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3He (1987TI07)


Ground State:

Jπ = 1/2+,

μ = -2.127624 ± 0.0000011 nm,

M - A = 14.93132 ± 0.00003 MeV.

General properties of the ground state of the A = 3 system are under 3H above. The wave function is predominantly S-state (≈ 90%) with S'-state (1 - 2%) and D-state (≈ 9%) admixtures (1975FI08, 1980PA12, 1984CI05, 1984CI09).

For 3He the measured magnetic moment is μ = -2.127624 ± 0.0000011 nm (1978LEZA, 1978NE12). Calculations which include both impulse and pion exchange contributions (1985TO21) are adequate to explain magnetic moments of 3He and 3H. Results obtained with a six-quark bag model are also compatible with the data according to (1986BH05) which includes a discussion of other published calculations. Exchange current contributions to the 3He magnetic properties are calculated by (1983ST11). See also reaction 9 (a).

The rms charge and magnetic radii of 3He determined from electron scattering (see reaction 9 (a)) are γcrms = 1.976 ± 0.015 fm and γmrms = 1.99 ± 0.06 fm. See the discussion under 3H for comparisons with theory.

The binding energy of 3He is 7.718109 ± 0.000010 MeV (1985WA02). Calculations of the binding energy tend to underestimate the experimental results as is also true for 3H. See references under 3H above. Many calculations have been performed in an attempt to account for the 3H - 3He binding energy differences (≈ 0.76 MeV) and various methods are reviewed in (1986FRZU). Most two-body force calculations with realistic forces underestimate this difference, giving ≈ 0.64 MeV for the Coulomb energy of 3He and the problem is not resolved by three-body force calculations (1986GIZS).

Charge and magnetic form factors for 3He have been determined in electron scattering experiments (see reaction 9 (a)). The 3He magnetic form factor has a diffraction minimum at a higher value of q than predicted by impulse approximation calculations (1984FR16) but the isobar model of (1983ST11) satisfactorily accounts for the difference. The 3He charge form factor has a diffraction minimum at q2 ≈ 11 fm-2 and a very large secondary maximum. The charge densities derived from the data indicate a deep "hole" near the origin which remains a problem for theorists (1986FRZU). Impulse approximation calculations significantly underestimate the secondary maximum, and three-body force calculations have improved the predictions but have not solved the problem (1986GIZS).

References not mentioned above or under the 3H discussion, relating to the 3H - 3He binding energy difference and other charge asymmetry effects include ( 1975GI06, 1975ZA03, 1976ZA04, 1978BR03, 1978FR07, 1978FR09, 1978FR17, 1978SI15, 1980PA13, 1981SA04, 1981YA03, 1982BA41, 1982YA01, 1983SA17, 1983SH10, 1985BA24, 1985BA70, 1985BE57, 1985DE56, 1986BE39, 1986CH16, 1986FR23, 1986OS04, 1986SA02, 1986SC03, 1987DR04).

1. 3H(β-)3He Qm = 18.651 keV

See reaction 1 under 3H.

2. 2H(p, γ)3He Qm = 5.494 Eb = 5.494

Measurements of differential cross sections and analyzing powers carried out since the previous compilation (1975FI08) are listed in Table 3.10 (in PDF or PS).

Experimental data on 2H(p, γ)3He and the inverse reaction prior to 1979 were reviewed in (1979BE2C, 1979TO2A). For the 3He excitation energy region Ex < 30 MeV the existing data and theory are reviewd in the experimental papers of (1974MA18, 1979SK01). These papers also described attempts to resolved the discrepancies in the published cross section which are subtantial, e.g. at Ex near 12 MeV the measured differential cross sections for 3He(γ, p)2H range from 90 to 120 μb/sr. Measurements of (1979SK01) at Ex = 10.83 MeV gave 117 ± 11 μb/sr and 1.07 ± 0.11 mb respectively for the detailed balanced differential (θlab = 90°) and total cross section. The T-matrix analysis of the differential cross sections and analyzing power data of (1979SK01) gave an E2 cross section of (12 ± 5)% of the total at Ex = 10.83 MeV which is ≈ 10 times the theoretical estimates of (1975FI08, 1981AU02). Measurements and calculations by (1983KI11) demonstrated the sensitivity of the extracted a2 angular distribution coefficients in the region Ep = 6.5 - 16 MeV to the inclusion of D-state components in the 3He wave function, and are consistent with 5 - 9% D-state probabilities. This effect was incorporated in the analysis (1984KI06) of an improved data set (relative to (1979SK01)), and the results are consistent with an E2 strength of (2 ± 3)% of the total cross section at Ex = 10.8 MeV and an s = 3/2 (E1) strength of (3 ± 5)%, which could arise from the D-state admixture in the 3He ground state. This lower E2 strength is consistent with the electrodisintegration results of (1983SK01). Measurements of the vector analyzing power in 2H(p, γ)3He and 1H(d, γ)3He at very low excitation energies (Ex = 6 MeV) (1984KI14) indicated the presence of s = 3/2 capture strength and the results are consistent with an M1 strength amounting to 1 - 8% of the total cross section. The tensor analyzing power T20 in 1H(d, γ) was measured (1985VE02) and compared with an effective two-body direct capture calculation which used the Faddeev-generated ground state wave functions of (1984GI01). The results were in good qualitative agreement although the calculated T20 was about 20% too small when 3He wave functions having 5 - 9% D-state probabilities were assumed. The data were also analyzed to extract a D/S asymptotic ratio of 0.035 ± 0.01 in the 3He wave function. This results is consistent with the range (0.038 < η < 0.050) calculated (1984GI01) for 3He D-state probabilities between 5 and 9%. The tensor analyzing power Ayy was measured (1985JO05, 1986JO06) and compared with a full Faddeev calculation using the Reid soft-core interaction as a check of the 3He D-state component. The comparison shows that the calculated D-state wave function is about 20% too large (in the 2 - 5 fm region).

In the intermediate energy region, measurements at Ep = 337 and 576 MeV were made (1976HE2A) to compare with measurements of the inverse reaction for a test of time reversal invariance. The results were consistent with no violation but the conclution was a matter of controversy (1980NE03) because of discrepancies in existing data for 3He(γ, p)2H. The situation is reviewed in (1981FA2B) and most recently in (1985BR23). Additional measurements were made by (1980NE03, 1982AB09, 1984CA23, 1985CA42, 1987PI01) with none reporting any evidence for time-reversal invariance violation. See also (1982BR12, 1983SO10). The most recent measurements were those of (1987PI01) and (1985BR23) which report final values which supercede the preliminary data of (1980NE03) and which are in agreement with those of (1984CA23). The data of (1984CA23, 1985CA42) were compared with several theoretical calculations showing that inclusion of meson-exchange current contributions are important in reproducing the cross sections, but the analyzing powers measured at Ep = 500 MeV were not explained by microscopic models. Comparison of the data of (1985BR23) wtih calculations showed that the contribution of delta effects is undramatic but must be included. The recent measurements of σ(θ) and A(θ) for Ep = 99.1, 150.3, 200.7 MeV (1987PI01) were well accounted for by a simple "quasideutero" model. See also (1984ME13).

Theoretical work on the 2H(p, γ)3He reaction and its inverse has focused in large part on the effects on the cross sections and other observables of D-state components in the 3He bound state wave function. In (1973HE20) 3He wave functions generated from Faddeev equations with separable Yamaguchi interactions were used in calculating cross sections, and it was concluded that the isotropic part of the cross section was unlikely to yield information on D-state components in 3He and 2H. Realistic bound state wave functions obtained with NN interactions given by the Reid soft-core potential were used in (1977CR01) in calculations over a wide energy region from threshold to 600 MeV. The results indicated substantial contributions of D-state to both total and differential cross sections, but gave pronounced structure in the cross sections in disagreement with experiment. The calculations of (1981AU02) used the same physical input as (1977CR01) but used different methods and found no distinct signature of D-state components in 3He and 2H for Eγ < 35 MeV. On the other hand the work of (1983KI11) mentioned above demonstrated the sensitivity of the differential cross section to D-state effefcts. In addition, calculations reported in (1984AR07) used the Sasakawa wave function for 3He and found that the tensor analyzing powers for the 1H(d, γ)3He are very sensitive to D-state components in 3He. The data were shown to be consistent with an asymptotic D- to S-state ratio of η = -0.029. At intermediate energies dispersion methods were used to calculate angular distributions for the 2H(p, γ) reaction (1979PR12). Comparisons with data 52.5, 100, and 140 MeV gave reasonable agreement with angular and energy dependence.

3. (a) 2H(p, π0)3He Qm = -129.471 Eb = 5.494
(b) 1H(d, π0)3He

A measurement of differential cross section and tensor-analyzing power T20 at θcm ≈ 0°, 180° for 1H(d, π0)3He was reported at 19 energies between 500 MeV and 2.2 GeV in (1986KE18).

4. 2H(p, n)1H1H Qm = -2.225 Eb = 5.494

Measurements of particle spectra, cross sections, and polarization observables from experiments on deuteron breakup by protons published from 1974 to the present are listed in Table 3.11 (in PDF or PS). A large body of earlier work is reviewed in the previous compilation (1975FI08). A three-particle reaction is completely determined if five kinematic variables are measured. This requires that at least two particles be detected in coincidence for kinematically complete experiments, and this is specified in the table by indicating the particles detected and coincidence requirements. Detector angles are not given explicitly, but the type of geometry and the main emphasis of each experiment is indicated along with the region of phase space explored.

Reviews of three-body breakup reactions are given in (1978SU2A) which includes 3- and 4-body elastic scattering and breakup and emphasizes the precision of the measurements, and in (1978KU13) which contains an extensive discussion of three-particle kinematics, experimental techniques, and the basic theoretical equations of three-particle scattering as well as a review of existing data and theoretical work. See also (1978SL2A) which includes the 2H(p, n)2p reaction in discussion of few-nucleon experiments and theory in general.

The 2H(p, n) excitation curve at 0° rises from threshold to ≈ 50 mb/sr at Ep = 7 MeV (1975FI08). The total cross section for breakup rises from threshold to ≈ 180 mb at Ep = 13 MeV and drops off gradually to ≈ 130 mb at Ep = 25 MeV. The particle spectra contain structure corresponding to pn and pp quasifree scattering (QFS) and to pn and pp final state interactions (FSI). The structure is similar to that of 2H(n, p)2n.

As noted in (1975FI08), the ratio of the np to pp QFS peaks varied between 2 and 3 depending on Ep in the region between 4.5 - 60 MeV and is larger than that of free nucleon-nucleon cross sections especially at low energies. This topic is discussed in (1978KU13 and 1981BL09). Empirical rules for the energy behavior of this ratio are proposed in 1977FU05). Good agreement between the measured ratio with estimates based on the impulse approximation is obtained by (1979JA20). Agreement of pp and np QFS with the spectator model is obtained (1975WI29, 1976FE05) for spectator momenta up to ≈ 200 MeV/c, significant discrepancies are found at higher momenta. The measurements of (1982SH07) indicate that polarization effects on the spectator nucleon in pp QFS is quite different from that of pn QFS.

It has been established (1975FI08, 1978KU13) that deuteron breakup measurements with complete kinematics allow the determination of the two-nucleon scattering parameters with good accuracy and that the np and pp scattering lengths agree with the corresponding free scattering lengths. See also the section of this review on 2H(n, p)2n and the references cited there.

Comparisons with Faddeev calculations show that both the structure and absolute value of the cross sections are described very well (1975FI08) even if the two-particle interaction is taken as a separable potential that reproduces the NN data only at low energies (1978KU13).

A major aim of pd and nd breakup studies is to obtain information about the off-shell behavior of nuclear forces and to explore the role of three-body forces. Much theoretical efforts has gone into attempting to separate the two. Numerical solutions of the integral equations of scattering theory were used by (1983ZA04) to study the effect of the form of the two-particle interaction on the breakup amplitude. The authors of (1981SL02) studied pp correlation spectra at very low kinetic energy with Faddeev calculations which included Coulomb corrections and discuss the possible role of three-body forces. Calculations of cross sections and polarization observables in the approximation of pole and triangular diagrams reported in (1980GO03) gave satisfactory agreement with experiment for Ep = 200 - 340 MeV. Backward inelastic pd scattering for Ep = ≈ 1 GeV was calculated in (1978AM06) and attributed primarily to "triangle" diagrams with single-pion exchange. Observed asymmetry in the angle between the proton momentum transfer and the direction of the spectator nucleon was explored with the separable potential model (1977AL04). Calculations with several separable potentials by (1976HA38) were done to explore the short-range behavior of the nuclear force and suggest that FSI angular distributions between 20 and 50 MeV would be useful. See also (1974ST19) for potential effects. Off-shell and multiple scattering effects were explored (1975LH02) in analysis of Ep = 156 MeV data. Realistic potentials were used (1975IS06) in analysis of QFS data for Ep between 60 and 160 MeV. See also (1975DU13). Differences in pp and pn QFS were stuied (1975HA03) with an energy-dependent-core model. A general discussion and review of quasifree processes in few-body systems is given in (1974SL04). See also (1974HA07, 1974HA36, 1974ME06).

5. (a) 2H(p, p)2H Eb = 5.494
(b) 1H(d, d)1H

Measurements of differential cross sections and polarizations in 2H(p, p)2H and 1H(d, d)1H since the compilation of (1975FI08) are listed in Table 3.12 (in PDF or PS). Reviews of the experimental data and theory may be found in (1975SI2A, 1978SI2B, 1981GR1A, 1982IG2A, 1983ZA01). See also ( 1978DU2B, 1981OH2A).

A phase-shift analysis of pd elastic scattering based on measurements of differential cross section and proton and deuteron analyzing powers for energies below the breakup threshold was performed (1983HU08), and S- and j-split P-phases including the channel-spin mixing, unsplit D- and F-phases and SD tensor coupling were determined. A phase-shift analysis at the three-body threshold using Faddeev equations in configuration space was reported in (1980LA19). Doublet phases were extracted also (1975CH20), and a phase-shift analysis of combined cross-section and spin-correlation data was performed. An analysis of σ(total), σ(θ), and spin correlation-parameter data for Ep = 1.1 - 1.7 GeV was reported in (1980HA50). Theoretical calculations of phase shifts have been done in a Faddeev formalism using different rank-one separable interactions (1975CH20), or using S-wave NN potentials in which the Coulomb interaction was incorporated (1983HU08). Doublet and quartet phase shifts for pd and nd scattering have been calculated for nucleon energies between 2 and 10 MeV using a method based on modified Faddeev differential equations in which the Coulomb interaction is included, and they are found to agree with experiment (1983KU08). Theoretical phase shifts for nd and pd scatterings in the 4P, 2P, 4D and 2D states near threshold were calculated (1977EY01) with an off-shell model with Coulomb corrections taken into account approximately.

The effective range functions calculated from this model (1977EY01) and from a simple on-shell partial wave dispersion model (1977EY02) agree well with each other. The quartet scattering length and effective range reported in (1977EY01) are 4apd = 10.9 fm and 4γpd = 1.3 fm respectively; while the corresponding quantities obtained in (1977EY02) are 4apd = 11 fm, 4γpd = 1.44 fm. The doublet scattering length is 2apd = 1.8 fm, while the parameters of the effective range expansion for the P- and D-states are listed in a table in (1977EY01). In (1976TI02) an analytic expression is derived for the difference in nd and pd quartet scattering lengths and a value 4apd = 10.4 fm is calculated. In (1983FR21) a value of 4apd = 14 fm and 2apd ≈ 0 fm is calculated using a configuration space formalism of the Faddeev equations including the Coulomb interaction. This paper emphasizes the need for new low-energy pd data.

Differential cross sections and polarization data around 800 MeV incident proton energies have been analyzed by Glauber theory (1980WI07) and by non-eikonal approximations to Glauber theory and multiple scattering theory (1979BL08, 1981BL13, 1983IR03). Non-eikonal corrections are seen to be important in explaining tensor asymmetries (1980AL2C) and proton elastic scattering from polarized deuterons (1975GU17, 1979GU14). Data in the Coulomb interference region around 600 MeV are reproduced by taking into account spin effects (1981GA15) and the virtual-deuteron effect (1976GA36) in the Glauber model.

Low energy (Ep ≈ 10 MeV) data have been analyzed in the Faddeev formalism (1975CH19, 1978GR04, 1981SP05, 1982SP03, 1983SA05). The analysis of (1981SP05) and the three-body calculation of (1981KO39) show that the data are sensitive to the S-wave part of the deuteron wave function, and there is evidence for NN off-shell effects in nucleon-deuteron scattering. The difference in the 3S - 3D interactions, which do not appear in the low-energy pd scattering clearly, appear distinctly at 65 MeV (1982KO34). One set of low-energy data has been analyzed in terms of Legendre polynomials (1983GR05).

Coulomb effects in pd scattering have been taken into account in the framework of multiple scattering theory by (1975FR13) and in a three-body formalism by (1976AL13, 1976TI02). See also (1983BL15). In a first attempt to include an approximation for the Coulomb effects in Faddeev calculations, the work of (1982DO07) took into account the influence of the asymptotic Coulomb phase shifts in pd and dp scattering. See Also (1981HA30). Calculations performed in (1981ZA06) at a few energies between 5 and 15 MeV predict differences between the nd and pd analyzing powers. Except for a small angle shift this was borne out by experiment (1982TO06). The effect of Coulomb distortion on the proton analyzing powers in elastic pd scattering is calculated by an effective two-body approximation that includes nd on-shell information only, in (1983ZA01). The agreement with the measured analyzing power at 10 MeV is good but only fair at 14 MeV. A rigorous approach for solving the three-body Coulomb problem in configuration space based on Faddeev differential equations is presented in (1982PO08, 1983KU08). Differential cross sections at 2 MeV and 10 MeV agree well with experiment.

Backward pd elastic scattering in the energy range 0.3 - 2 GeV has been extensively studied. See (1982IG2A) for a review. See also the study of (1974NO2A) who concluded no convincing evidence for N* isoscalar exchange or pion-nucleon exchange beyond the usual nucleon transfer. A phenomenological analysis made in (1974DU05) suggests a mechanism in addition to one-nucleon exchange. The cross sections are roughly reproduced by a calculation in the framework of the pole mechanism (1975KA27). Rescattering corrections to the single-nucleon exchange model were found to be important (1975LE21). Single scattering and n-exchange are shown to account for large-q2 pd data (1976GU2A, 1979GU14, 1979GU2B). The deuteron charge form factor is predicted from the extracted two-body form factor. In (1976TE2A) a double-triangle diagram is considered, while in (1977KO48, 1979KO2A) it is found sufficient to take into account re-scattering with the delta-isobar in the intermediate and one-nucleon exchange. Calculations based on the model of resonance one-pion exchange produce cross sections which agree with experiment but depend strongly on the deuteron wace function (1977SM04). Absence of a peak in the cross section for energies greater than 1 GeV is predicted in (1979KO2A) where light-front-dynamics is applied to describe the scattering. In (1974SH2B, 1977SH17, 1980JE03) calculations are performed in the light of the Kerman-Kisslinger model using a generalized baryon-transfer mechanism on the assumption that N*s exist in the deuteron and that the backward peak is caused by their exchange. The tensor polarization of the deuteron was calculated on the basis of a triangle diagram without free parameters and found to be small in agreement with experiment (1980VE07, 1981VE15). The contribution of the intermediate Δ(1236) resonance is found to dominate the cross section in the 0.3 to 1 GeV region in (1980TO10) where a two-loop diagram is evaluated. A double diagram with intermediate Δ(1232) excitation is used in (1981AN03) to reproduce cross sections at about 600 MeV. In (1981KO09, 1981KO17) it is found necessary to include tribaryon resonances in addition to quasiresonant contributions from the delta isobar, one-nucleon exchange and nucleon-deuteron single scattering to explain the data. Elastic pd backward scattering in the energy range 0.6 - 2.7 GeV has been measured and discussed in terms of one-nucleon exchange and one-pion exchange mechanisms (1982BE30). The experimental plateau in the 180° excitation function for energies > 1 GeV could be explained as excitation of the Δ(1950) in the intermediate state. Experimental data on the sensitivity to the proton polarization and to the deuteron alignment are described in (1981KA45, 1981KA29). In 1980GU16) it is shown that it is possible to explain backward pd scattering at intermediate energies in the framework of multiple scattering theory by searching for the "optimal" approximation for the formal exact solution of the problem. The analysis also permits an extraction of the deuteron two-body form factor for values of q2 which far exceed those measured in e, d elastic data. The accuracy of the "optimal" approximation is studied for a wide range of momentum transfer in (1983LE16).

Cross sections and tensor analyzing powers in dp elastic scattering data at Ed = 10 and 20 MeV were used in a pole extrapolation technique to determine a value of ρD = 0.027 ± 0.005 for the asymptotic D- to S-ratio of the deuteron wave function (1978AM2B). Data at 35 MeV and 45 MeV (1979CO12) gave a value ρD = 0.023 ± 0.0013, while an analysis by (1980GR06) of data at ten different deuteron energies between 5 and 45 MeV gave ρD = 0.0259 ± 0.0007. Note however that the method has been criticized in more recent work as subject to large systematic errors (1981CO2C, 1983LO03, 1984BE2B, 1985PU01). A different method of pole extrapolation was used in (1986HO07) to obtain a D/S ratio of 0.0270 with a statistical error of 2%. The dependence of ρD on the asymptotic S-state amplitude As was studied and reported in (1982AL04).

Elastic dp scattering data in conjunction with data on pp and np elastic scattering between 10 - 26 GeV have been used in (1973ZO05) to determine the deuteron form factor. The ratio of pd inelastic/elastic differential cross sections has been calculated using Glauber theory in (1977DU02). Polarization data at 1 GeV have been analyzed in terms of Glauber theory and the spin-orbit proton-nucleon amplitude has been determined in (1980AL09). Parity non-conserving effects in low energy pd scattering which manifest themselves as an asymmetry in the total pd cross section for longitudinally polarized protons have been examined in (1978HE2A, 1978HE2B, 1979DE27, 1983KL05). The calculations of (1979DE27) indicate an asymmetry of about -0.8 x 10-7.

6. (a) 3He(γ, π0)3He Qm = -134.964
(b) 3H(γ, π0)3H Qm = -134.964

For reaction 6 (a) the previous compilation (1975FI08) cited only one measurement (1969BL10). A 340 MeV bremsstrahlung beam was used, and differential cross sections for coherent π0 photoproduction were obtained by detecting 3He recoils at angles of 20, 30, 40, and 50°. The values ranged from ≈ 2 to 84 μb/sr. Reasonable agreement with impulse-approximation calculations was obtained. More recently, measurements of π0 photoproduction relative yields from 1H, 2H, 3He and 4He were made in the region 1 - 10 MeV above threshold by (1980AR06, 1981AR10). Dipole photoproduction amplitudes E+0 on nucleons were deduced, but were strongly dependent on the theoretical description of the process. Large rescattering effects were observed for 3He. These data were included in the review (1979DE2A) of pion photoproduction experiments and theory. Measurements of differential cross sections near θ = 0° in the P33 resonance region were reported for 3He, natLi and 9Be in (1981BE13). The bremsstrahlung beam from a 500 MeV synchroton was used, and the π0 was measured by detection of the decay photons.

Measurements on both reactions 6 (a) and 6 (b) were carried out in a recent experiment (1984BE08, 1984BE36) in which π0 photproduction on a 3H target was observed for the first time. Bremsstrahlung radiation from a 500 MeV electron beam was used, and the 3H and 3He recoils were detected. The energy-averaged differential cross section in the Δ(1232) resonance region was obtained as a function of momentum transfer both for 3H(γ, π0) and 3He(γ, π0). The averaged cross section is characterized by: (i) A steep fall-off for | t | < 5 fm-2 characteristic of a coherent process. The cross section falls from ≈ 10 μb/sr at | t | = 3 fm-2 to ≈ 1.5 μb/sr at | t | ≈ 5 fm-2; (ii) A change in slope at | t | ≈ 5 fm-2 attributed to the rescattering of the photoproduced pions; (iii) Equal cross sections for 3He(γ, π0)3He and 3H(γ, π0)3H suggesting direct production on one nucleon without final state interactions. The results are compared with an uncorrected impulse approximation calculation, and the agreement is good for | t | < / = 5 fm-2. The experiment also shows that the charge exchange reaction 3He(γ, π+)3H is down by about an order of magnitude from the π0 production.

A number of theoretical investigations of the (γ, π0) reaction on 3H and other few-body targets near threshold have been carried out. For early work see (1975FI08). It is noted in (1976KO04) that whereas charged pions are produced mainly on the nuclear surface, neutral pions can be produced coherently, and π0 photoproduction is in principle sensitive to the entire nuclear matter distribution. In addition, the small π0 photoproduction cross section for a single nucleon (≈ an order of magnitude smaller than that of charged pions) suggests a mechanism for π0 photoproduction in nuclei whereby a charged pion photoproduced on one nucleon can undergo charge-exchange scattering on another nucleon. This two-nucleon mechanism is found (1976KO04) to be important. For a discussion of these and other aspects of the (γ, π0) process in 1H, 2H, 3H, and 4He see the review of (1979DE2A). Other calculations of threshold π0 photoproduction on 3He and 3H are reported in (1978BO13, 1982BE25). Threshold effects in π0 photoproduction on 2H and 3He are treated in (1979LA21). The case of π0 photoproduction by linearly polarized photons on 3H and 3He has been treated in the impulse approximation (1979GA18) for Eγ = 180 - 700 MeV, and the asymmetry in the angular distribution has been evaluated with the use of multipole amplitudes. Finally, an investigation reported in (1984DR07) included both a calculation of π0 photoproduction for the 3H/3He isodoublet in terms of nucleons, and a calculation of π0 photoproduction for nucleons in terms of constituent quarks.

7. (a) 3He(γ, π+)3H Qm = -140.098
(b) 3He(e, e'π+)3H Qm = -140.098

Only a few measurements for reaction (a) have been reported since the previous compilation (1975FI08). Measurements in the energy region of the Δ(1232) pion nucleon resonance were made (1973BA15, 1975BA58) by using bremsstrahlung photons from an electron beam and detecting coincidences between pions and recoil tritons. Differential cross sections were measured at fixed values of the squared four-momentum q2 for Eγ between 227 and 453 MeV. Values for σ(θ) ranged from 1.55 ± 0.13 μb/sr at Eγ = 282 MeV, q2 = 3.1 fm-2 to 0.035 ± 0.008 μb/sr at 452 MeV, q2 = 13 fm-2. At fixed q2 the resonance was shifted toward low energies relative to the same process for a free nucleon. The shift increased with increasing q2 at a fixed angle. The results are compared with several theoretical calculations, and it was concluded that pion rescattering is important (especially at large q2) and that this effect as well as the resonance shift is very sensitive to the S-, S'-, and D-state percentages in the wave functions of the mass-3 nuclei and also to the relative weight of spin-flip and non spin-flip terms in the elementary process. Other measurements of coherent π+ and π0 photoproduction from 3He in the Δ(1232) resonance region are reported in (1984BE08). The differential cross section averaged over the resonance was obtained as a function of momentum transfer. Charged and neutral pions photoproduced on 3He were distinguished by detection and charge-identification of the recoil nuclei. A measurement (1979AR08) of the π+ photoproduction cross section from 3He relative to the cross section for this reaction on a free proton was carried out at incident photon energies 1 - 5 MeV above threshold. Positrons from the π+ → μ+ → e+ decay were detected by Cerenkov counters. The transition matrix element was extracted, and the pion - 3He coupling constant was determined. The results were discussed in relation to magnetic eletron scattering data and the properties of the pionic 3He atom. A recent measurement of π+ photoproduction on 3He is reported in (1986ZA10). The pion-nucleon coupling constant is deduced. The status of pion production near threshold was reviewed in (1979DE2A), and both experimental and theoretical aspects of the process were discussed.

Early theoretical work on π+ photoproduction on 3He is reviewed in (1975FI08). More recently several impulse-approximation calculations (1973LA39, 1975LA12, 1980TI01, 1983BA12) for incident photon energies that included the first pion-nucleus resonance have been carried out. An estimate of rescattering terms is made in (1973LA39), and in (1975LA12) the contribution of meson exchange effects is explored. Calculations in impulse approximation of pion photoproduction near threshold have been reported in (1976OCZZ, 1981TI02, 1981TO13, 1983BA12). See also the review of (1979DE2A). The effects of pion momentum, Fermi momentum, and delta resonance terms on the cross section near threshold were studied in (1980DR05). Realistic wave functions generated from Reid soft-core potentials with the Faddeev equations were used in the claculations reported in (1981TI02, 1981TO13, 1983BA12), while in (1980TI01) account was taken of Fermi motion on the resonance structure. In (1984DR07) threshold photoproduction of pions is calculated for nucleons in terms of constituent quarks and for 3H and 3He, in terms of nucleons. A determination of the π - 3He - 3H coupling constant from threshold pion photoproduction data was made in (1979LE09), and discussions of various methods for determining the coupling constant are presented in (1980DU01, 1984KL02).

The related process of electroproduction of pions from 3He (reaction (b)) has been studied experimentally and theoretically. In the work reported in (1978SK01) triton recoil cross sections were measured at incident electron energies and triton recoil energies corresponding to excitation energies near 20 MeV above the pion threshold. Model calculations were reported in (1977AS07). Calculations to describe coincident cross sections for coherent pion electroproduction in the impulse approximation using realistic wave functions were reported in (1981TI01).

8. (a) 3He(γ, p)2H Qm = -5.494
(b) 3He(γ, n)1H1H Q m = -7.718

Photonuclear cross sections for 3He measured at photon energies ranging from 5.5 - 800 MeV were summarized in (1975FI08). In the most recent measurements included in (1975FI08), differential cross sections for 3He(γ, p)2H at proton cm angles of 60° and 90° for photon energies ranging from 170 - 370 MeV (1975AR01) were reported. Bremsstrahlung photons were used, and protons and deuterons were detected in coincidence. As noted in (1975FI08) the total cross section rises rapidly from threshold to a peak at 1.0 mb at Eγ ≈ 11 MeV and falls off smoothly to < 10 μb at Eγ < 150 MeV. The 90° cross section has a similar shape with a nearly flat peak value of ≈ 100 μb at Eγ ≈ 12 MeV. Differential cross sections measured for 3He(γ, d)1H between 150 and 300 MeV at θcm = 60°, 98° were reported in (1982BR12, 1983SO10) and compared with the time-reversed reaction 2H(γ, p)3He. No evidence for time-reversal-invariance violation was found. The photoneutron cross section for 3He (reaction (b)) was measured from threshold to ≈ 25 MeV with monoenergetic photons (1981FA03) in an experiment which included 3H(γ, n), and 3H(γ, 2n). For 3He(γ, n) the cross section rises from threshold at 7.72 MeV to ≈ 1 mb at ≈ 13 MeV, remains nearly flat to ≈ 17 MeV, reaches ≈ 1.1 mb at 18 MeV and drops to ≈ 0.3 mb near 30 MeV. See the section on 3H(γ, n)2H and (1981FA03) for results of comparison of 3He and 3H photodisintegration cross sections. See Table 3.7 (in PDF or PS) for integrated cross sections and first and second moments.

Many excellent reviews exist in the literature on the photodisintegration of 3He and 3H nuclei (1979TO2A, 1979BE2C, 1977CI2A, 1975WE2A, 1976GO2A, 1975FI08). Since theoretical calculations are often made simultaneously for both nuclei, the section on 3H should be consulted as well. References to the earliest theoretical calculations on the photodisintegration of 3He may be found in the compilation of (1975FI08).

The two-body breakup reaction 3He(γ, p)2H has been investigated and reported in (1977CR01). Cross sections at intermediate energies (Eγ < 600 MeV) are calculated using realistic bound state wave functions obtained with the Reid soft-core potential, but neglecting final state interactions. In (1981AU02) an independent calculation using the same physical input as (1977CR01) is reported. Considerable differences in the results are found and discussed in detail. The importance of final state interactions and possible meson exchange effects is also discussed. Electromagnetic and pion-ecxhange contributions were studied in calculations for Elab = 165 and 330 MeV (1976FI11). For Eγ < 40 MeV, cross sections are calculated (1975GI01) for the two-body photodisintegration of 3He and 3H in the electric-dipole approximation. The calculations were performed within the context of exact three-body theory with the two-nucleon interactions represented by s-wave spin-dependent separable potentials. The numerical results indicate: (i) the 3He and 3H 90°-photodisintegration cross sections are essentially identical in shape; (ii) the 3He(γ, d)p 90° differential cross section has a peak value of approximately 95 μb/sr. (See (1981FA03) for comparison with experiment where it is concluded that agreement is not notably good).

In a later work (1976GI02) the same theory applied earlier (1975GI01) for the two-body breakup for 3H and 3He targets was applied to the three-body breakup reaction 3He(γ, n)1H1H. The numerical results indicate: (i) the 3He(γ, n)1H1H cross section has a peak value of one mb; (ii) the neutron spectra for 3He(γ, n)1H1H and a proton spectrum for 3He(γ, p)np peak sharply in the region of the strong pp final state interaction. In (1975FA05, 1976FA12) hyperspherical harmonics were used for continuum three-body states in the calculation of cross sections for E1 transitions in 3He to final isospin-3/2 states (trinucleon photoeffect). The use of a soft-core potential gives fair agreement with calculations of (1976GI02). In (1978FA01) this work was extented by including an additional grand orbital in the final state and finding reasonable agreement with measured total cross sections. The same formalism has been used in (1978LE11) to calculate several new examples of the trinucleon photoeffect. Agreement with experiment was in general unsatisfactory. The method of hyperspherical harmonics has also been used (1977VO11) to calculate three-body photodisintegration cross sections of 3He and 3H, and good agreement with experiment was obtained. The suppression of the isospin-1/2 three-body photodisintegration of 3He is investigated and explained in (1979LE03), in which exact three-body calculations and evaluation of isospin sum rules are also reported.

The role of mesonic and isobaric degrees of freedom for electromagnetic processes in light nuclei including 3He is discussed in (1983AR21).

9. (a) 3He(e, e)3He
(b) 3He(e, e'p)2H Qm = -5.494
(c) 3He(e, e'n)1H1H Qm = -7.718

Measurements of elastic and inelastic electron scattering cross sections since the compilation of (1975FI08) are summarized in Tables 3.13 (in PDF or PS), 3.14 (in PDF or PS), 3.15 (in PDF or PS).

The elastic charge form factor has been measured for a range of q2 (four-momentum squared) from 0.032 fm-2 to 100 fm-2. Extension of the data beyond q2 = 20 fm-2 shows the charge form factor continues to fall until q2 = 65 fm-2 and then goes up slightly (1978AR05). Recent determinations of the rms radius of the charge density distribution in 3He gave γcrms = 1.976 ± 0.015 fm (1985OT02) and γcrms = 1.93 ± 0.03 fm (1985MA12). Earlier evaluations gave γcrms = 1.877 ± 0.019 fm (1984RE03), 1.935 ± 0.03 fm (1983DU01), 1.89 ± 0.05 fm (1977SZ02) and 1.88 ± 0.05 (1977MC03). The elastic magnetic form factor has been measured for q2 = 0.2 - 31.6 fm-2. The data of (1982CA15) define a diffraction minimum in the magnetic form factor at q2 = 18 fm-2 and a second maximum at 25 fm-2. See also the very recent measurement of the isoscalar and isovector form factors for 3H and 3He for momentum transfers between ≈ 0.3 and 2.9 fm-1 reported in (1987BE30). Values of the rms radius for 3He obtained from the magnetic form factor measurements are in agreement with one another. The values for γmrms are 1.93 ± 0.07 fm (1985MA12), 1.99 ± 0.06 fm (1985OT02), 1.935 ± 0.04 (1983DU01) and 1.95 ± 0.11 (1977MC03).

No theory has yet been successful in reproducing the charge form factor data over the entire range of q2. Inclusion of a six-quark admixture in the 3He wave function results in better agreement with experimental data in the whole region of momentum transfer up to q2 = 36 fm-2 as compared with pure nuclear models (1984BU24, 1984BU42). A second diffraction minimum is predicted at q2 = 50 fm-2 (1978HA09, 1982HA09, 1984BU24). The effects on the calculated charge form factor of the nucleon polarization (1982DR01) and the pair current (1983BE08, 1983DR12) calculated in the constituent quark model have been discussed as have multi-quark clusters (1982NA09, 1984HO22, 1985KI12, 1985MA24). The dimensional-scaling quark model is discussed in (1978CH2A). Isobar currents, mesonic exchange currents and other corrections of relativistic order (1976DU05, 1976HA33, 1976KL02, 1977HA03, 1977RI15, 1978HA09, 1978SI15, 1979GI08, 1979SA39, 1981FI05, 1981HA07, 1981TO08, 1982HA09, 1983AZ01, 1983GI11, 1983HA04, 1983HA18, 1983MA58, 1983SA28) have been examined. The 3He charge density determined from the charge form factor is seen to exhibit a central depression when the protons are treated as point charges (1978SI2B). This feature of the charge density is not reproduced by non-relativistic Faddeev calculations (1978SI2B), even when different potentials are used (1981FR15). A suggestion (1981NO04) based on a variational calculation using a simple trinucleon wave function, that the central depression could be attributed to a two-pion exchange three-body force, is not borne out by a more rigorous Faddeev calculation in which a two-pion exchange three-body force is added to a realistic nucleon-nucleon interaction (1981TO08). A variational method was employed (1984HU09) to calculate the trinucleon ground state properties, and it was concluded that the charge form factor is rather insensitive to the addition of different three-body forces. See also (1986SA08). Inclusion of meson exchnage currents, isobaric processes and other corrections of relativistic order is able to reproduce the central depression (1978HA09, 1982HA09). The bearing of these ingredients on current conservation is discussed in (1986LI09). Arguments based on QCD presented in (1986AB02) indicate that the central depression is due to the presence of large hidden-color components. Ambiguities in the point charge density are discussed in (1982HA30). Errors in the determination of the charge distribution are discussed in (1978BO21, 1981BO13, 1982BO08, 1984CO06).

The magnetic form factor data are not theoretically reproduced over the entire range of q2. Inclusion of meson exchange currents in the 3He wave function is essential to explain the diffraction minimum (1980RI04, 1982CA15, 1984MA26). The importance of the D-state of the trinucleon and the short-range behavior of the S- and D-state wave functions in determining the magnetic form factors of the three-body system is shown in (1975BA08). The role of the nine-quark state is discussed in (1985AN13). Parity violating asymmetries in elastic electron-nucleus scattering are considered in (1981FI05). The effect of clustering on the electromagnetic form factors of 3He and 3H is studied in (1976TA06). A brief review of theories on elastic electron scattering by 3He and 3H is contained in the talks reported in (1977CI2A, 1978SI2B). See also (1977NE2A, 1984FR16, 1985BO44) for a discussion of 3He electromagnetic form factors. Pionic contributions to very-forward elastic scattering are discussed in (1986KA01). An analysis of inclusive quasielastic electron scattering data which can be interpreted to imply an increase in the nucleon radius in 3He compared to the free nucleon radius is presented in (1986MC03). For other elastic scattering work see also (1974AR09, 1977DI10, 1977DU01, 1982TO08, 1986KI10).

In inelastic electron scattering experiments, a 2S - 2S monopole transition has been observed (1975KA04, 1975KA28) and a possible excited state at 10 MeV has been discussed (1979JO02). The first experimental separation of the transverse and longitudinal response functions has been carried out and reported in (1980MC01). The structure function has been derived from experimental data (1982RO16), while longitudinal and transverse form factors were derived from data in (1984KO05). The inelastic electron scattering data cover a momentum transfer range 0.09 < q2 < 1 fm-2 (1975KA28), q2 = 5 fm-2 (1976MC01), 2.5 < q2 < 7.1 fm-2 (1978KU11), 4 < q2 < 4.9 fm-2 (1979DA14), 20 < q2 < 128 fm-2 (1982RO16) and 1 < q2 < 2.5 fm-2 (1984KO05).

Theoretical fits to the data are made mainly using the impulse approximation (1981BI01) with wave functions calculated by the Faddeev technique (see (1976DI09) and the experimental papers). The spectral function is derived (1983ME03) in the plane wave impulse approximation. Contributions of meson-exchange currents and final state interactions to the longitudinal and transverse response functions of 3He are estimated in (1985LA04). The effect on inelastic electron scattering from 3He of meson exchange currents (1983BI05) and quark clusters (1981PI04, 1981PI2B) has been studied. Theoretical descriptions of y-scaling effects in inclusive electron scattering are discussed in (1982BO30, 1983CI11, 1983CI14, 1986GU10). The question of loose quarks in nuclei was raised (1986OE02) in connection with structure function calculations. The use of quasi-elastic scattering of polarized electrons on polarized 3He as a probe of the subdominant components of the 3He wave function has been explored in (1982WO05, 1984BL02).

The channels associated with two- and three-particle electrodisintegrations of 3He have been separated using 3He(e, e'p)2H reactions (1981KO25, 1982GO06, 1982JA06, 1983GO01). The proton momentum distribution of 3He (1982GO06, 1982JA06, 1983GO01) and spectral function (1980GO09, 1982JA06) have been determined and fitted with various theoretical models for the 3He wave function and nucleon-nucleon potential. A theoretical calculation in the framework of the Faddeev fromalism in which a one-term s-wave spin-dependent separable interaction fitted to the two-nucleon scattering data is used, is found capable of explaining two-body electrodisintegration of 3He near threshold and possibly at higher excitation energies (1977HE03, 1977HE22). High resolution (e, e'p) experiments are reviewed in (1985DE56) where it is concluded that (e, e'd) data of (1985KE05) constitute evidence for direct coupling of the virtual photon with correlated nucleon pairs.

Sum rules for electron scattering are discussed in (1979JO02, 1980MC01, 1981TO11) and in other references cited in (1975FI08). A recent calculation (1986EF01) involving sum rules in analysis of longitudinal (e, e') spectra gave agreememt with traditional descriptions involving only nucleon degrees of freedom. For other work see also (1978CI2A, 1979CI2A, 1982BO30, 1983CI14).

10. (a) 3He(μ-, ν)3H Qm = 105.130
(b) 3He(μ-, ν)2H, n Qm = 98.872
(c) 3He(μ-, ν)1H, 2n Qm = 96.648
(d) 3He(μ-, νγ)3H Qm = 105.130

No experiments on the above reactions have been reported since the compilation of (1975FI08). Theoretically estimated values of the total capture rate for 3He + μ- are 2253 s-1 (1978TO01) and 1391 - 2408 s-1 (1980HA46). Partial capture rates calculated for reaction (a) are 1264 s-1 (1978TO01), 1500 s-1 (1978HW01), 1433 ± 60 s-1 (1975PH2A), 1476 s-1 (1975KI2A), and 1375 - 1537 s-1 (1976SA06). Calculations were also made and reported in (1986CO13). Polarizations and asymmetry parameters for reaction (a) treating the nuclei as elementary particles are calculated as well in (1976SA06). The elementary particle method and impulse approximation method are compared in (1975PH2A) where a capture rate of 414 s-1 for reaction (b) and 209 s-1 for reaction (c) is calculated. The total capture rate is calculated (1978RA25) for the reaction 3He + μ- and for reaction (a) as a function of the ratio of the induced pseudoscalar and axial vector coupling constant (gp/gA). The extracted values for gp/gA lie between 10 and 18.

The photon spectrum for the radiative capture reaction (d) has been calculated (1981KL03, 1984KL02) using the impulse approximation with a realistic function and the elementary particle method. A relativistic calculation made in (1980FE02) disagrees with the calculations of (1978HW2B) which are based on current conservation and a special linearity hypothesis. In (1976BE04, 1980GO2D, 1981GM01) the elementary particle method is employed to analyze reaction (d).

A review of muon capture by 3He is contained in (1977PH2A).

11. (a) 3He(π±, π±)3He
(b) 3He(π-, π0)3H Qm = 4.075
(c) 3He(π+, p)2p Qm = 125.855
(d) 3He(π-, p)2n Qm = 130.557
(e) 3He(π-, n)2H Qm = 132.782
(f) 3He(π-, π+)3n Qm = -10.305

Measurements of the pion elastic scattering reaction (a), charge exchange reaction (b) and pion absorption reactions (c) - (e) on 3He since the compilation of (1975FI08) are listed in Tables 3.16 (in PDF or PS), 3.17 (in PDF or PS), 3.18 (in PDF or PS) and 3.19 (in PDF or PS) respectively.

The angular distributions for π± scattering by 3He at energies between 260 - 310 MeV comfirm the fixed angle (θ ≈ 75°) minimum seen at lower energies and show a deep minimum at θ ≈ 110° (1980KA17). The data of (1976SH2B, 1978FA06, 1980FA12, 1981KA17, 1984FO18) for reaction (a) are not reproduced at all energies by optical model calculations. A value of 1.95 fm for the magnetic radius of 3He is extracted by the authors of (1980FA12) from their data. Estimates of the π-3He - 3H coupling constant are made in (1976SH2B, 1978FA06), and a theoretical value obtained in (1979LE09, 1984KL01). The observation of the violation of charge symmetry in π± scattering on 3H and 3He in (1984NE01, 1984NEZY) is questioned by the authors of 1984KI13) who comment that the experimental results can be explained as the manifestation of multiquark resonances in interacting hadronic systems. See also (1986KI08). A theoretical model for the distribution of matter in the 3He - 3H system (1985BA24) is, however, able to explain the observed charge-symmetry violating effects. Off-shell effects in pion 3He scattering are examined in (1980MU16, 1984GM01). A theoretical optical potential including spin is used in (1975LA15, 1975LA19) to analyze π- - 3He data and it is proposed that π- - 3He scattering can provide information on the magnetic form factor of 3He. A Glauber theory calculation reported in (1975GO29) examines the effects on π- - 3He scattering of the details of the nuclear wave function and of a repulsive core. A model based on the use of a simple pion-nucleus potential proposed in (1981NI05) has been used to determine the value of the nuclear mass radius of 3He in the region of the Δ33 resonance. Scattering length for π - 3He are calculated in work reported in (1978LO16, 1978TH2A, 1979BE13, 1979BE2C, 1981BE63, 1982MU13, 1983GE12, 1985BE56).

In references reported here all experimental data for reaction (b) are analyzed using Glauber theory which gives good to fair fits. The authors of (1979KA02, 1982OR06) have performed optical model calculations as well and get an unsatisfactory fit to their data by both methods. Dominance of spin-flip contributions is suggested by the data (1980BO03, 1982CO01, 1982KA02). The effective number of nucleons and Pauli blocking effects are deduced in (1982CO01) from measurements reported there of the continuum angular distributions. Pauli principle effects were also studied in (1986NA05). Optical model calculations (1982MA26) and Glauber model calculations (1980GE06) are used to show that the differential cross sections are insensitive to the magnetic form factor of 3He. The importance of spin-flip contributions first pointed out in (1975SP06) in a Glauber calculation was later confirmed in (1977LO13). Both reactions (a) and (b) are investigated theorectically using coupled Schrodinger equations (1982AV2A), four-particle equations (1979BE13, 1980BE55) modified in the spirit of the impulse approximation (1981BE46), and optical potentials (1976MA11, 1977LA06, 1980WA09). The effect of center-of-mass correlations and intermediate states of π - 3He scattering can be ignored (1981ME14). A review of these relations is contained in (1978NE2B).

Proton spectra for the reactions (c) and (d) with emphasis on the kinematic region of two-nucleon pion absorption have been measured and reported in (1980KA37, 1981KA41, 1981KA43) and (1983KA14) which reports measurements of quasifree scattering as well. The isospin dependence of pion absorption by nucleon pairs has been studied experimentally in work reported in (1981AS10, 1984MO03). The strong suppression of pion absorption by nucleon pairs having isospin equal to one, in the resonance region, is explained by theories based on the delta-isobar intermediate excitations (1982LE18, 1982TO18, 1984SI03). See also (1985OH09, 1986MA21). The same suppression of absorption on isospin-one nucleon pairs for low energy s-wave pions has been used to relate the 1s absorption width in the pionic atom 3H to that of 3He (1985WE04). See also (1980SC24).

Reactions (d) and (e) with stopped pions have been measured (1982GO04) and branching ratios deduced for all observed final states. Theories for pion absorption on 3He at threshold have been proposed in work (1978JA02) based on the two-nucleon absorption model, and in (1980AV2A) in which coupled Schrodinger equations are solved. The energy dependence of the cross sections for reaction (e) measured for pion energies between 50 - 575 MeV suggests the formation of an isospin equal to 1/2πN resonance in the intermediate state (1981KA26, 1981OR01, 1982OR06).

The photon spectrum from radiative and charge exchange capture of pions in 3He was measured (1974TR2A) and a value of the Panofsky ratio P3 = 2.68 ± 0.13 was obtained. An impulse approximation calculation gives P3 = 2.82 (1978GI13). The Panofsky ratio and photopion production crosss section at threshold on 3He are investigated in a soft-pion approach to the 3He - 3H weak axial-vector form factor reported in (1978GO11, 1980GO2D). See (1977BA2A) for a review on radiative pion capture reactions.

Information about the interaction between pions and nuclei at low relative momenta has been extracted from measurements of X-rays from pionic 3He and reported in (1977AB2A, 1978MA12, 1980MA20, 1982BA43, 1983BA39, 1984SC09). For a discussion of reaction (f) see reaction 2 in 3n.