
^{4}He (1992TI02)(See Energy Level Diagrams for ^{4}He) GENERAL: Ground state:Due to noncentral forces, the wave function for the J^{π} = 0^{+} ground state of ^{4}He can be a positiveparity mixture of three ^{1}S_{0}, six ^{3}P_{0}, and five ^{5}D_{0} orthogonal states (1967BE74). Of course, the symmetric Swave component is the dominant part of the wavefunction, with significant Dwave and almost negligible Pwave contributions. Since the Dstate admixture can be inferred from measurements such as the tensor analyzing powers for ^{2}H(d, γ)^{4}He (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 Dstate probability as calculated in (1988CA19, 1990CH06, 1991AR01). Recent variational and Green function Monte Carlo (GFMC) calculations [(1988CA19, 1991CA35)] using realistic nucleonnucleon potentials have been highly successful in reproducing the groundstate properties of light nuclei. These calculations for ^{4}He give Dstate probabilities ranging from 15  17.5%, depending on the potential model (including threebody forces) used, and Pwave probabilities that are much smaller (≈ 1%). Other theoretical and experimental estimates of the Dstate percentage are considerably lower, but these inferences can be complicated by the presence of more than one multipole and other Dstate effects (see the discussion for reaction 1). The latest GFMC calculation (1991CA35), using a truncated version of the Argonne V14 NN interaction (1984WI05), overbinds ^{4}He by 0.9 MeV, whereas most variational calculations underbind it by more than 1 MeV. In both cases, threebody 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 kineticenergy and twonucleon potentialenergy terms, so that the threebody forces, though small in comparison to the twobody forces, make a significant contribution to the binding energy. Since the nuclear forces are assumed to be chargeindependent, 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 electronscattering 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 protonpair 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. Excited states: The unbound excitedstate level structure presented here is based on the comprehensive, Coulombcorrected, chargeindependent Rmatrix analysis of (1989HA2A). This analysis takes its isospin1 parameters from an analysis of p^{3}He scattering data (see ^{4}Li, GENERAL section), but with the eigenenergies shifted by the internal Coulomb energy difference ΔE_{C} = 0.64 MeV and the p^{3}H and n^{3}He reducedwidth amplitudes scaled by the isospin ClebschGordan coefficient √1/2 (square root of 1/2). The isospin0 parameters are then varied to fit the experimental data for the reactions among the twobody channels p + ^{3}H, n + ^{3}He, and d + ^{2}H, at energies corresponding to excitations in ^{4}He below approximately 29 MeV. In this fit, the T = 0 nucleontrinucleon reducedwidth amplitudes are constrained by the isospin relation
and a small amount of internal Coulomb isospin mixing is introduced by allowing
which is necessary to reproduce the differences between the two branches of the d + d reaction (reactions 3 and 4). Although the ^{4}He 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 a_{pt} = a_{n3He} = 4.9 fm and a_{dd} = 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 [1] states are lowered and the [15] states are raised by an attractive particlehole interaction. The Pwave [15] 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 ^{4}Hesystem reactions for a separate 0^{+} or 1^{+}, T = 0 level at E_{x} = 25.5 MeV as has been seen in the α + ^{4}He* 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 E_{x} = 20.21 MeV, or that the true position of the 0^{+} state is several MeV higher, as is indicated by the position of the Smatrix pole (see discussion below). Nestled among a series of four negativeparity, T = 1 levels in the range E_{x} = 23  26 MeV (which were at least 3 MeV higher in (1973FI04)) is a new 1^{}, T = 0 level at E_{x} = 24.25 MeV that has important effects on the d + d reactions at low energies. Isospin mixing between this state and the ^{3}P_{1} , T = 1 level at E_{x} = 23.64 MeV causes significant differences in the pwave part of the d + d reactions, as have been observed in muoncatalyzed (1984BA1W) and polarized (1981AD07) d + d fusion experiments. The 1^{}, T = 0 level was seen by (1981GR16) in their ^{2}H(d, p)^{3}H analyzingpower data, but no evidence of their proposed 4^{+} level at E_{x} = 24.6 MeV was found by (1989HA2A) in fitting their measurements. The remaining T = 0 levels at E_{x} = 27  30 MeV are primarily d + d states, except for the 1^{+} level at E_{x} = 28.31 MeV. The ^{5}S_{2} level at E_{x} = 27.42 MeV is interesting on two accounts: it marks the first appearance of a state from the [20] representation, and it probably corresponds to a resonance that had been seen by (1966LE1A) in ^{6}Li(d, α)^{4}He* 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 ^{5}S_{2} 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 ^{1}S_{0} transitions were important due to Pauli exclusion of the quintet d + d Swaves. The series of ^{3}P_{J} levels concentrated near E_{x} = 28.5 MeV are clearly the ones from the [15] representation predicted by (1972SE02). These broad levels are not apparent in the data, but they are required primarily by the crosssection and analyzingpower measurements for d + d elastic scattering. The 1^{} level in this sequence has been seen in the decay of ^{4}He* in the final states of reactions 25, 28, and 32. The ^{1}D_{2} resonance that was previously thought to be at 33 MeV is at E_{x} = 28.67 MeV, and another 2^{+} resonance, primarily in the ^{5}D_{2} d + d channel, gives a second [20] state at E_{x} = 29.89 MeV. Estimated uncertainties on the parameters given for ^{4}He 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 Smatrix. 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 Smatrix poles are located at least 3 MeV higher in excitation energy than is the pole of K_{R}, meaning that the 0^{+} state is no longer the first excited state of ^{4}He. This might explain the great difficulty shellmodel 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^{3}H and n^{3}He thresholds. Other differences involve the ordering of the Pwave levels, and the appearance of lowlying, positiveparity, 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 previous compilation (1973FI04) reported measurements of the ^{2}H(d, γ)^{4}He reaction from E_{d} = 0.8  482 MeV. Measurements and summaries since 1973 are presented in Table 4.4 (PDF or PS). The early measurements of (1973PO01) at E_{d} = 6.05, 8.96, and 11.67 MeV gave σ(θ) ≈ sin^{2} 2θ, and it was concluded that the process proceeded through an E2 transition by ^{1}D_{2} → ^{1}S_{0} . Measurements at 376 MeV (1984SI01), however, corroborate deviations reported in the inverse reaction by (1976AR05) from the sin^{2} 2θ angular dependence. The cross section results are consistent with timereversal invariance. A measurement (1984WE14) of tensor analyzing power T_{20} at E_{d} = 9.7 MeV gave a nonzero isotropic result which was used in connection with a heuristic model calculation assuming E2 radiation to imply a 4.8% Dstate admixture in the twodeuteron wave function of ^{4}He. Earlier evidence for the ^{4}He Dstate was provided in a study (1975PL01) of phase shifts for p + ^{4}He elastic scattering. Calculations reported in (1985SA04) examined the ^{2}H(d, γ)^{4}He analyzing powers for E_{d} < 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 T_{20} 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 E_{d} = 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 Dstate admixture in ^{4}He unless the deuteron Dstate 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 ^{4}He wave functions which were obtained from variational calculations (1986SC03) and which indicated a value for the ^{4}He Dstate parameter (1986TO11) D_{2} ≈ 0.2 fm^{2}. The energy dependence of vector and tensor analyzing powers at 130° from 0.3 to 50 MeV (1988WE15) indicates that A_{yy}(130°) is sensitive to ^{4}He Dstate components and has its maximum value near E_{d} = 30 MeV. Some of these results are reviewed in (1987GR08). A recent measurement (1989PI06) of cross sections and analyzing powers at intermediate energy (E_{d} = 95 MeV) indicated the dominance of the <^{1}D_{2} E2^{1}S_{0}> transition involving the Sstate component of ^{4}He. Experiments on the ^{2}H(d, γ)^{4}He 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 Γ_{γ}/Γ_{p} ratio was measured, and it was noted that a Dstate component in the ^{4}He wave function is a possible explanation for the result obtained. The measured cross section for E_{d} between 0.7 and 4.5 MeV and angular distributions of cross sections at E_{d} = 1.38, 2.05, 9.6 and 15 MeV (1986WE07) were interpreted to indicate that the ^{4}He Dstate has large effects on the energy and angle dependence of the lowenergy 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 Sstate ratio ρ = 0.2 ± 0.05. Measurements of σ(E) and σ(θ) for E_{c.m.} = 50  500 keV (1987BA58) were interpreted to indicate that the ^{5}S_{2} → ^{5}D_{0} amplitude is dominant for E_{c.m.} < 200 keV. The indicated astrophysical Sfactor (1984FO1A) is 32 times larger than previously estimated and may affect inhomogeneous bigbang nucleosynthesis models. Theoretical studies (1987AS03) of the ^{2}H(d, γ)^{4}He reaction based on a microscopic description of the nuclear wave function reproduce the data for E_{d} < 3 MeV and indicate a 5  7% Dstate admixture in the ^{4}He ground state. The study reported in (1987BL12) finds that conclusions about Dstate components based on simple potential model analysis of experimental data are very sensitive to the parametrization of the nucleusnucleus potential and may be misleading. The phenomenological study of ^{2}H(d, γ)^{4}He (1987PI08) allows for the Dstate component of the colliding deuterons and concludes that it is important in estimating the effects of Dstate components in ^{4}He. 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 Dstate properties in ^{4}He is demonstrated in the work of (1988WA02), using a microscopic multichannel resonatinggroup model. This model was used by (1988LA14, 1990LA16) in the analysis of measurements of cross sections and vector and tensor analyzing powers at E_{d} = 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 A_{y} and A_{yy} for E_{d}(lab) = 0.3  50 MeV. Good agreement was obtained with A_{yy}, but A_{y} was overpredicted at low energies (1  2 MeV). See also (1990WE03). This model predicts a Dstate probability of 2.2% in ^{4}He, but this is only the twodeuteron part of the Dstate. An extensive review of the manifestations of the DState in ^{4}He 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 Dstate probability in ^{4}He 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 E_{d} ≤ 500 keV indicated that at these energies the reaction proceeds through the Dstates in the deuteron and the alpha particle, and that the contribution of the ^{2}H or ^{4}He Dstates can either add to produce a large cross section or cancel. A recent review of nonspherical components of ^{4}He and other light nuclei is presented in (1990EI01).
Measurements of the chargesymmetrybreaking reaction (a) reported in (1987BA15) established an upper limit of σ(θ) ≈ 0.8 × 10^{6} μb/sr at E_{d} = 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 E_{d} = 1.89 GeV, θ_{c.m.} ≈ 79°. See also (1981EG03). A theoretical calculation (1982CH27) assuming various chargesymmetrybreaking 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 E_{d} = 1.95 GeV assuming virtual η and η' production and π^{0}η and π^{0}η' 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 ^{4}He have been reported. Measurements of σ(E, θ) at 70  150 keV (1975PO04) indicate no evidence for a resonance near the dd threshold in ^{4}He. 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 ^{4}He at 23.9 MeV, but do not differentiate between suggested assignments of 2^{+} or 1^{}. A measurement of P_{n}(θ) (1976TO03) is discussed in relation to possible fwave admixtures on the 2^{+} state in ^{4}He 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 ^{4}He near 30 MeV. Several measurements of the ^{2}H(d, n)^{3}He cross section have been made at low energies (E_{d} < 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 E_{c.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 E_{d} = 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 acceleratorbased monoenergetic neutron source reactions, including ^{2}H(d, n), for fusionrelated applications. Measurements of observables for the mirror reactions ^{2}H(d, n)^{3}He and ^{2}H(d, p)^{3}H and the implications of possible differences on the question of chargesymmetry 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 negativeparity T = 0 levels with small nucleon and singleparticle deuteron widths. Analysis (1987KO21) of polarization data for the (d, p) and (d, n) reactions indicates no evidence for a J^{π} = 1^{} level in ^{4}He at 24.1 MeV. Analyzing powers and polarizations for ^{2}H(d, n)^{3}He and ^{2}H(d, p)^{3}H were calculated (1980BE21) in a generalized Rmatrix 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 "Rmatrix approach" and a "direct approach" to the reaction were discussed. Soluble fourbody models have been used (1976FO13, 1979FO08, 1983OS05) to predict the (d, n) cross section. A fournucleon Kmatrix approach is discussed in (1985SO07). See also (1976SA02). The parameterization of polarization observables in terms of matrix elements for ^{2}H + d reactions is given in (1982AD04). The mirror reactions ^{2}H(d, n)^{3}He and ^{2}H(d, p)^{3}H were studied (1990VA04) in a multichannel resonating group framework, and the parameters of J^{π} = 0^{+}, 0^{}, 1^{}, 2^{} resonances in ^{4}He are established. An analysis of all available data on these mirror fusion reactions was carried out (1990LE23) to extract reaction matrix elements for E_{d} ≤ 500 keV. The effect of the ^{2}H(d, n) reaction rate on predicted abundances of light isotopes from primordial nucleosynthesis is investigated in (1991RI03). The ^{2}H(d, n)^{3}He reaction at very low energies (E_{d}(c.m.) < 55 keV) is calculated in a onestep 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 secondorder DWBA calculation in (1990KO26). The fusion of polarized deuterons is considered in (1984HO10) and it is argued that a "neutron lean" d^{3}H 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 ^{2}H(d, p)^{3}H reaction and a comparison with model calculations, see (1987GR08). Recent measurements at low energies (1987KR18) have provided more accurate determinations of the astrophysical factor S(E). See also (1985JA16, 1986BR20). A considerable number of experiments have examined the cross section and polarization observables for differences between the chargesymmetric reactions ^{2}H(d, p)^{3}H and ^{2}H(d, n)^{3}He. 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 E_{d} = 1.5  15.5 MeV are interpreted (1979KO23) to indicate strong evidence for chargesymmetry violation. Measurements of these observables at E_{d} < 5.5 MeV (1979DR01) and at E_{d} = 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 P^{y'}(θ) is a slowly varying function of E_{d}, 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 ^{4}He at 23.9 MeV but do not distinguish between 2^{+} and 1^{}. Measurements (1981GR16) of the cross section and tensor analyzing power for E_{d} = 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 fourbody scattering and breakup including the (d, p) and (d, n) reactions focusing on the integralequation 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 Rmatrix 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 ^{4}He were carried out. Microscopic multichannel calculations reported in (1981HO04) propose an additional lowlying 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 ^{4}He with J^{π} = 0^{+}, 0^{}, 1^{}, 2^{}. An Rmatrix 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 ^{4}He. 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 ^{2}H(d, p) is presented in (1989BO32). See also the study of threebody Coulomb effects in oneparticle 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 ^{2}H(d, n) and ^{2}H(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 E_{d} ≤ 500 keV. The effect of the ^{2}H(d, n) reaction rate on predicted abundances of light isotopes from primordial nucleosynthesis is investigated in (1991RI03).
Measurements and summaries of particle spectra from the breakup reactions (a) and (b) reported since 1973 are presented in Table 4.7 (PDF or PS). Earlier work is reviewed in (1973FI04). The dp and dn spectra obtained for E_{d} = 6  13 MeV and reported in (1972VA04, 1972VA05) are dominated by a broad peak associated with dnucleon quasifree scattering (QFS). A simple quasifree 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. Quasifree scattering was analyzed (1976DJ01) in terms of the modified singleimpulse approximation (MSIA). The finalstate 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 quasifree scattering that is constant and close to one. Energy spectra at E_{d} = 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 nonconservation 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) ^{1}S_{0} pn final state. Protondeuteron coincidence spectra were used in (1972VO13) to test the TriemanYang criterion. The results indicate that the onepole graph is not sufficient to describe the reaction. Threebody breakup energy spectra for E_{d} = 60 MeV (1982FU10) show large forwardangle enhancements and can be reproduced by calculations in the singlescattering fourbody model. Absolute cross sections for the fourbody breakup reaction (b) were measured (1975WA09), and evidence for a double finalstate interaction was obtained. Planewave analysis of measurements made at E_{d} = 34.7 MeV (1978AL21) under the twospectator condition gave an experiment/theory ratio of about 0.14. At 80 MeV (1978LE01) analysis indicated that, in addition to the doublespectator process, the process of double spinflip excitation is important. (See also (1985KO01)). However, good fits to these same data were obtained (1981WA29) by assuming finalstate interactions between both final np pairs and ignoring the doublespectator process. Measurements at 15.7 MeV are reported in (1987ZH11) and interpreted to indicate evidence for a ^{2}He resonant state with a breakup energy of 0.45 MeV. A review of quasifree processes in fewbody systems is presented in (1974SL04). See also (1973SL04) for a critical analysis of models. Offenergyshell corrections to nucleondeuteron scattering amplitudes are explored in (1972DU12). Absolute magnitudes and shapes for QFS processes in reaction (a) are correctly predicted by the use of Eckart clustermodel wave functions. A possible explanation of the colinearity effect involving rescattering is examined in (1976RE08). Calculation of the threebody 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 quasifree scattering are explored (1987BA27) by the use of exact threebody scattering theory for Coulomblike potentials. Fourbody 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 E_{d} = 40 MeV (E_{x} = 24  44 MeV in ^{4}He). In the very low energy region, E_{d} = 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 E_{d} = 9.8  36 MeV (1985NE04) showed a smooth pattern with no indications of resonances. Measurements of vector and tensor analyzing powers at E_{d} = 6  11.5 MeV (1972GR29) show a vector component which is small but nonzero and changes sign between 6.0 and 10.0 MeV, and tensor components which increase monotonically with energy. No resonancelike behavior is observed, but arguments are made that the sign change of iT_{11} suggests a broad resonance near E_{x} = 28 MeV in ^{4}He. (See also (1972ME20)). At E_{d} = 50 MeV the vector analyzing power maximum is 0.32 at about θ_{c.m.} = 60°. Since the earlier compilation on the A = 4 system, a considerable amount of theoretical work on ^{2}H(d, d)^{2}H 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 MalflietTjon twonucleon potential were found to predict no resonance, in agreement with experiment (1975MA43). Microscopic multichannel calculations for A = 4 from the first breakup threshold to E_{c.m.} = 10 MeV carried out (1981HO04) in the framework of a refined resonatinggroup model gave agreement with the wellestablished resonance structure, but ruled out a dd threshold resonance. An additional lowlying broad 1^{} T = 0 resonance was proposed. The work reported in (1985XU01) used singlechannel RGM with a centralforce NN potential having a soft repulsive core. The calculated (d, d) scattering phase shifts and cross sections for E_{d} < 20 MeV agree very well with experiment. The ground and evenparity excited states and the scattering problems for the ^{4}He 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 phaseshift analysis. A study for the case of nonconservation 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 Kmatrix approach is applied to the fournucleon problem (1977BA46), and satisfactory agreement with experiment is obtained for all reactions except ^{2}H(d, d). Work reported in (1979FO08) uses a nonrelativistic field theoretic formalism to develop a solvable model of the fournucleon 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 fourbody solvable model involving intermediate quasiparticle states and calculates cross sections for E_{d} between 6.1 and 51.5 MeV for (d, p), (d, n), and (d, d). Good agreement with experiment is obtained. In (1984FO08) a twobody separable Tmatrix between pairs is used to solve the fourbody equations and oneparameter models are developed to describe lowE phase shifts and cross sections for reactions and scattering. The fourbody equations of Alt, Grassberger, and Sandhas (AGS) are solved (1986FO07), and contributions of pwave (3 + 1) subamplitudes to the ^{4}He binding energy and scattering observables below the fourbody breakup threshold are studied. See also the calculation of tensor analyzing powers in (1989FO13). A review of progress in fourbody scattering and breakup in the integral equation approach is presented in (1987FI03). Calculations of (d, d) cross sections with a threebody formalism including Coulomb interactions are reported in (1986AG03). In (1977BE02) a new model for ^{4}He which treats structure and reaction aspects on an equal footing in a dynamical Rmatrix 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 manybody correlations induced by the shortrange repulsion and mediumrange 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 ^{4}He 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 multiplescattering model is described in (1984BA68). See also (1989ET04). An integral formula for calculating Glauber multiplescattering amplitudes is derived in (1990TA27). A geometric model is applied to highenergy 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 E_{p} ≈ 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 ^{4}He. 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 foreaft asymmetry in the angular distribution were interpreted as providing evidence for a 2^{+} level at 40 MeV in ^{4}He with Γ_{c.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 ^{3}D_{2} 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 ^{3}D_{2} contribution. The absolute cross section for ^{3}H(p, γ) has been studied extensively along with that of the mirror reaction ^{3}He(n, γ) to test isospin mixing, and there are many discrepancies in the published results. Accurate measurements of the ^{3}H(p, γ)^{4}He 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 ^{4}He(γ, p)^{3}H results of (1988BE38). These new results bring the (γ, p)to(γ, n) ratio for ^{4}He 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 timereversal 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 ^{3}H(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 E_{p} = 1.5  5.0 MeV in (1972SM03) and for E_{p} = 1.3  2.9 MeV in (1974BR09). Contour maps of P(θ) are presented. A number of measurements relating to the use of ^{3}H(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 E_{p} = 6  16 MeV are given in (1972MC23). See also (1972PA41) for measurements of flux density for E_{n} = 250 keV, and (1982TH07, 1989BO41) for measurements of tritium breakup contributions. Practical aspects of acceleratorbased neutron source reactions including ^{2}H(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 chargeindependent Rmatrix calculations based on the level parameters of (1968WE14). Similar conclusions were drawn from the polarizationtransfer coefficient measurements presented in (1972HA36, 1974JA20). However, remeasurement of P^{y}, and further measurements of A_{y} 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 chargeindependent Rmatrix calculations is included in (1981DO10). The calculations establish the order of the lowest pwave T = 0 levels in ^{4}He as J^{π} = 0^{}, 2^{}, 1^{}. The reported differences between polarization and analyzing power were investigated in (1974AR01) and related to ^{3} P_{2} ↔ ^{3 }F_{2} transitions enhanced in the region of the 2^{} state. They were also calculated (1977BE28) within the framework of a generalized Rmatrix method. See also the recoilcorrected continuum shellmodel calculations of (1983HA21). Microscopic calculations of the ^{4}He continuum were carried out by a coupledchannels method (1975RA31, 1976RA13, 1977DO03, 1980RA17), by a Kmatrix approach (1977BA46), and within the framework (1980BE18) of a dynamical Rmatrix formalism. Excited states of ^{4}He are discussed as are comparisons with ^{3}H(p, n) and other reaction data. See also the [3N + N] clustermodel study of (1981FU08). Calculations of elastic scattering and charge exchange at intermediate energies using Glauber multiple scattering theory are reported for E_{p} = 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 + ^{3}H interaction is described in (1990DU11).
Measurements of cross sections and analyzing powers for ^{3}H(p, p)^{3}H 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 ^{4}He excited states. Using microscopic multichannel calculations, the investigation of (1981HO04) finds the wellestablished resonance structure, rules out the dd threshold resonance, and predicts a lowlying J^{π} = 1^{}, T = 0 resonance. However, no evidence for a 0^{} or 1^{+} state near E_{x} = 25.5 MeV is found. This same work identifies the observed differences in ^{2}H(d, pol. p)^{3}H and ^{2}H(d, pol. n)^{3}He as resulting from Coulomb effects alone, and explains the differences between the ^{3}H(p, pol. p)^{3}H polarization data of (1976KA12) and the ^{1}H(t, pol. t)^{1}H data of (1978HA38) as resulting from the odd spinorbit component of the nucleonnucleon force. Microscopic calculations of the resonance states in ^{4}He were carried out by (1984CA20) using a modified Rmatrix method and a variational approach, and by (1980BE18) within the framework of a dynamical Rmatrix methodology. See also (1977BE53). Momentum distributions of single nucleon, twonucleon cluster relative motion, etc. were reported in (1988MO09). Scattering and reactions in the A = 4 systems within a Kmatrix formalism were studied (1980BA55). A coupled channels treatment was applied to interpret the positive (1980RA17) and negativeparity (1975RA31) resonances in ^{4}He. See also (1978RA01). The Amado model was used (1977AA01) to investigate Dphase anomalies in ^{3}H(p, p)^{3}H for E_{p} = 4  12 MeV. All possible couplings of p^{3}H and n^{3}He were considered in a calculation of Smatrix elements by (1972HE15). A twodimensional integral equation solution of the A = 4 system was used (1978KR01) to calculate the ^{4}He binding energy and n^{3}He and p^{3}H phase shifts. See also (1977PE13) and the review (1987FI03) of fourbody scattering in the integral equation approach. Cross sections for intermediate energies were calculated by diffraction multiplescattering theory by (1978PE20, 1976LE32), and by the Glauber formalism (1973NA06, 1976FR12, 1979ME08, 1981BI08). A generalized potential description of the p^{3}H interaction is presented in (1990DU11). Collective excitations of ^{4}He are included in a study (1990FI06) of the structure of the continuum spectra in p + ^{3}H scattering at ≈ 30 MeV.
Measurements of the ^{3}H(p, d)^{2}H reaction published prior to 1972 are reported in the previous compilation (1973FI04), and some possible evidence of timereversal invariance violation is discussed. More recently, measurements of angular distributions of the analyzing power for ^{3}H(pol. p, d)^{2}H 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 ^{2}H(d, pol. p)^{3}H reaction. Comparisons were made with the mirror reaction ^{2}H(d, pol. n)^{3}He, and good agreement is found when the reactions are compared at the same exitchannel energies. It is concluded that these results give no evidence for violations of charge symmetry. One additional measurement for the ^{3}H(p, d)^{2}H reaction was reported in (1974JA15). Differential cross sections for E_{p} = 13.600 MeV for θ_{lab} = 15  55° were measured with an accuracy better than 1%. Calculations of differential cross sections for the ^{3}H(p, d)^{2}H 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 ^{3}H(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 ^{4}He 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 chargesymmetry breaking include the ^{3}H(d, pol. n)^{4}He polarization measurements of (1972SM05) and the ^{3}H(pol. d, n)^{4}He and ^{3}He(pol. d, p)^{4}He analyzing power measurements of (1980DR01). In the latter work the authors note large differences for the two reactions for E_{d} below 1.65 and above 4 MeV. Comparisons of the analyzing powers for the inverse reactions ^{4}He(pol. n, d)^{3}H and ^{4}He(pol. p, d)^{3}He are reported in (1982SA05) to be consistent with charge symmetry. A review of acceleratorbased neutron source reactions including ^{3}H(d, n) is presented in (1990DR10). See also (1984MA71, 1984TS01, 1989CO14, 1989CR05, 1989SH17). 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 A_{yy}(θ) in the vicinity of isolated resonances. See also the multichannel resonating group calculations of (1990BL08). A nondynamical calculation of polarization observables for E_{d} 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 particletransfer reactions is used to analyze σ(θ) for reaction (a) at E_{d} = 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 ^{3}H(t, 2n)^{4}He at E_{t} = 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 threebody 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^{3}H system. The twobody decay (b) was used (1988TA29, 1989TA16, 1989TA19) in measurements of the formation probability of _{Λ}^{4}H from K^{} absorption at rest on light nuclei. Theoretical studies of _{Λ}^{4}H production, structure, and decay are reported in (1982KO13, 1984CO1E, 1986DZ1B, 1987YA1M, 1988MA09, 1989TA17, 1989WA25). Calculations of Coulomb effects and chargesymmetry breaking for A = 4 hypernuclei are described in (1985BO17). A fourbody calculation of the 0^{+}  1^{+} binding energy difference is reported in (1988GI1F). Nonmesonic decays are discussed in (1985TA1E, 1986SZ1A, 1990LY1B). Evidence for the existence of a Σnucleus bound state formed in a (K^{}, π^{}) reaction on ^{4}He was reported in (1989HA39). See also (1990HA08, 1990HA11). The possibility of forming doubly strange Ξhypernuclei is considered in (1983DO1B).
Measurements for the ^{3}He(n, γ)^{4}He 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 ^{3}He are reviewed in (1981SH25). Calculations (1981TO03) including mesonexchange currents were able to account satisfactorily for the thermal neutron cross section. A recent Monte Carlo variational calculation in which the scatteringlength 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 twobody meson exchange currents are reported for both ^{3}He(n, γ)^{4}He reaction and the weak ^{3}He(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 (E_{n} = 6.0  17 MeV) the detailedbalanced cross sections of (1981WA18) confirmed the reported ^{4}He(γ, n) cross section (see the section on the ^{4}He(γ, n) reaction) which, when combined with the previously reported ^{4}He(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 ^{4}H. 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 recoilcorrected 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 ^{4}H, excluding the "anomalous" (γ, p)to(γ, n) ratio. For additional related information see reaction 7 on ^{3}H(p, γ) and reaction 21 on ^{4}He(γ, n), ^{4}He(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 measured values for the thermal neutron capture cross section of the ^{3}He(n, γ)^{4}He reaction are listed in Table 4.14 (PDF or PS). 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 ^{3}H(p, γ)^{4}He 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 neutroncapture cross section at 24.5 keV was measured by (1991WE06) to be σ_{nγ} (24.5 keV) = 9.1 ± 0.8 μb. The thermalneutroncapture cross section has been used to estimate the astrophysical Sfactor for the ^{3}He(p, e^{+}γ)^{4}He reaction (1989WO10, 1991WE06). The results indicate that about 10% of the solarneutrino flux in the Davis' experiment can be ascribed to the highenergy ^{3}He + 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 ^{3}He(n, n)^{3}He 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 ^{3}He(n, n)^{3}He and the A = 4 system. A variety of theoretical approaches have been used to describe n^{3}He scattering. At thermal energies, the complex incoherent scattering length for ^{3}He was estimated (1975SE06) on the basis of effective range theory and a BreitWigner analysis. Lowenergy n^{3}He scattering was studied in the integral equation approach (1976KH01, 1976TJ01) and scattering lengths were calculated. Higher energy observables for nucleon reaction channels in ^{4}He were calculated by recoilcorrected continuum shell model techniques (1979HA22), and excellent agreement with experiment was reported. Proton and neutron polarization differences in ^{3}He(pol.n, n)^{3}He and ^{3}H(pol.p, p)^{3}H were analyzed (1977BE53) in the framework of a dynamical Rmatrix model methodology, and quantitative agreement with experiment was obtained. Several resonances are predicted in the vicinity of a narrow resonance near E_{x} = 37 MeV suggested by the phaseshift analysis of (1976LI03). The Rmatrix methodology is used to construct a detailed theoretical model of ^{4}He (1980BE18). Scattering results and phaseshift calculations are presented and discussed and are also compared with resonating group and fieldtheoretic models. Clustermodel calculations of ^{4}He 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 ^{4}He in the ≈ 30 MeV region. The ground and evenparity 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 resonatinggroup calculations, which include distortion effects due to the coupled deuteron cluster, were used (1986KA21) to examine the ground and evenparity excited states and the scattering problem of the ^{4}He 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 ^{1}S_{0} resonance at E_{n} = 0.25 to 1.0 MeV, and that the proton spectra from reactions (b) and (c) reveal no clear indication of an nd, threenucleon or twonucleon finalstate interaction. A more recent measurement (1975WI04) of the ^{3}He(n, p)^{3}H total cross section at E_{n} = 3.5 MeV gives σ_{total} = 422 ± 58 mb. The cross section was measured (1982BO19) in the energy range E_{n} = 0.15  150 keV with an accuracy of 2  3%, and the departure from the 1/v law was investigated. Measurements of the Podd asymmetry in ^{3}He(n, p)^{3}H were made (1981VE08), and an upper limit was obtained. Little theoretical work on reaction (a) has been reported since the previous compilation (1973FI04). A resonatinggroup model calculation was carried out (1976IO01) involving the groupings n + ^{3}He and p + ^{3}H. 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 ^{3}He(n, p) reaction was investigated in a KMatrix 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 chargedparticle spectra are summarized in (1973FI04) and a discussion of evidence bearing on excited states of ^{4}He 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 ^{3}He(d, p)^{4}He 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). Distortedwave calculations for reaction (a) are presented and discussed in (1975NE11). See also (1989BO22). Offdiagonal 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 singleresonance contribution to the cross section and reaction rate at thermonuclear energies is studied (1987GU25), and the effect of electron screening on lowenergy 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 quasifree processes and fewbody systems of (1974SL04). Calculations for reaction (c) in the region of small protontritium relative energies are presented in (1984DU10).
Reactions (a) through (d) are reviewed in the previous compilation (1973FI04). For reaction (a) measurements of analyzing powers A_{y}(θ) for E_{t} = 9.02, 12.86, and 17.02 MeV at θ_{c.m.} = 16°  159° as well as measurements of A_{y}(E) at 90° for E_{t} = 9.02  17.27 MeV were reported in (1977HA42). Marked deviations from the antisymmetric shape predicted by a simple particletransfer 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 E_{c.m.} = 16 MeV (1974RO01). The total cross section was measured for E_{c.m.} = 30  150 keV (1974DW01), and the astrophysical factor S(E) was measured at E_{c.m.} = 17.9  342.5 keV. Total cross section measurements for ^{3}He + ^{3}He at 17.9, 21.7, and 24.0 MeV were reported in (1987BR02). See also (1985SI12). Calculations to determine the NN scattering parameters from finalstate 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 lowenergy 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 Sfactor is calculated with the twochannel approximation of the RGM in (1989VA20). Triton spectra from reaction (b) are discussed in the previous compilation (1973FI04).
Measurements of photonuclear cross sections for ^{4}He 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 Δisobar 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). Momentumdependent terms in the operator and a twonucleon 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 fourbody 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 impulseapproximation calculations involving a reaction amplitude described by the sum of two pole diagrams with a virtual neutron and a ^{3}He 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 impulseapproximation calculation in terms of quasifree nucleons in ^{4}He 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). Clustermodel calculations for energies of a few MeV above threshold are reported in (1974ST08). A lowenergy 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 ^{4}He at E_{γ} = 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 E_{γ} ≈ 80 MeV, and it was concluded that the main mechanism for reaction (g) in this energy region is twonucleon 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, ^{4}He(γ, p)^{3}Hto^{4}He(γ, n)^{3}He, below E_{x} = 35 MeV has constituted a longstanding anomaly in lowenergy 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 excitationenergy range E_{x} = 25  35 MeV, in substantial disagreement with the ratio predicted by conventional isospinconserving theoretical calculations. Data obtained in recent years change this picture substantially.
Relevant measurements include: Theoretical work related to the question includes: (1972GI14, 1972LO11, 1974CH50, 1981HA10, 1983HA21, 1984BA73, 1988WA20). 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 E_{x} = 35 MeV. However, since that time a measurement using monoenergetic photons (1988BE38) indicated that the ^{4}He(γ, p)^{3}H cross section was substantially smaller below E_{x} = 35 MeV than previously thought, and was essentially in agreement with the monoenergeticphoton results for the ^{4}He(γ, n)^{3}He reaction (1954FE16, 1963ZU03, 1966FE07, 1968GO19, 1971BE43, 1972BE06, 1973MA57, 1975IR01, 1977BA35, 1978AR26, 1980BE45). This (γ, p) result has received additional support from a new ^{3}H(p, γ)^{4}He 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) crosssection measurements we obtain, for E_{γ} = 24  31 MeV, a (γ, p)to(γ, n) ratio which is about 1.1, consistent with conventional theoretical predictions and indicating that no chargesymmetry violation is required in ^{4}He 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 ^{4}He between E_{x} ≈ 23  30 MeV. A recent simultaneous measurement of ^{4}He(e, e'p)^{3}H and ^{4}He(e, e'n)^{3}He cross sections (1989SP05) gave a ratio less than 1.2, consistent with the predictions of a microscopic model which assumed a chargesymmetric 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 ^{4}He 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 < r^{2} >^{1/2} = 1.671 ± 0.014 fm. A number of theoretical calculations relating to ^{4}He(e, e) elastic scattering have been carried out. The contribution of twophoton exchange in highenergy largeangle scattering was examined (1972BO63). The elastic scattering form factor was computed (1972CA40) in the localdensity approximation and in the oscillator model with shortrange correlations (1972FI10). Relativistic corrections and their effect on the diffraction minimum were examined (1973FR21). Calculations utilizing selfconsistent BruecknerHartreeFock wave functions (1974CI02) provided estimates of the effects of centerofmass spuriosity. Charge form factors were calculated with manybody meson exchange operators (1977RI15). The effect of shortrange threenucleon correlations was studied (1978HE19). Elastic and inelastic form factors calculated in the method of hyperspherical functions were discussed in (1981BU04). A multiquark cluster effect on the charge form factor was postulated in (1982NA09). The role of tensor and shortrange 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 groundstate structure of ^{4}He. Calculations of electromagnetic form factors for ^{4}He based on quantum hadrodynamics is discussed in (1989LI16). The influence of shortrange 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 twobody operators are reported in (1990SC01). A study of elastic and inelastic electron scattering on ^{4}He 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 ^{4}He is suggested to interpret the details of the charge distribution obtained from the electron scattering form factors for q^{2} ≤ 20 fm^{2}. A study of the 0^{+} state at 20.1 MeV in ^{4}He reported in (1974ZO04) utilized the inelastic form factor and threebody 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. Centerofmass corrections for calculations related to electron scattering are studied and reported in (1980DE30). The effect of finalstate interactions in inclusive electron scattering is discussed in (1980HO26). The method of hyperspherical functions is discussed in (1981BU04). Quasifree peak parameters from calculated (e, e') cross sections are related to sum rules in (1981KO10). Data for electron scattering from ^{2}H, ^{3}He, and ^{4}He are found (1982BO30) to be unified by a nuclear scaling function. The (e, e') cross section was calculated using an interactiontime approximation for dynamic form factors (1982KO26). The existence of yscaling for the quasielastic cross section was demonstrated in (1983DE13). See also the study of (1985KO19). A continuum RPA calculation with finiterange 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 quasielastic peak maximum in ^{4}He(e, e') relative to the eN scattering peak was explored (1985KU02) on the basis of ^{4}He 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 hypersphericalharmonics calculation of the (e, e') form factor (1987SA23). The form factor for (e, e') excitation of the 0^{+} resonance in ^{4}He is discussed in connection with a collective and cluster model calculation (1987VA33) and a symplectic shell model calculation (1988VA22). More recent work includes a recoilcorrected continuum shell model study of the 0^{+} first excited state in (1989HA02, 1990HAZN), a (0 + 2)hbar ω modelspace calculation of ^{4}He observables in (1990WO10), an extrapolation of nucleonmomentum distributions in ^{4}He 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 ionion optical potentials (1989RE07), and the microscopic study of the NN interaction (1989YA11). ^{4}He(e, e') data is utilized in a determination of a phenomenological Δnucleon potential in (1990OC01).
Experiments and data analysis for pion scattering on ^{4}He 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 pionnucleon interaction and the effects of the nuclear medium. Related theoretical work includes the DWIA calculations of (1975HE06), a coupled channel method in the Kmatrix approach (1979GM01), and the pole extrapolation method for separating strong and electromagnetic contributions (1982DA15). Investigation of medium effects by studying quasielastic scattering is discussed in (1983SI21). The question of isospin mixing in ^{4}He and possible chargesymmetry 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 ^{4}He 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 ^{5}He.
Reaction (a) was reviewed by (1984AJ01) under the discussion of ^{5}Li. 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 ^{4}He(p, p)^{4}He 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 distortedwave 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 selfconsistent wave function BruecknerHartreeFock calculation is described in (1974CI02). A review of experimental and theoretical advances in highenergy proton scattering is presented in (1981WA1A). The effect of coupling between the ground state and the first excited state (0^{+}, T = 0) in ^{4}He was estimated in (1984AH03) using a breathingmode model. Phaseshift 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 Dstate admixtures to the dominant Sstate configurations exist in the ^{4}He 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 ^{4}He are discussed in the previous compilation (1973FI04). No recent work has been reported. A formula to represent amplitudes for threebody breakup (reactions (b), (c), (d)) is developed and compared with data in (1987FU10).
Reaction (a) was reviewed by (1984AJ01) under the discussion of ^{6}Li. 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 ^{4}He(d, d)^{4}He elastic scattering have been reported since the previous compilation (1973FI04). Phaseshift 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 orthogonalitycondition model (1980NI07), microscopic coupledchannel model (1983SA39), and the threecluster coupling model (1986MI23, 1987MI06) have been carried out. Nucleonnucleonalpha Faddeev calculations were reported in (1987HA34, 1990BL13). Calculations utilizing a threebody 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 pseudostate method were investigated in (1988KA25). See also the recent work of (1990KU06, 1990KU16, 1991KR02). Early experimental evidence for levels in ^{4}He 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 ^{8}Be. The previous A = 4 compilation (1973FI04) reviews early work on reactions (a)  (d) giving information on excited states in ^{4}He. More recently, the work reported in (1982FI16) studied the effects of ^{4}He 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 ^{4}He of 25.5, 27.8, 29.7, 31.7, and 35.3 MeV. Angular correlations were used to assign J^{π} = 2^{+}, 2^{+}(1^{}), and 2^{+} to the last three of these. An investigation (1981BA39) of the excitation spectra of ^{4}He near E_{x} = 20 MeV by means of an (α, α') experiment at 64 MeV used an Rmatrix representation to extract level parameters E_{λ} = 20.29 ± 0.02 MeV, Γ_{0} = 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 ^{4}He based on the summed neutron and proton spectra from reactions (a) and (b), respectively is cited. No new evidence for ^{4}He levels based on reaction (a) has been reported. However, the tripledifferential cross section measurements of reaction (b) described in (1986RI01) indicate strong population of the ^{4}He 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).
This reaction was reviewed in (1988AJ01) under the discussion of ^{7}Li. No work giving information on levels in ^{4}He has been reported. See, however (1986BA68, 1986CA29, 1986FA13).
These reactions are reviewed by (1988AJ01) under the discussion of ^{7}Be. The previous compilation (1973FI04) summarizes early experimental and theoretical work on these reactions that relate to the structure of ^{4}He. More recently, differential cross sections for reaction (a) (1974SC24) were measured and analyzed by clustermodel direct reaction formulae, and possible contributions from compound structures within the ^{3}He  ^{4}He*(0^{+}) channel involving the first excited state of ^{4}He 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 spinflip knockout processes in reaction (b) is presented. The distribution of effective numbers of np pairs in ^{6}Li over the excitation spectrum of ^{4}He is given. Quasielastic knockout of excited ^{4}He clusters by fast protons at large momentum transfers is discussed in (1987ZH10). The excitation spectrum of ^{4}He is calculated.
This reaction is reviewed by (1988AJ01) under the discussion of ^{8}Be. The previous compilation (1973FI04) cites two reported experiments which provide information on excited states of ^{4}He. More recently, an experiment (1978FU03) at E_{d} = 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 oddparity state at 27.5 MeV. See also (1975GL08). A recent experiment at E_{d} = 18.2  36.8 MeV is reported in (1989BA88). See also (1973HE06, 1973MI20, 1974MI10, 1979WA02, 1981YU01, 1990YA11). An analysis of tensoranalyzingpower data is described in (1990SA40).
This reaction is reviewed by (1988AJ01) under the discussion of ^{8}Be. The previous compilation (1973FI04) cites two experiments which provide information on excited states of ^{4}He at 20.06 and 21.2 MeV. A recent measurement at incident energy E_{i} = 29.1  44.6 MeV is reported in (1989BA88). See also the analysis of data at thermonuclear energies in (1990RA28).
