, 1983DM01, 1983DR16, 1983EI01, 1983FR20, 1983GE12, 1983GO04, 1983KH01, 1983MA31, 1983ME06, 1983NE08, 1983NE12, 1983NI06, 1983RI07, 1983TE05, 1983TH06, 1983WI05, 1984BA06, 1984BE17, 1984BO08, 1984CA24, 1984GA26, 1984GA34, 1984GO01, 1984GO19, 1984HE21, 1984HU04, 1984KR10, 1984LA05, 1984LI08, 1984LO09, 1984MA04, 1984MA11, 1984MO24, 1984OR01, 1984PR09, 1984RE09, 1984SH07, 1985AL12, 1985AN11, 1985AR05, 1985BA45, 1985BO02, 1985BU02, 1985BU06, 1985CH01, 1985DE37, 1985FA02, 1985FR09, 1985HE19, 1985KA30, 1985KO03, 1985KR12, 1985KW02, 1985MA30, 1985PA10, 1985PR02, 1985SA32, 1985SO06, 1985SP05, 1985TH04, 1985TI08, 1985TO19, 1985TR03, 1986AB02, 1986AN08, 1986AN09, 1986AN35, 1986BA15, 1986BA69, 1986BI01, 1986CA28, 1986DE11, 1986DU06, 1986GR02, 1986HA45, 1986HO33, 1986JI01, 1986KE07, 1986KH02, 1986KH06, 1986KU11, 1986LE22, 1986NA05, 1986PA08, 1986PA15, 1986RA21, 1986SA02, 1986TA07, 1987AR11, 1987BA49, 1987BI22, 1987BO09, 1987BU02, 1987BU04, 1987CA13, 1987CA17, 1987CA27, 1987CA29, 1987GI01, 1987GM02, 1987GM04, 1987KO31, 1987KU03, 1987KU12, 1987LI34, 1987MA61, 1987MO33, 1987NE08, 1987PA13, 1987QI01, 1987SA15, 1987SC25, 1987SH09, 1987SO04, 1987TA06, 1987TA27, 1987TR07, 1987VA05, 1987VA29, 1987VA36, 1987ZO01, 1988AL12, 1988AN18, 1988BA63, 1988BA74, 1988BO04, 1988BO40, 1988CH16, 1988CO15, 1988DI10, 1988DO17, 1988DU04, 1988FO08, 1988FR02, 1988GO10, 1988GU07, 1988KA23, 1988KO32, 1988MA33, 1988MA56, 1988MO21, 1988MU11, 1988VA27, 1988WO04, 1988YA02, 1989AK01, 1989AL08, 1989AN10, 1989BA31, 1989BO29, 1989CH49, 1989CI05, 1989CU05, 1989DU05, 1989DZ02, 1989FO12, 1989GR15, 1989JI07, 1989KH06, 1989KR08, 1989KU06, 1989KU21, 1989LA05, 1989LE24, 1989MA06, 1989NA18, 1989RA14, 1989SA17, 1989SA32, 1989SC15, 1989SC19, 1989SC22, 1989TE04, 1989UC02, 1989US01, 1989VA06, 1989ZA07, 1990AN23, 1990AS06, 1990BE14, 1990BI01, 1990BI05, 1990BR09, 1990BU29, 1990CA12, 1990CI01, 1990CI04, 1990CO12, 1990FA08, 1990GE04, 1990GO09, 1990GO30, 1990GU23, 1990HA07, 1990HE13, 1990JO01, 1990KA06, 1990KA07, 1990KA42, 1990LE24, 1990LO10, 1990LO20, 1990MA63, 1990MO17, 1990MO25, 1990NI13, 1990OE01, 1990SA47, 1990SC01, 1990SC20, 1990SC32, 1990SH11, 1990ST17, 1990SZ07, 1990VA01, 1990YU02, 1991BA16, 1991CA05, 1991DE08, 1991OE01, 1991SC12, 1991US01, 1991WI05).
The early measurements of (1973PO01) at Ed = 6.05, 8.96, and 11.67 MeV gave σ(θ) ≈ sin2 2θ, and it was concluded that the process proceeded through an E2 transition by 1D2 → 1S0 . Measurements at 376 MeV (1984SI01), however, corroborate deviations reported in the inverse reaction by (1976AR05) from the sin2 2θ angular dependence. The cross section results are consistent with time-reversal invariance.
A measurement (1984WE14) of tensor analyzing power T20 at Ed = 9.7 MeV gave a non-zero isotropic result which was used in connection with a heuristic model calculation assuming E2 radiation to imply a 4.8% D-state admixture in the two-deuteron wave function of 4He. Earlier evidence for the 4He D-state was provided in a study (1975PL01) of phase shifts for p + 4He elastic scattering. Calculations reported in (1985SA04) examined the 2H(d, γ)4He analyzing powers for Ed < 20 MeV, and led to the conclusion that the tensor analyzing powers depend linearly on the asymptotic D/S ratio ρ. Using wave functions with phase shifts obtained from resonating group calculations, they found good agreement with the T20 data of (1984WE14) for -0.5 < ρ < -0.4. These large values of ρ were superseded by later, more detailed calculations (see below). Measurements of vector and tensor analyzing powers at Ed = 10 MeV reported in (1986ME02, 1986ME16) indicated the presence of multipoles other than E2, and arguments are presented that the reaction cannot be used to determine the D-state admixture in 4He unless the deuteron D-state and other tensor force effects in the entrance channel are taken into account. Calculations of (1986TO11) considered M1, E1, M2, and E2 transitions and obtained agreement with the results of (1986ME02, 1986ME16) using 4He wave functions which were obtained from variational calculations (1986SC03) and which indicated a value for the 4He D-state parameter (1986TO11) D2 ≈ 0.2 fm2. The energy dependence of vector and tensor analyzing powers at 130° from 0.3 to 50 MeV (1988WE15) indicates that Ayy(130°) is sensitive to 4He D-state components and has its maximum value near Ed = 30 MeV. Some of these results are reviewed in (1987GR08).
A recent measurement (1989PI06) of cross sections and analyzing powers at intermediate energy (Ed = 95 MeV) indicated the dominance of the <1D2| E2|1S0> transition involving the S-state component of 4He.
Experiments on the 2H(d, γ)4He reactions at low bombarding energies (50 - 150 keV) relevant to astrophysical processes were reported in (1985WI08). (This reaction had been proposed earlier (1984CE03) as a temperature diagnostic for plasmas). The Γγ/Γp ratio was measured, and it was noted that a D-state component in the 4He wave function is a possible explanation for the result obtained. The measured cross section for Ed between 0.7 and 4.5 MeV and angular distributions of cross sections at Ed = 1.38, 2.05, 9.6 and 15 MeV (1986WE07) were interpreted to indicate that the 4He D-state has large effects on the energy and angle dependence of the low-energy capture cross sections. In particular it was shown that the ratio σ(90°)/σ(135°) increased at low energies in such a way as to imply an asymptotic D- to S-state ratio ρ = -0.2 ± 0.05. Measurements of σ(E) and σ(θ) for Ec.m. = 50 - 500 keV (1987BA58) were interpreted to indicate that the 5S2 → 5D0 amplitude is dominant for Ec.m. < 200 keV. The indicated astrophysical S-factor (1984FO1A) is 32 times larger than previously estimated and may affect inhomogeneous big-bang nucleosynthesis models.
Theoretical studies (1987AS03) of the 2H(d, γ)4He reaction based on a microscopic description of the nuclear wave function reproduce the data for Ed < 3 MeV and indicate a 5 - 7% D-state admixture in the 4He ground state. The study reported in (1987BL12) finds that conclusions about D-state components based on simple potential model analysis of experimental data are very sensitive to the parametrization of the nucleus-nucleus potential and may be misleading. The phenomenological study of 2H(d, γ)4He (1987PI08) allows for the D-state component of the colliding deuterons and concludes that it is important in estimating the effects of D-state components in 4He. However, a more detailed calculation including these same effects (1988AR11) has shown that the value of ρ ≈ -0.4 suggested in (1987PI08) is too large and should be -0.2 as proposed in (1986WE07). The difficulty of extracting D-state properties in 4He is demonstrated in the work of (1988WA02), using a microscopic multi-channel resonating-group model. This model was used by (1988LA14, 1990LA16) in the analysis of measurements of cross sections and vector and tensor analyzing powers at Ed = 1.2 MeV to conclude that the cross section consists of nearly equal contributions of E2, E1, and M2 radiation, and that the tensor analyzing power is primarily due to the large E1/M2 strength. The results of this calculation are compared with experimental data on Ay and Ayy for Ed(lab) = 0.3 - 50 MeV. Good agreement was obtained with Ayy, but Ay was overpredicted at low energies (1 - 2 MeV). See also (1990WE03). This model predicts a D-state probability of 2.2% in 4He, but this is only the two-deuteron part of the D-state.
An extensive review of the manifestations of the D-State in 4He and other light nuclei is presented in (1988WE20). It is worth noting that the most recent calculations of (1988CA19), which use the Green function Monte Carlo method, indicate a total D-state probability in 4He ranging from 12 to 17.5%, depending on the details of the NN interaction assumed. A variational Monte Carlo calculation (1991AR01) of the reaction for Ed ≤ 500 keV indicated that at these energies the reaction proceeds through the D-states in the deuteron and the alpha particle, and that the contribution of the 2H or 4He D-states can either add to produce a large cross section or cancel. A recent review of non-spherical components of 4He and other light nuclei is presented in (1990EI01).
Measurements of the charge-symmetry-breaking reaction (a) reported in (1987BA15) established an upper limit of σ(θ) ≈ 0.8 × 10-6 μb/sr at Ed = 0.8 GeV, θ c.m. ≈ 100°. An historical synopsis of experiments and theoretical estimates of reaction (a) is also presented. An earlier measurement reported in (1974BA2H) gave an upper limit σ(θ) ≈ 1.9 × 10-5 μb/sr at Ed = 1.89 GeV, θc.m. ≈ 79°. See also (1981EG03). A theoretical calculation (1982CH27) assuming various charge-symmetry-breaking mechanisms gave 0.1 × 10-6 μb/sr for σ(θ) at 0° in the region of the Δ(3, 3) resonance. More recently σ(θ) at 0° was estimated (1986CO01) to be ≈ 0.8 × 10-6 μb/sr at Ed = 1.95 GeV assuming virtual η and η' production and π0η and π0η' mixing. See also (1976BA1A, 1985BA1X). For references to earlier work see (1973FI04).
Measurements and summaries of cross sections, polarizations, analyzing powers, and polarization transfer coefficients are presented in Table 4.5 (PDF or PS). Summaries and discussions of earlier works are given in the previous compilation (1973FI04). Several experiments which have a bearing on possible excited states in 4He have been reported. Measurements of σ(E, θ) at 70 - 150 keV (1975PO04) indicate no evidence for a resonance near the dd threshold in 4He. Measurements of σ(θ) made at lab energies of 300 - 700 keV (1973YI01) were expanded in even powers of cosθ and indicate some evidence for a state in 4He at 23.9 MeV, but do not differentiate between suggested assignments of 2+ or 1-. A measurement of Pn(θ) (1976TO03) is discussed in relation to possible f-wave admixtures on the 2+ state in 4He at 22.1 MeV. Measurements of σ(E, θ) between 18 and 26 MeV (1980JO07) and Legendre polynomial fits provide no evidence of a proposed level in 4He near 30 MeV.
Several measurements of the 2H(d, n)3He cross section have been made at low energies (Ed < 1 MeV) that are relevant to plasma physics or astrophysics. (See Table 4.5 (PDF or PS)). Recent work reported in (1987KR18) with windowless gas targets at Ec.m. = 2.98 - 162.5 keV extend into the plasma fusion region and deduce the astrophysical factor S(E) and present polynomial fits. Another measurement of S(E) at 125 keV is reported in (1986BR20).
Several experimental studies related to the use of the reaction for a source of monoenergetic neutrons have been carried out and are included in Table 4.5 (PDF or PS). See especially the work reported in (1978DR08), which establishes an absolute scale for σ(θ) for Ed = 6 - 17 MeV. Extensive tables of cross sections and Legendre coefficients are presented. See also (1972DI05, 1973SA20, 1973WE19, 1981PA26). Analyzing power measurements are reported in (1972DU02, 1972GR28, 1972HA49, 1972SM04, 1972SP05, 1974SA07, 1975GA07, 1976TO03, 1983GU03). Polarization transfer measurements are described in (1973SA20, 1974SA07, 1975LI08, 1984KL05). See also the recent review (1990DR10) of accelerator-based monoenergetic neutron source reactions, including 2H(d, n), for fusion-related applications.
Measurements of observables for the mirror reactions 2H(d, n)3He and 2H(d, p)3H and the implications of possible differences on the question of charge-symmetry violations are described in (1972GR28, 1973YI01, 1975PO04, 1978KO06, 1979DR01, 1979KO23, 1980BI08, 1981AD04). See also the compilations of (1987FI03, 1987GR08).
Theoretical work described in (1972SE02, 1972SE25) concludes that the different anisotropy observed for the (d, n) and (d, p) angular distributions at low energies can be explained by new negative-parity T = 0 levels with small nucleon and single-particle deuteron widths. Analysis (1987KO21) of polarization data for the (d, p) and (d, n) reactions indicates no evidence for a Jπ = 1- level in 4He at 24.1 MeV.
Analyzing powers and polarizations for 2H(d, n)3He and 2H(d, p)3H were calculated (1980BE21) in a generalized R-matrix methodology framework, and the differences predicted were an order of magnitude smaller than those reported by (1979DR01). The (d, p) and (d, n) reactions were also studied (1973FI10) at energies below 200 keV, and the relationship between an "R-matrix approach" and a "direct approach" to the reaction were discussed. Soluble four-body models have been used (1976FO13, 1979FO08, 1983OS05) to predict the (d, n) cross section. A four-nucleon K-matrix approach is discussed in (1985SO07). See also (1976SA02). The parameterization of polarization observables in terms of matrix elements for 2H + d reactions is given in (1982AD04). The mirror reactions 2H(d, n)3He and 2H(d, p)3H were studied (1990VA04) in a multichannel resonating group framework, and the parameters of Jπ = 0+, 0-, 1-, 2- resonances in 4He are established. An analysis of all available data on these mirror fusion reactions was carried out (1990LE23) to extract reaction matrix elements for Ed ≤ 500 keV. The effect of the 2H(d, n) reaction rate on predicted abundances of light isotopes from primordial nucleosynthesis is investigated in (1991RI03).
The 2H(d, n)3He reaction at very low energies (Ed(c.m.) < 55 keV) is calculated in a one-step reaction model and discussed in (1988AB03). An extended elastic model is applied in (1989SC25, 1989SC36) to calculate reaction rates for very low energies (T ≈ 300 K). Branching ratios in (d, n) and (d, p) reactions at low energies are estimated in a second-order DWBA calculation in (1990KO26). The fusion of polarized deuterons is considered in (1984HO10) and it is argued that a "neutron lean" d-3H fusion reactor is unlikely to actually be so. On the other hand, the DWBA calculation of (1986ZH05) indicates that such a reactor may be feasible.
Measurements and summaries of cross sections, polarizations, analyzing powers, and polarization transfer coefficients are given in Table 4.6 (PDF or PS). Earlier work is reviewed in the previous compilation (1973FI04). For a review of recent measurements of polarization observables for the 2H(d, p)3H reaction and a comparison with model calculations, see (1987GR08).
A considerable number of experiments have examined the cross section and polarization observables for differences between the charge-symmetric reactions 2H(d, p)3H and 2H(d, n)3He. Measurements of vector polarization at 1 MeV (1987KO22) for both reactions give differences outside of the experimental uncertainties. Analyzing power measurements for both reactions for deuteron energies between 60 and 485 keV (1981AD04) are presented in contour plots which are very similar for the two reactions. Differential cross sections measured for (d, p) and (d, n) at 13.2 MeV (1979OK01) coincide closely. Precision polarization transfer measurements at 10 MeV (1974GR30) and for energies between 6 and 15 MeV (1973CL05) are compared with (d, n) values and show little or no differences within uncertainties. On the other hand, measurements of vector and tensor analyzing powers for Ed = 1.5 - 15.5 MeV are interpreted (1979KO23) to indicate strong evidence for charge-symmetry violation. Measurements of these observables at Ed < 5.5 MeV (1979DR01) and at Ed = 2.5 - 11.5 MeV (1978KO06, 1978KO26) show significant differences between the two reactions, while measurements at 13.39 and 17.00 MeV (1979BR18) indicate smaller differences at these higher energies.
Polarization measurements below 1 MeV (1985KO20) indicate that Py'(θ) is a slowly varying function of Ed, and that the l = 1 barrier penetration factor is sufficient to describe the energy dependence. Cross section measurements between 70 - 150 keV (1975PO04) indicate no evidence for a resonance near the d + d threshold. Tensor analyzing power data measured in the same region are discussed along with other available data and fail to provide conclusive evidence for a resonance. Cross section data measured between 300 - 400 keV (1973YI01) indicate the need for a state in 4He at 23.9 MeV but do not distinguish between 2+ and 1-. Measurements (1981GR16) of the cross section and tensor analyzing power for Ed = 1 - 13 MeV are fitted with Legendre polynomials and give clear evidence (1987GR08) for a 1- level at 24.1 MeV and strong indications of a 4+ level at 24.6 MeV.
A review of recent progress in theoretical studies of four-body scattering and breakup including the (d, p) and (d, n) reactions focusing on the integral-equation approach is presented in (1987FI03). Calculations of this type reported in (1977BA46, 1977PE13, 1982BL15, 1983OS05, 1984BA17, 1984FO08, 1985SO07, 1986FO07, 1989FO13, 1990FO02).
Calculations (1980BE21) within the framework of a generalized R-matrix methodology compare the analyzing powers and polarizations for the (d, p) and (d, n) reactions. See also (1977BE02). A number of theoretical studies and analyses related to possible states in 4He were carried out. Microscopic multi-channel calculations reported in (1981HO04) propose an additional low-lying 1- T = 0 level, but rule out a d + d threshold level and find no evidence for a 1+ level around 25.5 MeV. A calculation reported in (1990VA04) for (d, n) and (d, p) establishes the parameters of resonances in 4He with Jπ = 0+, 0-, 1-, 2-. An R-matrix approach (1987KO21) used to analyze (d, p) and (d, n) polarization data finds no evidence for a 1- level at 24.1 MeV. Theoretical arguments (1972SE02) are used to suggest T = 0 states in 4He. Criteria for analysis of polarized deuteron reactions, and signatures of excited states and level parameters are derived in (1975SE07). See also (1974NE13, 1982AD04). A method for empirical continuation of polarization observables for 2H(d, p) is presented in (1989BO32). See also the study of three-body Coulomb effects in one-particle transfer reactions (1990KA17). Calculations related to the (d, p) and (d, n) reaction at low energies include (1987AS05), which examines the effect of electron screening at fusion energies. An elastic model for subbarrier fusion for the 2H(d, n) and 2H(d, p) reactions is applied at very low energies in (1989SC25, 1989SC36). Branching ratios for these reactions at very low energies are estimated in second order DWBA in (1990KO26). See also (1973FI10, 1981AD07). An analysis of all available data on these mirror fusion reactions was carried out (1990LE23) to extract reaction matrix elements for Ed ≤ 500 keV. The effect of the 2H(d, n) reaction rate on predicted abundances of light isotopes from primordial nucleosynthesis is investigated in (1991RI03).
The dp and dn spectra obtained for Ed = 6 - 13 MeV and reported in (1972VA04, 1972VA05) are dominated by a broad peak associated with d-nucleon quasi-free scattering (QFS). A simple quasi-free scattering model predicts general behavior, but not the magnitude of the cross section. Spatial localization effects were considered in (1973VO06) in a phenomenological explanation of the peaks in some coincidence spectra. Quasi-free scattering was analyzed (1976DJ01) in terms of the modified single-impulse approximation (MSIA). The final-state interaction (FSI) coincidence spectra agreed with the triplet np enhancement factor. See also (1972BU03). Work reported in (1972AN02) indicates a ratio of peak cross sections for nd and pd quasi-free scattering that is constant and close to one. Energy spectra at Ed = 12 MeV are explained (1982JE04) with a superposition of triplet np FSI and QFS. It is reported in (1978KL07) that the angular distribution of np pairs with zero relative energy can be predicted absolutely from dd elastic scattering. No evidence of isospin non-conservation is found. The measured nd and pd angular distributions are identical. FSI studies reported in (1973CH05) give no indication of any contribution from the (isospin forbidden) 1S0 pn final state. Proton-deuteron coincidence spectra were used in (1972VO13) to test the Trieman-Yang criterion. The results indicate that the one-pole graph is not sufficient to describe the reaction. Three-body breakup energy spectra for Ed = 60 MeV (1982FU10) show large forward-angle enhancements and can be reproduced by calculations in the single-scattering four-body model.
Absolute cross sections for the four-body breakup reaction (b) were measured (1975WA09), and evidence for a double final-state interaction was obtained. Plane-wave analysis of measurements made at Ed = 34.7 MeV (1978AL21) under the two-spectator condition gave an experiment/theory ratio of about 0.14. At 80 MeV (1978LE01) analysis indicated that, in addition to the double-spectator process, the process of double spin-flip excitation is important. (See also (1985KO01)). However, good fits to these same data were obtained (1981WA29) by assuming final-state interactions between both final np pairs and ignoring the double-spectator process. Measurements at 15.7 MeV are reported in (1987ZH11) and interpreted to indicate evidence for a 2He resonant state with a breakup energy of 0.45 MeV.
A review of quasi-free processes in few-body systems is presented in (1974SL04). See also (1973SL04) for a critical analysis of models. Off-energy-shell corrections to nucleon-deuteron scattering amplitudes are explored in (1972DU12). Absolute magnitudes and shapes for QFS processes in reaction (a) are correctly predicted by the use of Eckart cluster-model wave functions. A possible explanation of the colinearity effect involving rescattering is examined in (1976RE08). Calculation of the three-body breakup cross section in the Alt, Grassberger and Sandhas (AGS) formalism reported in (1986MD02) gives good agreement at low energies for the shapes but not the magnitudes. Agreement with the magnitudes improves at higher energies. Coulomb effects in quasi-free scattering are explored (1987BA27) by the use of exact three-body scattering theory for Coulomb-like potentials. Four-body AGS calculations for reaction (a) are extended (1988MD01) to regions where final state interactions are important.
Measurements and summaries (S) of cross sections and analyzing powers are presented in Table 4.8 (PDF or PS). Summaries and discussions of earlier work can be found in the previous compilation (1973FI04). As noted there, the cross section has no pronounced structure below Ed = 40 MeV (Ex = 24 - 44 MeV in 4He). In the very low energy region, Ed = 80 - 360 keV, measurements of the cross section (1975MA43, 1975NI06) provided no evidence for a resonance near the d + d threshold. Similarly, the cross section measured at Ed = 9.8 - 36 MeV (1985NE04) showed a smooth pattern with no indications of resonances. Measurements of vector and tensor analyzing powers at Ed = 6 - 11.5 MeV (1972GR29) show a vector component which is small but non-zero and changes sign between 6.0 and 10.0 MeV, and tensor components which increase monotonically with energy. No resonance-like behavior is observed, but arguments are made that the sign change of iT11 suggests a broad resonance near Ex = 28 MeV in 4He. (See also (1972ME20)). At Ed = 50 MeV the vector analyzing power maximum is 0.32 at about θc.m. = 60°.
Since the earlier compilation on the A = 4 system, a considerable amount of theoretical work on 2H(d, d)2H elastic scattering has been done. A number of these calculations involved resonating group methodologies. A resonating group method (RGM) with imaginary potential was applied (1972CH20) to d + d scattering. Comparison to experiments at 6.9 - 19.9 MeV gave good agreement with cross section data. Calculations (1975ME25) of d + d near threshold with the RGM using exact deuteron wave functions evaluated with a Malfliet-Tjon two-nucleon potential were found to predict no resonance, in agreement with experiment (1975MA43). Microscopic multichannel calculations for A = 4 from the first breakup threshold to Ec.m. = 10 MeV carried out (1981HO04) in the framework of a refined resonating-group model gave agreement with the well-established resonance structure, but ruled out a dd threshold resonance. An additional low-lying broad 1- T = 0 resonance was proposed. The work reported in (1985XU01) used single-channel RGM with a central-force NN potential having a soft repulsive core. The calculated (d, d) scattering phase shifts and cross sections for Ed < 20 MeV agree very well with experiment. The ground and even-parity excited states and the scattering problems for the 4He system were examined (1986KA21) within the framework of the multichannel resonating group method and good agreement with experiment was obtained. See also the partial amplitude calculations with resonating group methods of (1987IS06).
A study of d + d elastic scattering in the helicity formalism for polarized beam is reported in (1972LI01) and includes a phase-shift analysis. A study for the case of non-conservation of channel spin is reported in (1972PH07). Expressions for σ and P are given in terms of phase shifts. The work of (1976FO13) applies a solvable model involving four identical particles to A = 4 scattering and reactions. A microscopic K-matrix approach is applied to the four-nucleon problem (1977BA46), and satisfactory agreement with experiment is obtained for all reactions except 2H(d, d). Work reported in (1979FO08) uses a nonrelativistic field theoretic formalism to develop a solvable model of the four-nucleon system and predicts the correct shape for the (d, d) cross section, but the magnitude is much too small. The work of (1983OS05) uses a four-body solvable model involving intermediate quasiparticle states and calculates cross sections for Ed between 6.1 and 51.5 MeV for (d, p), (d, n), and (d, d). Good agreement with experiment is obtained. In (1984FO08) a two-body separable T-matrix between pairs is used to solve the four-body equations and one-parameter models are developed to describe low-E phase shifts and cross sections for reactions and scattering. The four-body equations of Alt, Grassberger, and Sandhas (AGS) are solved (1986FO07), and contributions of p-wave (3 + 1) subamplitudes to the 4He binding energy and scattering observables below the four-body breakup threshold are studied. See also the calculation of tensor analyzing powers in (1989FO13). A review of progress in four-body scattering and breakup in the integral equation approach is presented in (1987FI03). Calculations of (d, d) cross sections with a three-body formalism including Coulomb interactions are reported in (1986AG03).
In (1977BE02) a new model for 4He which treats structure and reaction aspects on an equal footing in a dynamical R-matrix methodology is presented. Results are given for the spectrum of resonances obtained within the model and for (d, d) elastic scattering. See also (1980BE18) which presents detailed results obtained with this model. Comparisons are made with data and resonating group and field theoretic approaches, noting that none of these models provides a complete description. A potential description of dd scattering is presented in (1990DU05).
The work of (1985KU19) applies nuclear collision theory (including many-body correlations induced by the short-range repulsion and medium-range attraction of the NN interaction) to (d, d) elastic scattering. Phase shifts are calculated and compared to RGM results. In (1988BE06) it is shown that the polarizability of the deuteron has a negligible effect on the total inelastic cross section at very low energies. Collective excitation of 4He in d + d scattering at energies ≈ 30 MeV is studied in (1990FI06). An analysis of (d, d) scattering data at 1.65, 2.00, and 2.29 GeV in the framework of a Glauber NN multiple-scattering model is described in (1984BA68). See also (1989ET04). An integral formula for calculating Glauber multiple-scattering amplitudes is derived in (1990TA27). A geometric model is applied to high-energy d + d collisions (1990HU09).
Measurements of cross sections and analyzing powers are summarized in Table 4.9 (PDF or PS). Summaries and discussions of earlier work can be found in the previous compilation (1973FI04). As noted there, the total cross section is mostly E1 and has a broad peak near Ep ≈ 4 MeV, but no fine structure in the measured energy range. The broad peak is attributed to the presence of two 1-, T = 1 levels in 4He. The determination (1978KIZQ) of the singlet E1 strength distribution indicates that the lower of the two levels (at 27.4 MeV) contains the larger fraction of the singlet E1 strength. Measurements (1980MC06) of the fore-aft asymmetry in the angular distribution were interpreted as providing evidence for a 2+ level at 40 MeV in 4He with Γc.m. = 3.5 MeV. An E1, E2 analysis of the differential cross section and analyzing power measurements of (1978KIZQ) confirmed the dominant singlet E1 character of the outgoing radiation, but also indicated an anomalously large 3D2 contribution to the E2 strength. See also (1980DE32, 1985WA28). However, measurements of (1989WA03) showed that the inclusion of a small M1 strength (0.5 - 1% of the total capture cross section) in the analysis gave better fits and eliminated the need for a large 3D2 contribution. The absolute cross section for 3H(p, γ) has been studied extensively along with that of the mirror reaction 3He(n, γ) to test isospin mixing, and there are many discrepancies in the published results. Accurate measurements of the 3H(p, γ)4He cross section at 8.34 and 13.6 MeV are reported in (1983CA14) and earlier published results are reviewed. However, a new result (1990FE06) gives considerably lower cross sections in agreement with the recent monoenergetic 4He(γ, p)3H results of (1988BE38). These new results bring the (γ, p)-to-(γ, n) ratio for 4He into agreement with standard model predictions. [See sects. 14 and 21.] The whole range of experimental and theoretical evidence bearing on the σ(γ, p)/σ(γ, n) ratio is summarized in a separate discussion at the end of reaction 21. Measurements of the cross section and analyzing power at intermediate energies 227, 300, and 375 MeV were carried out (1986TH05) and compared with the inverse photodisintegration reaction, and no violation of time-reversal invariance was found. Analysis of these results with DWIA methods indicated that meson exchange currents are important at these energies. See also the review of capture on light nuclei of (1985CA42).
Theoretical calculations of (1981HA10, 1983HA21) done within the framework of recoil corrected continuum shell model (RCCSM) determine σ(γ, p)/σ(γ, n), and it is concluded that the value near 2 that was indicated by some experiments cannot be obtained within standard theoretical assumptions. However, the authors of (1988WA20) conclude that calculations done within the framework of a microscopic multichannel resonating group model demonstrated that all types of experimental data except for the integrated (n, γ) cross section can be reproduced. Calculations of the 3H(p, γ) cross section at intermediate energies were done at 156 MeV by (1973BA27) within the framework of a direct reaction peripheral model. Calculations for σ(θ) at 30 - 100 MeV described in (1978GA13) are discussed in terms of information about the effects of meson exchange currents and NN correlations at forward and backward angles. Calculations at 40 and 140 MeV are presented in (1976HE12).
Measurements of cross sections and analyzing powers are summarized in Table 4.10 (PDF or PS). Summaries and discussions of earlier work can be found in the previous compilation (1973FI04). Legendre polynomial expansions of σ(θ) and P(θ) are given for Ep = 1.5 - 5.0 MeV in (1972SM03) and for Ep = 1.3 - 2.9 MeV in (1974BR09). Contour maps of P(θ) are presented. A number of measurements relating to the use of 3H(p, n) as a source of polarized and unpolarized neutrons have been made. See especially (1978DR08) in which an absolute scale for σ(θ) is established. Relative and absolute differential cross sections for Ep = 6 - 16 MeV are given in (1972MC23). See also (1972PA41) for measurements of flux density for En = 250 keV, and (1982TH07, 1989BO41) for measurements of tritium breakup contributions. Practical aspects of accelerator-based neutron source reactions including 2H(p, n) are reviewed in (1990DR10). Neutron polarizations and polarization transfer coefficients have been measured over a wide range of angles and energies (1972HA36, 1972SM03, 1974JA03, 1974JA20, 1976DO07, 1981TO12).
The analyzing power measurements of (1972HA33, 1974JA06) were compared with neutron polarization data, and it was found that above 4 MeV the two quantities were essentially equal, but below 4 MeV the observed differences in the magnitudes exceeded those predicted by charge-independent R-matrix calculations based on the level parameters of (1968WE14). Similar conclusions were drawn from the polarization-transfer coefficient measurements presented in (1972HA36, 1974JA20). However, remeasurement of Py, and further measurements of Ay between 2 and 4 MeV resolved the discrepancies (1981DO10, 1981TO12), and it was concluded that there are no anomalously large differences between P and A outside the uncertainties of predictions of present models. A review of existing data and discussions of charge-independent R-matrix calculations is included in (1981DO10). The calculations establish the order of the lowest p-wave T = 0 levels in 4He as Jπ = 0-, 2-, 1-.
The reported differences between polarization and analyzing power were investigated in (1974AR01) and related to 3 P2 ↔ 3 F2 transitions enhanced in the region of the 2- state. They were also calculated (1977BE28) within the framework of a generalized R-matrix method. See also the recoil-corrected continuum shell-model calculations of (1983HA21). Microscopic calculations of the 4He continuum were carried out by a coupled-channels method (1975RA31, 1976RA13, 1977DO03, 1980RA17), by a K-matrix approach (1977BA46), and within the framework (1980BE18) of a dynamical R-matrix formalism. Excited states of 4He are discussed as are comparisons with 3H(p, n) and other reaction data. See also the [3N + N] cluster-model study of (1981FU08). Calculations of elastic scattering and charge exchange at intermediate energies using Glauber multiple scattering theory are reported for Ep = 156 MeV (1973NA06) and for 415 and 600 MeV (1981BI08). A microscopic, momentum space optical potential is used in the calculations of (1986LA02). The results are compared with data at 415 and 600 MeV, and the sensitivity to the removal of meson exchange currents from nuclear densities is discussed. A generalized potential description of the p + 3H interaction is described in (1990DU11).
Measurements of cross sections and analyzing powers for 3H(p, p)3H are summarized in Table 4.11 (PDF or PS). Summaries and discussions of earlier work including a discussion of the general behavior of the cross section and analyzing power as a function of energy can be found in the previous compilation (1973FI04).
Several multichannel resonating group calculations have been carried out (1981FU08, 1981HO04, 1982HO05, 1983FI14, 1986KA21). The [3N + 1] cluster model is found (1981FU08) to explain the general properties of the 4He excited states. Using microscopic multichannel calculations, the investigation of (1981HO04) finds the well-established resonance structure, rules out the dd threshold resonance, and predicts a low-lying Jπ = 1-, T = 0 resonance. However, no evidence for a 0- or 1+ state near Ex = 25.5 MeV is found. This same work identifies the observed differences in 2H(d, pol. p)3H and 2H(d, pol. n)3He as resulting from Coulomb effects alone, and explains the differences between the 3H(p, pol. p)3H polarization data of (1976KA12) and the 1H(t, pol. t)1H data of (1978HA38) as resulting from the odd spin-orbit component of the nucleon-nucleon force. Microscopic calculations of the resonance states in 4He were carried out by (1984CA20) using a modified R-matrix method and a variational approach, and by (1980BE18) within the framework of a dynamical R-matrix methodology. See also (1977BE53). Momentum distributions of single nucleon, two-nucleon cluster relative motion, etc. were reported in (1988MO09). Scattering and reactions in the A = 4 systems within a K-matrix formalism were studied (1980BA55). A coupled channels treatment was applied to interpret the positive- (1980RA17) and negative-parity (1975RA31) resonances in 4He. See also (1978RA01). The Amado model was used (1977AA01) to investigate D-phase anomalies in 3H(p, p)3H for Ep = 4 - 12 MeV. All possible couplings of p-3H and n-3He were considered in a calculation of S-matrix elements by (1972HE15). A two-dimensional integral equation solution of the A = 4 system was used (1978KR01) to calculate the 4He binding energy and n-3He and p-3H phase shifts. See also (1977PE13) and the review (1987FI03) of four-body scattering in the integral equation approach. Cross sections for intermediate energies were calculated by diffraction multiple-scattering theory by (1978PE20, 1976LE32), and by the Glauber formalism (1973NA06, 1976FR12, 1979ME08, 1981BI08). A generalized potential description of the p-3H interaction is presented in (1990DU11). Collective excitations of 4He are included in a study (1990FI06) of the structure of the continuum spectra in p + 3H scattering at ≈ 30 MeV.
Measurements of the 3H(p, d)2H reaction published prior to 1972 are reported in the previous compilation (1973FI04), and some possible evidence of time-reversal invariance violation is discussed. More recently, measurements of angular distributions of the analyzing power for 3H(pol. p, d)2H at eight energies from 6.7 to 14.7 MeV were reported in (1972HA14, 1972HA50). It is noted that by reciprocity these analyzing powers are the same as proton polarizations of the 2H(d, pol. p)3H reaction. Comparisons were made with the mirror reaction 2H(d, pol. n)3He, and good agreement is found when the reactions are compared at the same exit-channel energies. It is concluded that these results give no evidence for violations of charge symmetry. One additional measurement for the 3H(p, d)2H reaction was reported in (1974JA15). Differential cross sections for Ep = 13.600 MeV for θlab = 15 - 55° were measured with an accuracy better than 1%.
Calculations of differential cross sections for the 3H(p, d)2H reaction were carried out (1986KA21) in a multichannel resonating group approximation, and good agreement with experiment was obtained.
Measurements of cross sections and analyzing powers for 3H(d, n) reactions are summarized in Table 4.12 (PDF or PS). Earlier work is reviewed and discussed in the previous compilation (1973FI04). As noted there, the neutron spectrum from reaction (a) indicates no excited states in 4He between 1 and 13 MeV excitation. The properties of the neutron distributions from reactions (b) and (c) are also described.
Experiments bearing on the question of possible charge-symmetry breaking include the 3H(d, pol. n)4He polarization measurements of (1972SM05) and the 3H(pol. d, n)4He and 3He(pol. d, p)4He analyzing power measurements of (1980DR01). In the latter work the authors note large differences for the two reactions for Ed below 1.65 and above 4 MeV. Comparisons of the analyzing powers for the inverse reactions 4He(pol. n, d)3H and 4He(pol. p, d)3He are reported in (1982SA05) to be consistent with charge symmetry.
Relatively few calculations for reaction (a) have been carried out. For early work see the previous compilation (1973FI04). More recently, the work described in (1972SE09, 1975SE07, 1977SE09) derives criteria for a simplified analysis of measurements with polarized deuterons involving Ayy(θ) in the vicinity of isolated resonances. See also the multichannel resonating group calculations of (1990BL08). A nondynamical calculation of polarization observables for Ed below 1 MeV in terms of (l, s, j) matrix elements is described in (1986KO21). A new method for determination of the nuclear vertex constants from charged particle-transfer reactions is used to analyze σ(θ) for reaction (a) at Ed = 15 MeV. See also (1990KA22). Analytical approximations to the cross section for the purpose of calculation of resonant thermonuclear reaction rates are discussed in (1987GU25). See also the T ≈ 300 K reaction rate calculations of (1989SC25) and those of (1989AB21).
These reactions are reviewed by (1988AJ01). Early measurements of neutron spectra are noted in the previous compilation (1973FI04). No new work has been reported on reaction (a). A measurement of the 0° differential cross section for 3H(t, 2n)4He at Et = 160 keV and angular distributions at 55 - 80 keV were reported in (1977SE11). A resonating group method was used to calculate the energy dependence for the cross section and astrophysical factor in (1989VA20).
Early work on three-body decays (a) and (c) was summarized in the previous compilation (1973FI04). More recently, extensive reviews of experimental and theoretical work on hypernuclei were presented in (1975GA1A, 1978PO1A, 1990CO1D, 1990OS1A). A theoretical study (1985LY1A) found that the polarization of the protons and tritons in reaction (a) is largely determined by the strong interaction in the p-3H system. The two-body decay (b) was used (1988TA29, 1989TA16, 1989TA19) in measurements of the formation probability of Λ4H from K- absorption at rest on light nuclei. Theoretical studies of Λ4H production, structure, and decay are reported in (1982KO13, 1984CO1E, 1986DZ1B, 1987YA1M, 1988MA09, 1989TA17, 1989WA25). Calculations of Coulomb effects and charge-symmetry breaking for A = 4 hypernuclei are described in (1985BO17). A four-body calculation of the 0+ - 1+ binding energy difference is reported in (1988GI1F). Non-mesonic decays are discussed in (1985TA1E, 1986SZ1A, 1990LY1B). Evidence for the existence of a Σ-nucleus bound state formed in a (K-, π-) reaction on 4He was reported in (1989HA39). See also (1990HA08, 1990HA11). The possibility of forming doubly strange Ξ-hypernuclei is considered in (1983DO1B).
Measurements for the 3He(n, γ)4He reaction made since the previous compilation (1973FI04) are listed in Table 4.13 (PDF or PS). Measurements of the thermal neutron capture cross section were reported in (1973BO34, 1979SU05, 1980AL05, 1989WO10, 1991WE06). The results are listed in Table 4.14 (PDF or PS) below. Experimental and theoretical results for neutron radiative capture on light nuclei including 3He are reviewed in (1981SH25). Calculations (1981TO03) including meson-exchange currents were able to account satisfactorily for the thermal neutron cross section. A recent Monte Carlo variational calculation in which the scattering-length dependence was deduced was reported in (1990CA28). The results indicate that the cross section is almost entirely due to exchange currents.
Shell model calculations including two-body meson exchange currents are reported for both 3He(n, γ)4He reaction and the weak 3He(p, e+, νe) reaction (1991WE06).
Doubly radiative neutron capture cross sections were calculated and reported in (1976LE27). Cross sections in the 0 - 70 keV region are reported in (1979AL25), and are shown to be in general agreement with an E1 direct capture calculation. At higher energies (En = 6.0 - 17 MeV) the detailed-balanced cross sections of (1981WA18) confirmed the reported 4He(γ, n) cross section (see the section on the 4He(γ, n) reaction) which, when combined with the previously reported 4He(γ, p) cross section, implied a (γ, p)-to-(γ, n) ratio of 1.6 to 1.9 in the 23 - 33 MeV excitation region of 4H. Additional information on the capture process in this energy region is provided by the polarized neutron capture cross sections and analyzing powers of (1982WE05). Calculations carried out within the framework of the recoil-corrected continuum shell model (1981HA10, 1983HA21) indicated that standard theoretical assumptions were unlikely to account for the reported large (γ, p)-to-(γ, n) ratio. On the other hand, the microscopic multichannel resonating group model calculations of (1988WA20) imply that the effect of the Coulomb force on thresholds for the two mirror channels can account for the observed differences in measured observables in the 23 - 33 MeV excitation region of 4H, excluding the "anomalous" (γ, p)-to-(γ, n) ratio. For additional related information see reaction 7 on 3H(p, γ) and reaction 21 on 4He(γ, n), 4He(γ, p). The whole range of experimental and theoretical evidence bearing on the σ(γ, p)/σ(γ, n) ratio is summarized in a separate discussion at the end of reaction 21.
The two latest measurements (1989WO10, 1991WE06) are in excellent agreement, but disagree with the result of (1980AL05). It should be noted, however, that the results of (1989WO10) rely heavily upon the 3H(p, γ)4He cross section at E p = 3.82 MeV (1970ME07). If the lower value reported for this cross section in (1990FE06) is used, the σ (th)nγ cross section becomes 40 ± 4 μb, which agrees (within error) with that of (1980AL05).
A neutron-capture cross section at 24.5 keV was measured by (1991WE06) to be σnγ (24.5 keV) = 9.1 ± 0.8 μb. The thermal-neutron-capture cross section has been used to estimate the astrophysical S-factor for the 3He(p, e+γ)4He reaction (1989WO10, 1991WE06). The results indicate that about 10% of the solar-neutrino flux in the Davis' experiment can be ascribed to the high-energy 3He + p neutrinos. The double photon decay cross sections are also given in (1980AL05) and (1979SU05).
Measurements of cross sections, polarizations and analyzing powers for the 3He(n, n)3He reaction are summarized in Table 4.15 (PDF or PS). Earlier work is reviewed in the previous compilation (1973FI04). More recent experiments are reviewed in (1978SU1A, 1981GR1A). See also the discussions in (1983HA20, 1985KL03, 1988JA06) of the experimental and theoretical developments relating to 3He(n, n)3He and the A = 4 system.
A variety of theoretical approaches have been used to describe n-3He scattering. At thermal energies, the complex incoherent scattering length for 3He was estimated (1975SE06) on the basis of effective range theory and a Breit-Wigner analysis. Low-energy n-3He scattering was studied in the integral equation approach (1976KH01, 1976TJ01) and scattering lengths were calculated. Higher energy observables for nucleon reaction channels in 4He were calculated by recoil-corrected continuum shell model techniques (1979HA22), and excellent agreement with experiment was reported. Proton and neutron polarization differences in 3He(pol.n, n)3He and 3H(pol.p, p)3H were analyzed (1977BE53) in the framework of a dynamical R-matrix model methodology, and quantitative agreement with experiment was obtained. Several resonances are predicted in the vicinity of a narrow resonance near Ex = 37 MeV suggested by the phase-shift analysis of (1976LI03). The R-matrix methodology is used to construct a detailed theoretical model of 4He (1980BE18). Scattering results and phase-shift calculations are presented and discussed and are also compared with resonating group and field-theoretic models. Cluster-model calculations of 4He excited states based on (trinucleon + nucleon) (1976IO01, 1981FU08) as well as (trinucleon + nucleon) and d + d clusters (1983FI14) have been carried out. Collective and cluster degrees of freedom are included in a study (1990FI06) of the structure of the continuum spectra of 4He in the ≈ 30 MeV region. The ground and even-parity states were examined within the framework of a multichannel resonating group model approach (1986KA21), and agreement with the elastic scattering and polarization observables was reported. Multichannel resonating group calculations for A = 4 from the first breakup threshold to 10 MeV are presented (1981HO04), and reported to predict the established resonance structure and provide evidence bearing on other possible states. Multichannel resonating-group calculations, which include distortion effects due to the coupled deuteron cluster, were used (1986KA21) to examine the ground and even-parity excited states and the scattering problem of the 4He system.
Early work on reaction (a) is summarized in the previous compilation (1973FI04). It is noted there that the reaction proceeds almost 100% through the 1S0 resonance at En = -0.25 to -1.0 MeV, and that the proton spectra from reactions (b) and (c) reveal no clear indication of an n-d, three-nucleon or two-nucleon final-state interaction.
A more recent measurement (1975WI04) of the 3He(n, p)3H total cross section at En = 3.5 MeV gives σtotal = 422 ± 58 mb. The cross section was measured (1982BO19) in the energy range En = 0.15 - 150 keV with an accuracy of 2 - 3%, and the departure from the 1/v law was investigated. Measurements of the P-odd asymmetry in 3He(n, p)3H were made (1981VE08), and an upper limit was obtained. Little theoretical work on reaction (a) has been reported since the previous compilation (1973FI04). A resonating-group model calculation was carried out (1976IO01) involving the groupings n + 3He and p + 3H. Total cross sections were calculated and compared with experiment at 1, 3, 5, 6, and 14.4 MeV. The contribution of the triangle diagram for the 3He(n, p) reaction was investigated in a K-Matrix scattering calculation reported in (1984BA17).
Reactions (a), (b), and (c) are reviewed in the previous compilation (1973FI04). No new work has been reported.
Reactions (a) to (c) are reviewed by (1988AJ01). Early measurements of single and coincident charged-particle spectra are summarized in (1973FI04) and a discussion of evidence bearing on excited states of 4He is presented. Measurements of cross sections, analyzing powers, polarizations, and polarization transfer coefficients are summarized in Table 4.16 (PDF or PS). See also (1986HE16). Polarization observables for the 3He(d, p)4He reaction and other reactions relating to A = 4 - 6 were reviewed in (1987GR08). A considerable number of measurements of vector and tensor analyzing powers have demonstrated the suitability of reaction (a) as an analyzer of deuteron polarization (1973HA51, 1973KA08, 1974GA21, 1974TR02, 1976GR08, 1976GR10, 1976SC15, 1977ST06, 1980DR01, 1980GR14, 1981RO13, 1988SA40, 1989AB17). See also the related theoretical work (1976SE03, 1977SE09, 1978SE01). Design and calibration of polarimeters based on reaction (a) have been presented in (1980ST1A, 1982GR25, 1987GR30).
Distorted-wave calculations for reaction (a) are presented and discussed in (1975NE11). See also (1989BO22). Off-diagonal interaction spin dependence is discussed in (1975YA12). An estimate of cross sections for reaction (a) at intermediate energies in terms of the (p, π+) cross section is discussed in (1980WI02). The single-resonance contribution to the cross section and reaction rate at thermonuclear energies is studied (1987GU25), and the effect of electron screening on low-energy fusion cross sections is discussed in (1987AS05).
Measurements of the breakup reactions (b), (c), and (d) are summarized in Table 4.17 (PDF or PS). A discussion of these reactions is included in the review of quasi-free processes and few-body systems of (1974SL04). Calculations for reaction (c) in the region of small proton-tritium relative energies are presented in (1984DU10).
Reactions (a) through (d) are reviewed in the previous compilation (1973FI04). For reaction (a) measurements of analyzing powers Ay(θ) for Et = 9.02, 12.86, and 17.02 MeV at θc.m. = 16° - 159° as well as measurements of Ay(E) at 90° for Et = 9.02 - 17.27 MeV were reported in (1977HA42). Marked deviations from the antisymmetric shape predicted by a simple particle-transfer model incorporating charge symmetry were observed. Possible charge asymmetry effects in this reaction were also discussed in (1978FE07, 1978FE08). See also (1988RA31). No new work has been reported on reactions (b) through (d).
Measurements on reaction (a) reported since the previous compilation (1973FI04) include spectra and differential cross sections at beam energies of 9.11, 7.88, and 6.9 MeV (1972DE46) and at Ec.m. = 16 MeV (1974RO01). The total cross section was measured for Ec.m. = 30 - 150 keV (1974DW01), and the astrophysical factor S(E) was measured at Ec.m. = 17.9 - 342.5 keV.
Calculations to determine the NN scattering parameters from final-state interactions in reaction (a) were described in (1974DE18). Calculations of a diproton production mechanism in reaction (a) were reported in (1976MC04), and the effects of electron screening on cross sections for low-energy fusion reactions, including reaction (a), were studied in (1987AS05, 1989BE08). An extended elastic model was applied to calculate the reaction rate at astrophysical energies in (1989SC25, 1990SC15). The astrophysical S-factor is calculated with the two-channel approximation of the RGM in (1989VA20).
Triton spectra from reaction (b) are discussed in the previous compilation (1973FI04).
Measurements of photonuclear cross sections for 4He are summarized in Table 4.18 (PDF or PS). Earlier experimental and theoretical work is summarized and discussed in the previous compilation (1973FI04). Measurements and analyses of reaction (a) for energies near threshold are reported in (1980AR06, 1981AR10, 1988AR08), and for energies near the Δ(1232) resonance in (1985AN14). Measurements at GeV energies in the region of small momentum transfers are reported in (1982AL09). See also (1978AL08). A number of calculations have been made with the Δ-isobar model (1981OS1A, 1981SA01, 1983KO02) and in the distorted wave impulse approximation (1983GI02, 1983LE12, 1985KA22, 1986LE07, 1987CH24, 1987LE13). Impulse approximation calculations in the resonance region were reported in (1978TR03, 1979GA18). Screening corrections were calculated (1978ST21). Momentum-dependent terms in the operator and a two-nucleon exchange production mechanism were discussed in (1977VE05), and calculations near threshold were reported. Rescattering corrections were calculated in (1976OS03). A discussion and comparison of the various methods of calculating the amplitudes of partial reactions are presented in (1983TR02) for energies in the nucleon resonance region.
Reactions (b) and (c) have cross sections which are similar in shape at all energies as pointed out in the previous compilation (1973FI04), but there has been considerable disagreement among the results of the measurements of each. The whole range of experimental and theoretical evidence bearing on the σ(γ, p)/σ(γ, n) ratio is summarized in a separate discussion at the end of this section. The absolute measurement of σ(θ) for reaction (c) described in (1991JO04) includes useful evaluative discussions of existing experimental and theoretical work. See also (1978AR1B, 1978AR26, 1980AR20, 1984GU18). A considerable amount of theoretical work has been done on reactions (b) and (c) with a great deal of it related to the question of the σ(γ, p)/σ(γ, n) ratio (1974CH50, 1974GA10, 1974GA32, 1974ST08, 1980BE42, 1981AR21, 1981HA10, 1983BE13, 1983DE31, 1983HA21, 1984BA73, 1984GU18, 1985QU01, 1986CA05). See also (1974GA32, 1974NO10, 1974RA18, 1975GU23, 1976FI11, 1976NO06, 1977DE26, 1979GU13, 1980AR04, 1980BO13, 1980RA17, 1986CH05, 1988TE04, 1989VO01). A method for estimating the polarization of final particles in reactions (b) and (c) is developed in (1990GU21).
Structure effects in the E3 cross section for reaction (c) were investigated in (1989BE07). A review of progress on four-body scattering and breakup, in the integral equation approach, is presented in (1987FI03).
Reaction (d) was studied in two investigations reported in (1982AN16, 1984AN04). The experimental results were analyzed satisfactorily by means of impulse-approximation calculations involving a reaction amplitude described by the sum of two pole diagrams with a virtual neutron and a 3He nucleus. No recent work has been reported on reaction (e). Cross sections were measured in the energy region of the Δ(1236) resonance (1972AR23). An impulse-approximation calculation in terms of quasi-free nucleons in 4He was reported in (1972LE24).
Only a few measurements have been done for reaction (f), and those reported since the previous compilation (1973FI04) are listed in Table 4.18 (PDF or PS). Cluster-model calculations for energies of a few MeV above threshold are reported in (1974ST08). A low-energy theorem is applied to cross section calculations in (1981GO15). See also the review presented in (1978AR26). Comparisons of the cross section data with calculations were reported in (1980AR04, 1980GU25) to provide evidence for a 2+ state in 4He at Eγ = 30 - 35 MeV.
Measurements for reaction (g) reported since the previous compilation and listed in Table 4.18 (PDF or PS) have been carried out for photon energies from 28 - 400 MeV with cloud chambers and with combinations of magnetic spectrometers and neutron detectors. Relative cross sections for reactions (b), (c), (f), (g), and (h) were obtained (1977BA35) from threshold to Eγ ≈ 80 MeV, and it was concluded that the main mechanism for reaction (g) in this energy region is two-nucleon absorption. Similar measurements at 30 - 40 MeV (1979BA47) were used to study clustering effects, and the results suggested that the most important mechanism for reaction (h) is photoabsorption from a quasideuteron correlated with another quasi deuteron, both of which decompose. See also the review of (1985HO27). Theoretical calculations of reactions (b), (c), and (g) utilizing the quasideuteron mechanism are reported in (1974NO10, 1976NO06, 1984CH09). See also (1982AR11).
Theoretical studies of the total photonuclear absorption cross sections by means of sum rules have been described in (1974FI03, 1977LI12, 1980AR20, 1983EL07). See also the theoretical investigations of the integrated photonuclear cross sections reported in (1974GO13, 1977GR08, 1984KO33, 1985SA01).
The ratio of the two photonuclear cross sections, 4He(γ, p)3H-to-4He(γ, n)3He, below Ex = 35 MeV has constituted a long-standing anomaly in low-energy photonuclear physics. A review of the experimental data (1983CA08) concluded that the data indicated a (γ, p)-to-(γ, n) ratio which varied slowly from 1.7 to 1.2 in the excitation-energy range Ex = 25 - 35 MeV, in substantial disagreement with the ratio predicted by conventional isospin-conserving theoretical calculations. Data obtained in recent years change this picture substantially.
Relevant measurements include:
An examination of all of the (γ, p) and (γ, n) data, including inverse reaction studies, led the authors of (1983CA08) to conclude that the (γ, p)-to-(γ, n) ratio was substantially greater than 1.0 below Ex = 35 MeV. However, since that time a measurement using monoenergetic photons (1988BE38) indicated that the 4He(γ, p)3H cross section was substantially smaller below Ex = 35 MeV than previously thought, and was essentially in agreement with the monoenergetic-photon results for the 4He(γ, n)3He reaction (1954FE16, 1963ZU03, 1966FE07, 1968GO19, 1971BE43, 1972BE06, 1973MA57, 1975IR01, 1977BA35, 1978AR26, 1980BE45). This (γ, p) result has received additional support from a new 3H(p, γ)4He measurement (1990FE06) which agreed with it. The (γ, n) results of (1980BE45) are also supported by the capture measurements of (1981WA18). Thus, if we take the most recent (γ, n), (γ, p), (p, γ) and (n, γ) cross-section measurements we obtain, for Eγ = 24 - 31 MeV, a (γ, p)-to-(γ, n) ratio which is about 1.1, consistent with conventional theoretical predictions and indicating that no charge-symmetry violation is required in 4He to explain these data.
Additional support for this result is provided by the π+/π- cross section ratio measurement of (1986BL07). The measured ratio of 1.05 ± 0.08 indicated little or no isospin mixing in 4He between Ex ≈ 23 - 30 MeV. A recent simultaneous measurement of 4He(e, e'p)3H and 4He(e, e'n)3He cross sections (1989SP05) gave a ratio less than 1.2, consistent with the predictions of a microscopic model which assumed a charge-symmetric nuclear hamiltonian (1988WA20). Unfortunately, previous results which disagree with this conclusion have not been accounted for. The results of (1982MC03, 1983CA14) are especially disturbing. On the theoretical side, while the "new" data produce a ratio in agreement with essentially all calculations, the lower absolute cross sections, for both (γ, p) and (γ, n), disagree with most theoretical results (see especially (1983HA21, 1988WA20)). However, a flaw has been revealed recently in the manner in which Siegert's theorem was used in the calculations of (1988WA20). The correction brings the absolute cross sections down to the lower values, while keeping the ratio close to 1.1, in agreement with the new results. The impact of this correction on the (e, e'p) and (e, e'n) channels remains to be examined, but is expected to be small. Unfortunately, the ratio question continues to haunt many workers in the field, and it has not been unambiguously resolved.
Experiments and data analysis for elastic electron scattering on 4He are summarized in Table 4.19 (PDF or PS). Earlier work is described in the previous compilation (1973FI04). A recent determination (1985OT02) of the r.m.s. charge radius gave < r2 >1/2 = 1.671 ± 0.014 fm.
A number of theoretical calculations relating to 4He(e, e) elastic scattering have been carried out. The contribution of two-photon exchange in high-energy large-angle scattering was examined (1972BO63). The elastic scattering form factor was computed (1972CA40) in the local-density approximation and in the oscillator model with short-range correlations (1972FI10). Relativistic corrections and their effect on the diffraction minimum were examined (1973FR21). Calculations utilizing self-consistent Brueckner-Hartree-Fock wave functions (1974CI02) provided estimates of the effects of center-of-mass spuriosity. Charge form factors were calculated with many-body meson exchange operators (1977RI15). The effect of short-range three-nucleon correlations was studied (1978HE19). Elastic and inelastic form factors calculated in the method of hyperspherical functions were discussed in (1981BU04). A multi-quark cluster effect on the charge form factor was postulated in (1982NA09). The role of tensor and short-range correlations was investigated by (1982DE51, 1983OR05). An analytic parameterization of the charge form factor was presented in (1985AG05). The work of (1988MO32) utilized a quark model and examined symmetry of the ground-state structure of 4He. Calculations of electromagnetic form factors for 4He based on quantum hadrodynamics is discussed in (1989LI16). The influence of short-range correlations on the charge distribution is discussed in (1989LO06). Experimental data on inclusive longitudinal and transverse response functions in the context of theoretical developments are discussed in (1989PA12). Calculations of the charge form factor using realistic variational wave functions and consistent two-body operators are reported in (1990SC01). A study of elastic and inelastic electron scattering on 4He with the Monte Carlo method is described in (1990PA07).
Inelastic scattering experiments are summarized in Table 4.20 (PDF or PS). See also (1974GO15, 1980GO21, 1981GO03, 1988DY01). A review of the status of theoretical methods and principal results for elastic and inelastic scattering of electrons by nuclei was presented in (1974LU09). In (1974VI03) a simple model of 4He is suggested to interpret the details of the charge distribution obtained from the electron scattering form factors for q2 ≤ 20 fm-2. A study of the 0+ state at 20.1 MeV in 4He reported in (1974ZO04) utilized the inelastic form factor and three-body forces in a hyperspherical description. A microscopic treatment of coupled monopole and quadrupole T = 0 vibrations was used in (1975AB04) to calculate transition strengths and inelastic form factors. Center-of-mass corrections for calculations related to electron scattering are studied and reported in (1980DE30). The effect of final-state interactions in inclusive electron scattering is discussed in (1980HO26). The method of hyperspherical functions is discussed in (1981BU04). Quasi-free peak parameters from calculated (e, e') cross sections are related to sum rules in (1981KO10). Data for electron scattering from 2H, 3He, and 4He are found (1982BO30) to be unified by a nuclear scaling function. The (e, e') cross section was calculated using an interaction-time approximation for dynamic form factors (1982KO26). The existence of y-scaling for the quasi-elastic cross section was demonstrated in (1983DE13). See also the study of (1985KO19). A continuum RPA calculation with finite-range interaction was applied (1983DE39) to calculate (e, e') cross sections. The role of tensor correlations in inclusive electron scattering processes was studied and discussed in (1983OR05). The location of the quasi-elastic peak maximum in 4He(e, e') relative to the eN scattering peak was explored (1985KU02) on the basis of 4He properties. A calculation based on a quark description of the nuclear ground state is presented in (1986DA01). Several different NN interactions are used in a hyperspherical-harmonics calculation of the (e, e') form factor (1987SA23). The form factor for (e, e') excitation of the 0+ resonance in 4He is discussed in connection with a collective and cluster model calculation (1987VA33) and a symplectic shell model calculation (1988VA22). More recent work includes a recoil-corrected continuum shell model study of the 0+ first excited state in (1989HA02, 1990HAZN), a (0 + 2)h-bar ω model-space calculation of 4He observables in (1990WO10), an extrapolation of nucleon-momentum distributions in 4He using asymptotic scaling analysis (1990CI03), and a Monte Carlo study (1990PA07). See also the discussion of data on longitudinal and transverse response functions (1989PA12), the relativistic model investigation of ion-ion optical potentials (1989RE07), and the microscopic study of the NN interaction (1989YA11). 4He(e, e') data is utilized in a determination of a phenomenological Δ-nucleon potential in (1990OC01).
Experiments and data analysis for pion scattering on 4He are summarized in Table 4.21 (PDF or PS). See also (1973AN26, 1975BI08, 1976BA57, 1976BU19, 1976SH23, 1978FA06, 1980BA17, 1980KA17, 1982BA16, 1984FO18, 1984GM01, 1989AR16). These reactions were not included in the previous compilation (1973FI04). Much of the work (1978BI07, 1981MC09, 1982BA19, 1982BA65, 1983LE12, 1985BO41) is directed toward studies of the properties of the pion-nucleon interaction and the effects of the nuclear medium. Related theoretical work includes the DWIA calculations of (1975HE06), a coupled channel method in the K-matrix approach (1979GM01), and the pole extrapolation method for separating strong and electromagnetic contributions (1982DA15). Investigation of medium effects by studying quasi-elastic scattering is discussed in (1983SI21). The question of isospin mixing in 4He and possible charge-symmetry breaking implied by photonuclear reaction data (see sects. 7, 14, and 21 of this compilation) was studied through the π+/π- cross section ratio in (1986BL07) and the result implies little isospin mixing in contrast with the earlier photonuclear results. The calculations of (1989HA03) predict no significant deviation from unity of this ratio for isospin mixing at the 5% level. On the other hand, (π±, π±'p) measurements of (1990JO04) found dramatic differences between (π+, π+'p) and (π-, π-'p) in the 4He GDR region which, although in sharp contrast to predicted values, do not provide an unambiguous indication of isospin mixing and probably arise from the interference of several reaction amplitudes.
This reaction is reviewed in (1988AJ01) under the discussion of 5He.
Reaction (a) was reviewed by (1984AJ01) under the discussion of 5Li. Measurements for reactions (a) - (d) reported since the previous A = 4 compilation (1973FI04) are summarized in Table 4.22 (PDF or PS).
A great deal of theoretical work has been carried out to describe 4He(p, p)4He elastic scattering. Much of this work has involved optical model analyses (1973CL01, 1973SA09, 1976AR12, 1977AR01, 1977DY01, 1978LE23, 1978ME04, 1979AL12, 1979AR02, 1979DY07, 1980AR08, 1983GR20, 1985KO05, 1985KO07, 1985KO37, 1986BL02, 1986IS04, 1988FR06, 1989TA20, 1990BE53, 1990DU05, 1990LA17, 1990TA16). A distorted-wave impulse approximation calculation of the continuum analyzing power at 100 MeV is presented in (1990LA12). Glauber model multiple scattering calculations are presented in (1974BA38, 1974GU21, 1975BL04, 1975GU17, 1975NA07, 1975WA16, 1976AU04, 1977AL06, 1977YO04, 1978AU11, 1979SA09, 1980WA06, 1981AU07, 1981KH07, 1985TE02, 1986FR12, 1986SA30, 1990LO13). A multichannel cluster model approach is discussed in (1981FE02), and a self-consistent wave function Brueckner-Hartree-Fock calculation is described in (1974CI02). A review of experimental and theoretical advances in high-energy proton scattering is presented in (1981WA1A). The effect of coupling between the ground state and the first excited state (0+, T = 0) in 4He was estimated in (1984AH03) using a breathing-mode model. Phase-shift analyses and calculations are presented in (1975CA05, 1977TH07, 1979KA17, 1979SA35, 1985SO08, 1986SA05, 1989CO11, 1991CO05), and from a study of experimental phase shifts (1975PL01) it was concluded that small D-state admixtures to the dominant S-state configurations exist in the 4He ground state. For other theoretical studies, see (1973LA14, 1973PL02, 1973SI44, 1974BA38, 1974LY02, 1975AH07, 1975BA05, 1975GI07, 1975MA12, 1975RU07, 1976DU06, 1976LE22, 1976NA04, 1976RU04, 1977JA12, 1977PH01, 1978MA37, 1980AU09, 1981SH04, 1981ZH03, 1982PO12, 1982ZH08, 1983SA38, 1983SH12, 1984BL21, 1984FI20, 1984OK01, 1985FL04, 1985KI11, 1985KR15, 1985RO16, 1986AU05, 1986DU14, 1986KA35, 1986OK06, 1987ZH10, 1989KA39, 1990AU03, 1990HU09, 1990LO02).
Measurements of proton inelastic scattering and breakup reactions (b) and (c) showing evidence for the lowest 0+, 0-, 2-, T = 0 states in 4He are discussed in the previous compilation (1973FI04). No recent work has been reported.
A formula to represent amplitudes for three-body breakup (reactions (b), (c), (d)) is developed and compared with data in (1987FU10).
Reaction (a) was reviewed by (1984AJ01) under the discussion of 6Li. Measurements of reactions (a) - (c) published since the previous A = 4 compilation (1973FI04) are summarized in Table 4.23 (PDF or PS). See also (1973TR04, 1982IS06).
Many theoretical studies of 4He(d, d)4He elastic scattering have been reported since the previous compilation (1973FI04). Phase-shift analyses have been carried out by (1972SC14, 1975GR09, 1984BA19, 1985JE04, 1990KU16, 1991KR02). See also (1990KU06). Resonating group calculations are described in (1974TH05, 1976LE17, 1982KA24, 1983AO03, 1985FI01, 1985KA20), and optical model analyses in (1984FR14). Calculations based on Glauber theory (1978IN02, 1986FR12), the orthogonality-condition model (1980NI07), microscopic coupled-channel model (1983SA39), and the three-cluster coupling model (1986MI23, 1987MI06) have been carried out. Nucleon-nucleon-alpha Faddeev calculations were reported in (1987HA34, 1990BL13). Calculations utilizing a three-body formalism with Coulomb interaction were described in (1986AG03). A geometric model for dd collisions at high energies (> 6 GeV) is described in (1990HU09). Convergence properties of the pseudo-state method were investigated in (1988KA25). See also the recent work of (1990KU06, 1990KU16, 1991KR02).
Early experimental evidence for levels in 4He from reactions (b) and (c) are discussed in (1973FI04). No new work has been reported.
This reaction was reviewed in (1966LA04).
This reaction is reviewed in (1988AJ01).
Reaction (a) was reviewed by (1988AJ01) under the discussion of 8Be. The previous A = 4 compilation (1973FI04) reviews early work on reactions (a) - (d) giving information on excited states in 4He. More recently, the work reported in (1982FI16) studied the effects of 4He in the first excited (0+) state on the elastic αα scattering. Kinematically complete experiments on reaction (d) at 119 MeV reported in (1980KA20) found structure in the coincidence energy spectra corresponding to excitations in 4He of 25.5, 27.8, 29.7, 31.7, and 35.3 MeV. Angular correlations were used to assign Jπ = 2+, 2+(1-), and 2+ to the last three of these. An investigation (1981BA39) of the excitation spectra of 4He near Ex = 20 MeV by means of an (α, α') experiment at 64 MeV used an R-matrix representation to extract level parameters Eλ = 20.29 ± 0.02 MeV, Γ0 = 0.89 ± 0.04 MeV for the first excited state.
Reactions (a) and (b) are reviewed in the previous compilation (1973FI04) and evidence for the formation of the ground and excited states of 4He based on the summed neutron and proton spectra from reactions (a) and (b), respectively is cited. No new evidence for 4He levels based on reaction (a) has been reported. However, the triple-differential cross section measurements of reaction (b) described in (1986RI01) indicate strong population of the 4He 2- state at 22.1 MeV excitation. The energy dependence of the reaction around the Δ(1232) resonance was explored in (1990ZHZZ). See also (1986WH01, 1987HU13).
These reactions are reviewed by (1988AJ01) under the discussion of 7Be. The previous compilation (1973FI04) summarizes early experimental and theoretical work on these reactions that relate to the structure of 4He. More recently, differential cross sections for reaction (a) (1974SC24) were measured and analyzed by cluster-model direct reaction formulae, and possible contributions from compound structures within the 3He - 4He*(0+) channel involving the first excited state of 4He at 20.1 MeV were discussed. Measurements at incident energies E = 1 - 3 MeV are described in (1989ZAZX). See also (1987ZA07).
In (1974ZH01) an estimate of the contribution of spin-flip knock-out processes in reaction (b) is presented. The distribution of effective numbers of n-p pairs in 6Li over the excitation spectrum of 4He is given. Quasi-elastic knockout of excited 4He clusters by fast protons at large momentum transfers is discussed in (1987ZH10). The excitation spectrum of 4He is calculated.
This reaction is reviewed by (1988AJ01) under the discussion of 8Be. The previous compilation (1973FI04) cites two reported experiments which provide information on excited states of 4He. More recently, an experiment (1978FU03) at Ed = 13.6 MeV involving dα angular correlations showed evidence for a 0+ state at 25.52 MeV excitation with a width of 2.26 MeV and an odd-parity state at 27.5 MeV. See also (1975GL08). A recent experiment at Ed = 18.2 - 36.8 MeV is reported in (1989BA88). See also (1973HE06, 1973MI20, 1974MI10, 1979WA02, 1981YU01, 1990YA11). An analysis of tensor-analyzing-power data is described in (1990SA40).
This reaction is reviewed by (1988AJ01) under the discussion of 8Be. The previous compilation (1973FI04) cites two experiments which provide information on excited states of 4He at 20.06 and 21.2 MeV. A recent measurement at incident energy Ei = 29.1 - 44.6 MeV is reported in (1989BA88). See also the analysis of data at thermonuclear energies in (1990RA28).