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3He (2010PU04)


Ground State:

Jπ = 1/2+

μ = -2.127497718 ± 0.000000025 μN

Mass Excess, M - A = 14.93121475 ± 0.00000242 MeV

Decay Mode: stable

Binding Energy, EB = 7.718043 ± 0.000002 MeV

Proton Separation Energy, Sp = 5.493478 ± 0.000002 MeV

A topic of interest in connection with the mass 3 nuclei is the difference in binding energies of 3H and 3He and the relationship of this difference to charge symmetry breaking (CSB). The binding energy of 3H is larger than that of 3He by a little less than 764 keV. There are several reasons for this difference; see (1990MI1D, 2005FR02, 2006MI33) and references therein. The two most obvious differences between 3H and 3He are the presence of the two protons and their associated Coulomb interaction in 3He and the larger masses of the two neutrons in 3H. According to results presented in Table I in (2005FR02), the Coulomb interaction accounts for about 85% of the binding energy difference and the larger neutron masses produces about a 2% effect on the binding energy difference due to the different kinetic energies. Additional relativistic and electro-magnetic (EM) effects contribute a little less than 4%. Using chiral perturbation theory and Faddeev methods, two- and three-body interactions with CSB aspects included are found to contribute the remaining approximately 9% of the binding energy difference. The up-down quark mass difference and EM effects at the quark level are the sources of the CSB in the strong interactions (2005FR02).

In addition to having an effect on the 3H-3He binding energy difference, CSB should also be seen in differences of the distributions of neutrons and protons in these nuclei. If charge symmetry were exact, the rms radius of the neutron in 3He should be the same as that of the proton in 3H and similarly for the rms radii of two protons in 3He and two neutrons in 3H. By analyzing the results of π+ and π- elastic scattering from 3H and 3He, it is reported in (1991GI02) and discussed in (2007KR1B) that the rms radius of the neutron in 3He is larger than that of the proton in 3H by 0.035 ± 0.007 fm. Similarly; it was found that the rms radius of the protons in 3He is larger than that of the neutrons in 3H by 0.030 ± 0.008 fm.

For more on charge symmetry and charge symmetry breaking, especially as it relates to differences in the scattering lengths app and ann, and how that relates to the difference in binding energies of 3H and 3He, see (2009GA1D) and references therein.

In the discussion of the ground state of 3H, it was mentioned that - in an asymptotic sense - 3H can be considered to be a deuteron and a neutron in a mixture of an S and a D state with an asymptotic ratio CD/CS = ηt(ave.) equal to -0.0418 ± 0.0015. For the analogous case in 3He, the asymptotic form of the ground state can be considered to be a mixture of a deuteron and a proton in a mixture of S and D states. By studying TAP's for proton pickup reactions by polarized deuterons from 93Nb, 63Cu and 89Y targets with energies below the Coulomb barrier, a value for the D state to S state asymptotic ratio η3He = -0.0386 ± 0.0046 ± 0.0012 was reported; see (1995AY03). In addition, in a study of the TAP for capture of low energy polarized deuterons by protons, a value of η3He = -0.0399 ± 0.0091 is reported in (1997RI07, 1997SC31). An inverse square error weighted average of these two values is η3He(ave.) = -0.0389 ± 0.0042. See (1989VU01) for a detailed comparison of measured and calculated values of ηt and η3He.

By measurements of isotope shifts in helium, determinations of the nuclear rms charge radius of 3He are reported to be 1.9506 ± 0.0014 fm (1995SH12) and to be 1.9642 ± 0.0011 fm (2006MO08). Electron scattering results reported in (1994AM07) give rch = 1.959 ± 0.030 fm.

The magnetic dipole moment of 3He is -2.12749772 ± 0.00000003 nuclear magnetons; see (1993FL1B, 2000MO36).

A theoretical study of the electric dipole moment of the 3He nucleus is reported in (2008ST14).

An important experimental advance that has occurred since the previous evaluation is the widespread availability of polarized 3He targets. The techniques for producing polarized 3He targets are discussed in detail in the review article (1997WA39) and in (2002GO44) as well as in the context of scattering of polarized electrons from polarized 3He targets in (1993AN12, 1996AN25). Two methods have been used for producing polarized 3He targets. See section 4 of (2002GO44) for details.

An important theoretical advance is the ability to include the Coulomb interaction in scattering and break-up reactions such as occur in proton-deuteron scattering. In the hyperspherical harmonic approach, see (2009MA53) and references therein. In the Faddeev method, see (2009IS04, 2009WI16, 2009WI17) and references therein. In the momentum space Alt-Grassberger-Sandas method, see (2008DE1D, 2009DE47) and references therein.

As was mentioned in the Introduction, the Gerasimov-Drell-Hearn (GDH) sum rule relates the anomalous magnetic moment of a system to an energy weighted integral of the photoabsorption spin asymmetry. References to the original papers in which the sum rule is obtained can be found in (2008SL01), for example. This sum rule has been tested for protons (2004DR12, 2008DR1A). It is under investigation for the neutron and the deuteron; see (2009FI06) and (2004AR26, 2009WE1A) and references therein. The existence of polarized 3He targets allows this sum rule to be tested in this case as well.

The following comment, relevant to the standard notation related to the GDH sum rule, is a private communication from Dr. A.M. Sandorfi, JLab (2009):

The Gerasimov-Drell-Hearn-Hosoda-Yamamoto sum rule relates an energy-weighted integral of the total photo-reaction cross sections with photon and target spins parallel and anti-parallel to the anomalous magnetic moment of the target, ∫ dω(σP - σA)/ω = 4Sπ2α(κ/M)2. In the literature, helicity designations have sometimes been used for the parallel and anti-parallel cross sections, and this has created some level of confusion. The helicity of a particle or photon is defined as the dot product of spin and a unit vector in the direction of the momentum, S ⋅ p/|p|. The total helicity is only usefully defined in the center of momentum (CM) frame, since the target is stationary in the laboratory. In the CM frame, the photon and target momenta are opposed, so that when their spins are parallel, their helicities have opposite signs. Thus for γ + 3He reactions, the parallel-spin cross section is associated with a total channel helicity of 1/2 and similarly anti-parallel spins correspond to total helicity 3/2.

In Sandorfi's comment, the limits on the integral are the threshold energy for photoabsorption at the low limit and infinity at the upper limit. The mass of the target is M and must be expressed in units of inverse length to match the cross section units on the left-hand side of the integral. Note that all masses in this discussion are nuclear masses, not atomic masses. The ratio of the nuclear magnetic moment to the nuclear magneton can be written as μ/μN = 2(Mp/M)(Q/e + κ)S, where κ is the anomalous magnetic moment. For 3He, the measured value for μ is -2.1275 μN, which leads to a value of κ = -8.3678.

A second sum rule involving the same photoabsorption cross sections is the forward spin polarizability, γ0 = (-1/8π2)∫ dω(σP - σA)/ω3. The limits on the integral are the same here as in the GDH integral. See (2008AH01, 2009WE1A) for studies of the GDH and γ0 sum rules where indirect methods were used to obtain experimental values for the integrals for 2H. No experimental results have been reported for γ0 for 3He.

For 3He, using the value of kappa presented above, the value of the GDH integral is 497.94 μb. For the neutron, the value of the GDH integral is 233.15 μb. One would expect that, above the pion threshold, most of the contribution to the 3He GDH integral would come from the neutron, since the polarization properties of 3He are primarily due to the neutron in 3He. Thus, much of the difference of about 265 μb between the neutron and 3He values of the GDH integral must come from the energy region between the 3He photoabsorption threshold, 5.49 MeV, and pion emission threshold, about 135 MeV. Studies of the contribution to the GDH integral near the 3He photoabsorption threshold using the capture processes 2H(pol. p, γ)3He and 1H(pol. d, γ) are reported in (2000WU02, 2001WE07).

Generalizations of the GDH sum rule which make use of virtual photons have been obtained; see (2000KO1Q, 2001DR1A, 2001JI02, 2008SL01). See 3He reaction 11 for studies related to these generalized GDH sum rule.

1. 3H(β-)3He Qm = 18.5912 keV

The decay is to the ground state of 3He. The half-life is 12.32 ± 0.02 years or 4500 ± 8 days. The log ft value is 3.053 ± 0.001. See 3H reaction 1.

2. 1H(6Li, α)3He Qm = 4.0196

A study of this reaction at E(6Li) = 30 MeV is reported in (1994AL54). A peak in the α spectrum was observed corresponding to the 3He ground state, but no other structure was seen to indicate the presence of any excited states in 3He. See 3H reaction 2 for an analogous study with a 6He beam and 3H final state.

3. (a) 2H(p, γ)3He Qm = 5.4935
(b) 2H(p, e+e-)3He Qm = 4.4715
(c) 2H(p, p'γbrem)2H
(d) 1H(d, d'γbrem)1H

Shown in Table 3.2.1 of (1975FI08) are references for reaction (a) at Ep = 24 keV - 197 MeV available in 1975. Table 3.10 preview 3.10 (in PDF or PS) in (1987TI07) lists references for the period between 1975 and 1986 for Ep = 6 - 550 MeV. Table 3.5 preview 3.5 (in PDF or PS) of the present work contains a list of the experimental papers for this reaction that have appeared since (1987TI07). For Ep between about 0.1 MeV and 50 MeV, the angular distribution of the gamma rays shows a sin2θ pattern suggesting a predominant E1 capture process. At higher energies, it has been necessary to include additionally M1, E2 and M2 multipoles to obtain reasonable fits.

As will be discussed further below, in the limit as the center of mass energy approaches zero, the reaction 2H(p, γ)3He proceeds by roughly comparable s-wave and p-wave components of the three-body continuum wave function. To a large extent, this is to due an aspect of the Coulomb interaction which gives rise to a non-zero p-wave amplitude in the limit as the energy approaches zero. By contrast, the reaction 2H(n, γ)3H is 100% s-wave capture in the same energy limit since the p-wave amplitude goes to zero in this energy limit in the absence of the Coulomb interaction. Also note that the M1 multipole arises from s-wave capture and the E1 multipole comes from the p-wave capture.

The low energy behavior of the cross section for the reaction 2H(p, γ)3He has important astrophysical implications. This reaction is an essential part of the deuterium burning phase of protostellar evolution. At higher stellar temperatures, it is step two in the proton-proton chain for burning hydrogen into helium. For more details and further references, see (1997SC31, 2002CA28, 2005DE46). A compilation and R-matrix analysis of nuclear reaction rates involved in Big Bang nucleosynthesis was reported in (2004DE48, 2005DE46). Graph 1a, page 232, in (2004DE48) shows the astrophysical S-factor for the reaction 2H(p, γ)3He for Ecm from near zero up to 10 MeV, compiled from data sets stretching over forty years. The R-matrix analysis has the M1 multipole slightly larger than the E1 multipole for Ecm less than 10 keV and E1 being dominant for energies above 10 keV. The M1 contribution to S(E) is nearly flat from zero energy to around 100 keV. Specifically, as shown in Table 3 of (2004DE48), S(0) is found to be 0.223 ± 0.010 eV ⋅ b of which 60% (0.134 ± 0.006 eV ⋅ b) comes from the M1 contribution and 40% (0.089 ± 0.004 eV ⋅ b) from the E1 contribution. Table III and Fig. 16 in (1997SC31) show the percent M1 contribution of the capture cross section dropping from about 54% at zero energy to about 16% at 75 keV. The NACRE collaboration (1999AN35) used a polynomial fit to existing data and obtained S(0) to be 0.20 ± 0.07 eV ⋅ b. The LUNA collaboration (2002CA28) obtained cross sections and S-factors for energies below about 20 keV. The results are shown in Fig. 7 of that reference and the value of S(0) is given as 0.216 ± 0.006 eV ⋅ b. However, in (1997SC31) the value of S(0) is reported to be 0.166 ± 0.005 eV ⋅ b. An analysis of existing data reported in (2009AR02) results in a value of 0.162 ± 0.019 eV ⋅ b for S(0). Fig. 2 in (2000NE09) shows the S-factor for Ecm from near zero up to 10 MeV. This figure was obtained by combining the results of (1997SC31) up to 57 keV and the world data given in (1999AN35) for higher energies. Proton capture reaction rates calculated over the same energy range are given in Table 1 of (2000NE09). Low energy cross sections, S-factors and thermonuclear reaction rates are reported in (1997MA08) and compared to other measurements and theory. A weighted average of the two most recent measurements (1997SC31, 2002CA28) gives an S(0) value of 0.19 ± 0.03 eV ⋅ b where the uncertainty has been adjusted to represent the spread in the reported values. Note that this value agrees with that reported in (1997MA08). This reference gives S(0) to be 0.191 eV ⋅ b. In a study of the electromagnetic properties of A = 2 and 3 nuclei (2005MA54), the pair-correlated hyperspherical harmonics method was used with modern two- and three-body interactions and currents to calculate among other things the S-factor for low energy p + d capture. The results were in agreement with the LUNA data as well as some older data; the quoted value of S(0) is 0.219 eV ⋅ b. A calculation of the M1 contribution to S(0) is reported to be 0.108 ± 0.004 eV ⋅ b (1991FR03), where the given uncertainty is somewhat subjective.

A summary of experimental vales of the astrophysical S-factor for the reaction 2H(p, γ)3He is given in Table 3.6 preview 3.6 (in PDF or PS).

There have been two studies of the reaction (b); see Table 3.7 preview 3.7 (in PDF or PS). By observing the energies and angles of the outgoing electron-positron pairs, the energy and angle of the equivalent virtual photon is determined. A study reported in (1998JO15) used Ep = 98 and 176 MeV. Cross sections for both 2H(p, e+e-)3He and 2H(p, γ)3He reactions at laboratory angles of 40° and 80° of the real and virtual photons were measured and the ratio compared to calculations. With 98 MeV protons, it was found that the experimental results for this ratio exceeded theory by 60% to 75%, depending on the angle of the outgoing real or virtual photons. However, with 176 MeV protons better agreement was obtained between theory and experiment. The same model was used for both reactions and the authors comment that the model is in reasonably good agreement with the 2H(p, γ)3He data. The reaction 2H(p, e+e-)3He was studied also at Ep = 190 MeV at four center-of-mass angles between 80° and 140°, as reported in (2000ME14). Because the available energy is close to the threshold for pion emission, it was expected that mesonic degrees of freedom and nucleon excitation might be of importance. In addition to cross section measurements, this reference reports the determination of four electromagnetic response functions. The experimental virtual photon angular distribution is in reasonable agreement with calculations based on a relativistic gauge-invariant model, but the same is not true for the response functions. The authors suggest that virtual Δ excitation may be playing an important role in the response functions. The theory used for comparison is reported in (1998KO60).

The nucleon-nucleon interaction far away from elastic scattering can be studied by proton-proton bremsstrahlung and neutron-proton bremsstrahlung with high energy outgoing (so-called "hard") photons; see, for example (2001VO06, 2004MA71, 2005LI33) and references therein. A feature of proton-proton bremsstrahlung is that symmetry conditions forbid E1 photons and first order meson exchange currents; see (1998MA44), for example. In neutron-proton bremsstrahlung, however, first order effects are dominant; see (1992CL02, 2004VO07) where references to the few existing neutron-proton bremsstrahlung experiments are given. At intermediate energies, the neutron-proton bremsstrahlung cross section is about an order of magnitude larger than that for proton-proton bremsstrahlung (2003VO04). Thus the study of proton-deuteron bremsstrahlung becomes important for several reasons (1992CL03). It leads to a better understanding of the neutron-proton bremsstrahlung process since that is the dominant process in proton-deuteron bremsstrahlung. Also, proton-deuteron bremsstrahlung is an intermediate process between proton-neutron bremsstrahlung and proton-nucleus bremsstrahlung and ultimately to nucleus-nucleus bremsstrahlung for which it is usually assumed that proton-neutron bremsstrahlung is the basic process; see (1992CL03) and references therein.

Experiments from the current evaluation period involving reactions (c) and (d) are listed in Table 3.8 preview 3.8 (in PDF or PS). Studies from the 1960s reporting proton-deuteron bremsstrahlung are referenced and briefly discussed in (1990PI15, 1992CL02). As shown in Table 3.8 preview 3.8 (in PDF or PS), proton-deuteron bremsstrahlung studies reported during the period of this evaluation have been performed at Ecm from about 97 MeV to 186 MeV. In the experiment reported in (2002GR06), the energies are above the pion production threshold. These authors conclude that most (about two thirds) of the photon production in their experiment comes from the neutron-proton interaction in the presence of a spectator proton. With this interpretation, they obtain total cross sections that slowly increase from about 9 μb at Ecm = 145 MeV to about 18 μb at Ecm = 186 MeV. The same experimental group reported deuteron-proton reactions at the same energies resulting in π0 and π+ production (2000GR31). Since the primary decay mode of the π0 is into two γ-rays, it is of interest to compare the cross section for π0 production with that of bremsstrahlung at the same energies. According to authors of (2000GR31), the cross section for π0 production grows from about 0.6 μb at Ecm = 145 MeV to about 90 μb at Ecm = 186 MeV.

In the experiment performed at Kernfysisch Versneller Instituut (KVI) and reported in (2003VO04), a 190 MeV polarized proton beam was scattered from a deuterium target and the outgoing proton, deuteron and photon were detected in a coplanar geometry, which allows for the differential cross section and the analyzing power Ay to be measured. The results were compared with what the authors call a soft photon model, based on (1993LI1X). The model fits the data rather well. In a related KVI experiment with the same beam and target, studies of the four-body final state were reported in (2004VO07) in which the two protons, the neutron and the photon were all detected. The emphasis was on the geometries in which either the neutron or one of the protons was essentially a spectator, i.e., the quasifree geometries. Phase space considerations were used to obtain equivalent three-body final states for these cases. Thus, quasifree proton-proton bremsstrahlung or quasifree proton-neutron bremsstrahlung results were obtained. As long as the spectator neutron was at low energy, the quasifree proton-proton bremsstrahlung cross sections agree in shape with the free proton-proton bremsstrahlung cross sections reasonably well, but the magnitude of the quasifree cross section was 2.5 times larger than the free cross sections. Using a similar procedure, including the same scaling factor, the authors obtained cross sections for quasifree proton-neutron bremsstrahlung; only coplanar geometry cross sections are reported in (2004VO07). These cross sections are compared with three calculations of free neutron-proton bremsstrahlung: two soft photon models based on (1993LI1X) and a microscopic two-body model (1992HE06, 1992HE18). The agreement is reasonably good, particularly with the microscopic model. A direct comparison of the quasifree proton-neutron bremsstrahlung reported in (2004VO07) with measurements of proton-neutron bremsstrahlung cross sections is reported in (2007SA14). The role of meson exchange currents in proton-neutron bremsstrahlung is studied in (2008LI14) and references therein.

One objective of the experiment reported in (1990PI15) was to settle a discrepancy in the total photon emission cross section reported in two earlier studies; see the paper for relevant references. The authors also compared their results to a calculation of free neutron-proton bremsstrahlung (1989NA04) and they commented that agreement was found to be reasonable at lower photon energies, but failed at higher energies, possible due to the neglect of the neutron momentum in 2H and/or Pauli blocking effects.

4. (a) 2H(p + μ, γ + μ)3He Qm = 5.4935
(b) 2H(p + μ, μ)3He Qm = 5.4935

Muon catalyzed fusion of a proton and a deuteron is a process that has been studied for many years. The process is believed to proceed as follows (1991FR03): When a μ- particle enters liquid hydrogen which contains a small amount of deuterium, it is captured by a proton and quickly settles into an atomic 1S state. This small, electrically neutral entity can travel fairly freely through the material. If the μ- doesn't decay first, this muonic hydrogen-like atom can encounter a deuterium nucleus. Because of the larger mass of the deuterium and therefore the lower muonic energy levels (-2.66 keV vs. -2.53 keV; see (2003NA1F), page 72), the muon is transferred to the deuterium forming a muonic deuterium atom. The next step is the formation of a deuteron-proton-muon molecule with the proton and deuteron ultimately in a relative S state with essentially zero energy and an average p-d separation of about 500 fm (1990PO1H). Despite the large separation, the presence of the negatively charged muon can assist the fusion of the proton with the deuteron to form a 3He nucleus. This can occur in two ways: In reaction (a), which is radiative muon catalyzed p-d fusion, a 5.5 MeV gamma ray is emitted and the muon is left in a bound state around the 3He nucleus. In reaction (b), non-radiative muon catalyzed fusion, a 3He nucleus is formed from fusion of the proton and deuteron and the muon carries away 5.3 MeV and may then start another fusion process. It was the observation of these fixed energy muons in a hydrogen bubble chamber reported in (1957AL32) that was an early experimental indication of muon catalyzed fusion. The bubble chamber photograph of this discovery is reproduced in (1992PE1F). See also (1992FR1G) which contains a review and brief history of muon catalyzed fusion and (1985BO2G) for additional early references and more details of the fusion process. Reviews of muon catalyzed fusion can be found in (1989BR1O) and (1998NAZZ). However, both of these references deal primarily with d-d and d-t fusion.

Of interest here is the spin dependence of the p-d fusion processes and the information that a detailed study of these processes can produce about the low energy p-d system and the 3He bound state. The total spin of the p-d system is either 1/2 (doublet) or 3/2 (quartet). The radiative capture process, reaction (a), is predominantly an M1 transition. The fusion rate from the doublet state is somewhat larger than that from the quartet state. In liquid or solid mixtures of ordinary hydrogen and deuterium, it is possible to vary systematically the fusion yield from the quartet state relative to that of the doublet state by varying the concentration of deuterium and the temperature. This process is called the Wolfenstein-Gerstein effect; see (1992PE1F, 2004ES04). Using this procedure, the doublet and quartet fusion rates are found to be (0.35 ± 0.02) × 106 s-1 and (0.11 ± 0.01) × 106 s-1, respectively (1992PE1F). Calculations using the Faddeev method with realistic NN interactions and including 3N interactions and meson currents reported in (1991FR03) give (0.37 ± 0.01) × 106 s-1 for the doublet state fusion rate and (0.107 ± 0.06) × 106 s-1 for the quartet. The uncertainty quoted in the calculated fusion rates is somewhat subjective. Note that the doublet and quartet p-d radiative capture M1 cross sections have been directly determined, as reported in (1997RI15), and found to be in reasonably good agreement with the predictions in (1991FR03).

The non-radiative fusion process, reaction (b), is essentially an internal conversion process involving primarily the E0 multipole. A calculation of this fusion rate is also reported to be (0.062 ± 0.002) × 106 s-1 (1991FR03) as compared to the experimental value of (0.056 ± 0.006) × 106 s-1; see (1991FR03) for references. The same references also compares experimental and theoretical astrophysical S-factors for p-d fusion.

For both reactions (a) and (b), the agreement between experiment and theory is excellent. Since these zero energy fusion processes are complimentary to the usual bound state and scattering phenomena, they provide additional tests of three-body dynamics.

5. (a) 2H(p, π0)3He Qm = -129.4831
(b) 1H(d, π0)3He Qm = -129.4831
(c) 2H(p, π+)3H Qm = -134.0953
(d) 1H(d, π+)3H Qm = -134.0953
(e) 2H(p, pπ0)2H Qm = -134.9766
(f) 2H(p, 2π0)3He Qm = -264.4597
(g) 2H(p, π+π-)3He Qm = -273.6469
(h) 2H(p, π-)1H1H1H Qm = -141.0124
(i) 2H(p, 3He)η Qm = -542.35952

Reaction (c) is the same as 3H reaction 6 and reaction (d) is the inverse of that reaction. They are included here because of their relationship to the other pion production reactions listed here.

After the NN → NNπ reactions, the next simplest pion production reactions involving nucleons are the reactions (a) through (d). The fact that the nuclear systems involved - 2H, 3H, 3He - are reasonably well understood make these reactions of particular interest. It may also be possible to see at least the beginnings of the effects of the nuclear medium on the NN → NNπ reaction mechanism, effects that may show up in heavier nuclei. Table 3.9 preview 3.9 (in PDF or PS) lists references for reactions (a), (b) and (c). There are no reports of reaction (d).

An early theoretical study of the pion production reactions (a) and (c) is that of (1952RU1A), who introduced the so-called spectator or deuteron model. Refinements and developments of this model are referenced and discussed in (2005CA20). This latter reference contains calculations of the proton analyzing power Ay and differential cross sections for the reaction (a) using modern NN interactions and three-body Faddeev methods which are in rather good agreement with the data of (1987CA26) and (2003AB02). A study of the spin dependent form of the deuteron model is reported in (1994FA10, 2000FA03) in which vector and TAP's are calculated for the reactions (a) and (b) with polarized beams and comparisons with data of (1996NI06) are discussed.

Isospin symmetry was studied in (2001BE35) by measuring simultaneously the two reactions 2H(p, π+)3H and 2H(p, π0)3He. The authors make the point that their experiment falls in energy between the pion threshold and the Δ excitation region. They comment that the ratio of the cross section for the π+ channel to that for the π0 channel should equal 2 if isospin symmetry holds. By measuring the ratio for both total and differential cross sections as well as by comparing reaction matrix elements, the authors concluded that the amount of isospin symmetry breaking was small.

Table 3.10 preview 3.10 (in PDF or PS) shows references of experimental studies in which either a π+π- pair or two π0's are produced in the formation of 3He from the collision of a proton and a deuteron. It was found that, at energies near threshold for two pion production, a larger than expected production cross section is observed. The effect was originally observed in the 1960s by the authors Booth, Abashian and Crowe and is called the ABC effect; see the references in (2006BA29). As indicated in (2006BA29), the explanation for the effect is still unclear. Table 1 in (2000AN21) gives cross sections at incident Ep = 477 MeV for both T = 0 and T = 1 production of a π+π- pair and for the production of two π0's.

Table 3.11 preview 3.11 (in PDF or PS) lists references for reaction (e). The threshold proton energy for this reaction is 207 MeV. Total cross sections near threshold are reported in (1993RO08, 1993RO15). Fig. 3 in (1993RO08) shows a comparison of the total cross sections for the reactions (a) and (e) from (1992PI14) and 1H(n, π0)2H from (1990HU01) for small values of the outgoing pion momentum. The cross section for reaction (e) is smaller than the other two by factors of 102 to 103 at the lowest energies. Table 3.11 preview 3.11 (in PDF or PS) also lists references for the related reaction, 1H(d, pπ0)2H, for which the threshold deuteron energy is 414 MeV. In both (1988BO33) and (1996NI06), polarized deuterons were used to obtain σ(θ) and TAP's. Evidence is given in (1996NI06) for significant interference between the s- and p-wave pion production.

Reaction (e) has also been used to study quasi-free neutron-proton reactions such as 1H(n, π0)2H by using configurations such that the outgoing proton is essentially a spectator; see (2000BI09, 2001BI01, 2004LE32).

The η and π0 mesons both have spin zero and negative parity and are uncharged. The η is more massive than the π0, 547.85 MeV compared to 134.98 MeV. The π0 is part of an isospin triplet while the η has isospin zero. The π0 decays primarily into two photons with a mean lifetime of (8.4 ± 0.6) × 10-17 s; the η decays primarily into either two photons, one photon and two pions or three pions with a mean lifetime of about (5.06 ± 0.27) × 10-19 s. References for reaction (i) are listed in Table 3.12 preview 3.12 (in PDF or PS). The threshold energy for this reaction is 892 MeV. Also listed in the same table are references for the inverse reaction 1H(d, 3He)η, the threshold for which is 1783 MeV and the inelastic scattering reaction 2H(p, p'd)η, the threshold for which is 902 MeV.

As shown in Fig. 4 of (2007ME11) and Fig. 1 of (2007KH18), the total cross section for reaction (e) rises rapidly from zero to about 400 nb just above threshold and remains nearly flat for the next 10 MeV or so of excess energy. Of particular interest is the interaction between the η and the remaining nucleus and whether the system forms a bound or quasi-bound state; see (1993WI04, 1995FA12, 2003KH14, 2003ST01, 2004SI30, 2004SI32, 2007UP01). Total cross sections for 2H(p, 3H)η and 2H(d, 4He)η are compared in (1997WI11, 2002BI02). Cross sections for reactions (a) and (i) are compared in (2004SI32).

6. (a) 2H(p, n)1H1H Qm = -2.2246
(b) 1H(d, n)1H1H Qm = -2.2246
(c) 1H(d, pp)n Qm = -2.2246

Tables 3.4.1 in (1975FI08) and Table 3.11 preview 3.11 (in PDF or PS) in (1987TI07) contain references for these reactions for the periods covered by those evaluations. In both of these earlier evaluations, the number of references and the amount of work reviewed is quite extensive. Table 3.13 preview 3.13 (in PDF or PS) lists references for these reactions since 1987.

In kinematically complete three-body breakup experiments in which the two protons are observed, a commonly used way of viewing the coincidence spectrum of the two protons makes use of a three-body kinematical curve. If the observed protons are arbitrarily labeled p1 and p2, then the energy and emission angle of the unobserved neutron can be determined from energy and momentum conservation if the proton energies E1 and E2, their polar angles θ1 and θ2 and the relative azimuthal angle φ12 are measured. For any given set of values of θ1, θ2 and φ12 - determined by the locations of the detectors - the allowed values of E1 and E2 lie along a curve in E1-E2 space energy calculated using energy conservation. This curve is called the three-body kinematical curve; the arc length along this curve is called S and has units of energy. S is set equal to zero where E2 equals zero. Any pair of (E1, E2) values for coincidence protons corresponds to a point in this space on or near the kinematical curve. By dividing the S curve into bins, one can obtain differential cross sections d5σ/dΩ12dS as functions of S. A number of such curves can be seen in (2005KI19), for example, for different values of θ1, θ2 and φ12.

Some detector configurations have received special attention. If the angle φ12 is set to 180° and θ1 and θ2 are both set to 60°, then when E1 = E2 = 1/2Ecm, the neutron will be at rest in the center of mass system. For other values of θ1 and θ2, there will be (E1, E2) points at which the neutron is at rest. Such configurations which allow for the possibility of the neutron being at rest in the center of mass system are called collinearity configurations. Several examples are shown in (1994AL21) where differential cross section and Ay curves are shown as functions of the arc length S and the collinearity points are labeled.

7. (a) 2H(p, p)2H
(b) 1H(d, d)1H

Table 3.14 preview 3.14 (in PDF or PS) gives references for the scattering processes 2H(p, p)2H and 1H(d, d)1H since the previous evaluation. Tables 3.5.1a and 3.5.1b in (1975FI08) and Table 3.12 preview 3.12 (in PDF or PS) in (1987TI07) list earlier references for these reactions.

Low energy s-wave proton-deuteron scattering can be characterized by two quantities, the doublet scattering length, 2apd and the quartet scattering length, 4apd. As stated in 3H reaction 4, the corresponding neutron-deuteron quantities are 2and and 4and, the frequently quoted values for which are 0.65 ± 0.04 fm and 6.35 ± 0.02 fm respectively. (See 3H reaction 4 for references and more details.) The corresponding quantities for proton-deuteron scattering are less well known. Table 2 in (1999BL26) quotes three early experimental determinations of 4apd that have an average value of about 11.5 ± 0.2 fm while their own analysis gives 14.7 ± 2.3 fm. In Table 1 of the same reference, three calculated values of 4apd are quoted all near 13.8 fm. Less certain is the doublet length. The same two tables in (1999BL26) give experimental values ranging from 1.3 fm to 4.0 fm and calculated values that range from -0.1 fm to 0.257 fm. Their own data analysis gives -0.13 ± 0.04 fm. Table 1 and Fig. 1 in (2006OR07) illustrate the various values obtained for this quantity. In the opening sentence of (2006OR07), the authors state, "The problem of determining the doublet nuclear proton-deuteron scattering length 2apd has yet to be solved conclusively." For an early discussion of these matters, see (1989CH10, 1990FR18). In these references it is discussed that the doublet effective range function has a significant curvature at low energies. This makes it difficult to extrapolate to zero energy in order to determine the scattering length. A study of 2apd and 4apd using Faddeev methods and several interaction models is reported in (1991CH16). These authors present a Phillips line relating calculated 2apd values as a function of calculated 3He binding energy values. Near the experimental binding energy of 7.72 MeV, the resulting 2apd is approximately zero. Their calculated value for 4apd for two different two- and three-body interactions are 13.76 ± 0.05 fm and 13.52 ± 0.05 fm (where the quoted errors are somewhat subjective), respectively. It appears, then, that 2apd is approximately zero and 4apd is approximately 14 fm, both with significant uncertainties.

Most of the experiments referenced in Table 3.14 preview 3.14 (in PDF or PS) make use of either polarized proton or polarized deuteron beams. In addition to differential cross section measurements, such beams have enabled detailed measurements to be made of the vector analyzing power, Ay, with polarized proton beams and of vector and tensor analyzing powers iT11, T20, T21 and T22 with polarized deuteron beams. As NN and NNN interactions and three-body calculations became more sophisticated, it was discovered that the three-body models gave differential cross sections in reasonably good agreement with experiment, but resulted in a serious discrepancy between the calculated and experimental values of certain analyzing powers. This effect has become known as the Ay puzzle or more generally as the analyzing power puzzle, since the discrepancy was found to occur not only in Ay but also in iT11. This puzzle occurs also in neutron-deuteron scattering as discussed in 3H reaction 4. The references (1996GL05, 1998TO07, 2008TO12) contain examples of the effect for both n + d and p + d scattering. The energy dependence of the discrepancy in p + d scattering is illustrated in Fig. 5 of (2008TO12) which shows that it is essentially constant for Ep up to about 25 MeV, then starts to decrease and goes away at around 40 MeV. See 3H reaction 4 for additional comments and references concerning the analyzing power puzzle, its possible origins including relativistic effects. The reference (2008TO20) has a discussion of the history of the analyzing power puzzle. The analyzing power puzzle is still an open question as is illustrated by the recent study of the effects of three-body forces reported in (2009KI1B, 2010KI05). See also (2009MA53).

In the early days of calculations of p + d scattering, the Coulomb interaction was ignored. More recent calculations that include the Coulomb interaction have shown that it is important, especially at low energies and forward angles; see (2002AL18, 2006DE26, 2008DE1D). Figs. 2 through 7 in (2002AL18) show calculations of differential cross sections and VAP's and TAP's for a number of energies with and without the Coulomb interaction.

The influence of the three-body force may be appearing in a detailed analysis of elastic p + d scattering in what is referred to as the Sagara discrepancy. In (1994SA26), it was found that a small discrepancy existed between theory and experiment at the angle where differential cross section is a minimum. In (2002AL18, 2009IS04), it is shown that including the Coulomb interaction in the calculations has an effect on the details of the Sagara discrepancy, but it does not eliminate it. In (1998WI22), studies of n + d scattering show that when the three-body interaction is taken into account, most of the discrepancy is removed.

8. (a) 3He(γ, π0)3He Qm = -134.9766
(b) 3H(γ, π0)3H Qm = -134.9766
(c) 3He(γ, π+π-)X Qm = -279.1404

The only reference relating to reaction (a) since the previous evaluation is (1988AR08) where previous data on the photoproduction of π0 on 2H, 3He and 4He are reanalyzed using updated results for cross sections of the photoproduction of π0 from the proton.

There are no new references for reaction (b).

A study of reaction (c) was first reported in (1997WA09), in which photons of energies from 380 MeV to 700 MeV were used. Additional studies, some at higher energies, are reported in (1998HU10, 1998LO01, 1999KA38, 2003HU17). Of interest in these studies is the determination of the mass of the ρ meson in the nuclear medium.

9. (a) 3He(γ, π+)3H Qm = -139.5888
(b) 3He(e, e'π+)3H Qm = -139.5888
(c) 3He(e, e'K+)Λ3H Qm = -675.9408

References for reaction (a) since the previous evaluation are listed in Table 3.15 preview 3.15 (in PDF or PS).

In the introductory remarks in (1991KA32), there is a nice discussion of both experimental and theoretical aspects of reaction (a) for the period prior to 1991. These authors study final state interaction (FSI) effects in reaction (a) and find that they are considerable. They also study the two-step excitation process 3He(γ, π0)3He(π0, π+)3H and show that it is important in the higher energy region around the Δ excitation energy. Calculations of polarization observables for reaction (a) were reported in (1992KA31). Studies of the FSI effects in reaction (a) have also been reported in (1994CH15). The role of meson exchange currents near the Δ excitation peak in reaction (a) is studied in (1996GO37). This reference also reports studies of polarization observables for experiments using polarized photons.

Results of cross section measurements of 3He(γ, π+)X for X = 3H, nd and nnp are shown in (1993DH01) for several energies near the Δ excitation region. The results show a narrow peak at the highest outgoing pion momentum corresponding to the X = 3He channel and a broad peak at lower outgoing pion momenta corresponding to the X = nd and nnp channels. In the same energy region, cross sections for both 3He(γ, π+) and 3H(γ, π-) are reported in (1987BE27).

References with measurements related to reaction (b) are shown in Table 3.16 preview 3.16 (in PDF or PS).

The cross sections for the two reactions 3He(e, e'π+)X and 3He(e, e'π-)ppp as functions of the missing mass for the incident Ee = 555, 600, 675 and 855 MeV are reported in (1996BL20); see also (1997BL13). The channel with X = 3H is visible as a narrow peak at zero missing mass. The cross section for the breakup channels with X = nd and nnp is about a factor of two larger than that for the π-ppp channel for most missing mass values. However, since the π+nd channel has no equivalent in the π-ppp cross section, there are small differences in the shape of the two cross sections at low missing mass. In the references (1996BL20, 1997BL13) just mentioned as well as follow-up studies by the same group (2001KO23, 2002KO16), parallel kinematics (i.e., pion and virtual photon have same directions) are used and cross sections measured as functions of virtual photon polarization which allows transverse and longitudinal cross sections to be determined. The polarization and flux of the virtual photons can be calculated using kinematics of the scattered electrons; see (1997BL13) and references therein.

Studies of reaction (b) and 3He(e, e'π-)ppp at Ee = 0.845 - 3.245 GeV in parallel kinematics were reported in (2001GA63, 2001JA08, 2002GA02). As in the earlier, lower Ee studies mentioned above, the π+3H channel is separated from the π+nd and π+nnp channels. At larger values of the missing mass, the yields of the π+ channels are almost exactly twice that of the π- channels and the effect of the π+nd channel at intermediate missing mass values is seen; see Fig. 2 in (2001JA08). The reaction (b) results were compared with the analogous reactions using H and 2H targets in (2001GA63).

In a study reported in (2000HI09), an ultra-thin polarized 3He target is used to detect the recoil nuclei in the reactions pol. 3He(pol. e, e'3He)π0 and pol. 3He(pol. e, e'3H)π+.

With regard to reaction (c), studies of the production of kaons by inelastic scattering of electrons from light nuclei, including 3He, has been reported in (2001RE09, 2001ZE06, 2004DO16, 2007DO1D). As discussed in 3H reaction 11, Λ3H is the lightest hypernucleus. There is evidence for the production of this nucleus in the missing mass plots shown in these references. In all of these studies, the energy of the electron beams is 3.245 GeV. Cross sections were measured for 2H, 3He, 4He and 12C targets and compared with 1H. The effective proton numbers were obtained, which turned out to be 1.76 ± 0.26 for 3He.

10. (a) 3He(γ, p)2H Qm = -5.4935
(b) 3He(γ, n)21H Qm = -7.7180
(c) 3He(γ, np)1H Qm = -7.7180
(d) 3He(γ, pp)n Qm = -7.7180
(e) 3He(γ, pπ+)2n Qm = -148.0706
(f) 3He(γ, pπ-)21H Qm = -146.5059

Reaction (a) is the only two-body breakup channel possible for the photodisintegration of 3He. See Table 3.17 preview 3.17 (in PDF or PS) for references relative to reaction (a). For discussion of the three-body breakup reaction, it is convenient to indicate which outgoing particles are observed - the neutron only as indicated in (b), the neutron plus one proton as in (c) or both protons as in (d). There have been no reports of studies of reaction (b) since the previous evaluation. See (1988DI02) for a comprehensive review of photoneutron cross sections, including reaction (b). Table 3.18 preview 3.18 (in PDF or PS) and Table 3.19 preview 3.19 (in PDF or PS) contain references for reactions (c) and (d), respectively. Table 3.21 preview 3.21 (in PDF or PS) lists references for reactions (e) and (f). Table 3.20 preview 3.20 (in PDF or PS) lists references for the inclusive reaction 3He(γ, p)X, where only a single outgoing proton is observed.

Many experimental studies of some of these reactions were done in the 1960s and 1970s. Tables 3.8.1 and 3.8.2 in (1975FI08) contain extensive lists of references up to 1975. Eγ from 5.49 MeV to near 800 MeV were used for reaction (a) and 7.70 to 170 MeV for reaction (b). In some instances the outgoing proton or neutron was observed at a single 60° or 90° angle and sometimes angular distributions of the outgoing particles were measured. A few additional reaction (b) experiments were reported in (1987TI07). Cross sections for reaction (b) for Eγ from threshold to about 25 MeV are reported in (1981FA03), along with cross sections for the 3H(γ, n)2H and 3H(γ, 2n)1H reactions.

In the introductory section of (1992KL02), there is an extensive discussion and reference list dealing with two-body photodisintegration of 3H and 3He and pd-capture for the period prior to 1992. Also, in (1982BR12, 1983SO10, 1985BR23), reaction (a) and its time-reverse pd capture were compared; see (1994KO11) for additional references and commentary on this point.

Cross sections for reactions (a) and (d) and the sum of the two are shown in Fig. 12 in (2006NA10) for Eγ from thresholds up to about 30 MeV; see also Figs. 2, 3 and 4 in (2003SH18). The authors of (2006NA10) include results from earlier measurements along with their own. Most experiments have the cross section for reaction (a) rising to roughly 0.8 mb for Eγ of about 11 MeV, falling slowly to about 0.25 mb at 30 MeV and continuing to fall thereafter. There is considerable scatter in the experimental results around the peak; see Fig. 4 in (1992KL02). Note, however, that the most recent measurement reported in (2006NA10) has the two-body breakup cross section as 0.77 ± 0.05 mb at 10.2 MeV and 0.65 ± 0.05 mb at 16.0 MeV. The same reference shows that these experimental values fall below calculated values even when the calculations are performed using realistic NN and NNN interactions. For example, near the peak, the experimental cross section is smaller than theory by about 20%; see Fig. 12(b) in (2006NA10) and Fig. 2 in (2003SH18) while at 10.2 MeV the experimental cross section is less than the theoretical value by about 30%. As shown in (2007DE40), when the Coulomb interaction between the protons is included in the calculation, the theoretical value moves closer to the experimental value, but a sizable discrepancy is still present.

The cross section for reaction (d) rises to about 1 mb for Eγ of about 15 MeV and decreases from there; see Graphs 2A and 3A in (1988DI02) as well as Fig. 12(b) in (2006NA10) and Fig. 3 in (2003SH18). As in the reaction (a) case, the theoretical cross section is larger than the experimental values, especially at Eγ just above threshold, which is 7.72 MeV, and again above 25 MeV. For example, at about 10 MeV, the measured cross section is only about 1/3 of the theoretical value (2006NA10). The sum of the reactions (a) and (d) cross sections has a peak value of about 2 mb and occurs at about 15 MeV. Note also that at around 320 MeV, there is a broad peak in the reaction (d) cross section of about 16 μb, up from 1 to 2 μb before and after the resonance; see (1997AU02). This peak is probably due to the excitation of the Δ isobar in the 3He ground state.

Extensive theoretical studies of the photodisintegration of A = 3 nuclei are reported in (1987KO19, 1987KO26, 1987LE04, 1988LA29, 1988LA31, 1990KO23, 1990KO46, 1990NE14, 1991KO38, 1992KL02, 1994WI12, 1997SC04, 1999UM01, 2000EF03, 2000FO11, 2000VI05, 2001SC16, 2002GO24, 2002YU02, 2003SK02, 2003SK03, 2004DE11, 2005DE17, 2005DE56, 2005GO26, 2005SK01, 2005SK05). Frequently, in these references, two- and three-body breakup of both 3H and 3He are studied together as is the capture of either a neutron or a proton by 2H. Thus, the relevant sections - 3He reaction 3 and 3H reactions 3 and 8 - should be consulted for additional information.

Several approaches have been used to calculate photodisintegration of 3H and 3He cross sections. In the Faddeev approach, the bound and continuum wave functions are obtained by solving the Faddeev equations and calculating the appropriate matrix elements and response functions from which the cross section is obtained. See (2003SK02, 2003SK03) and references therein where the Faddeev approach has been used in A = 3 photodisintegration studies. A method related to the Faddeev approach makes use of the Alt-Grassberger-Sandhas (AGS) scheme to produce three particle wave functions. See (2001SC16, 2002YU02, 2004DE11, 2005DE17, 2007DE40) and references therein for applications of the AGS method to A = 3 photodisintegration. The role of the Coulomb interaction between the two protons using a screening technique is studied in (2005DE17, 2007DE40).

In a totally different approach, called the Lorentz integral transform method, it is not necessary to calculate the continuum wave functions. A localized auxiliary function related to the bound state wave function is calculated from which the response function is obtained by inverting an integral transform. As currently practiced, the bound state and auxiliary functions are obtained using correlated hyperspherical harmonics. The Faddeev and Lorentz integral transform methods are shown to give identical results in the context of the photodisintegration of 3H in (2002GO24). Some additional references that use the Lorentz integral transform method for photodisintegration studies are (1997EF05) and (2000EF03). For a more general discussion of the method, see (1988EF02, 2007EF1A) and references therein.

A third method for calculating photodisintegration cross sections is the Laget approach which uses diagrammatic techniques to evaluate the contributions of various photodisintegration mechanisms. There is a brief explanation of Laget's approach in the introduction of (2004NI18) which also contains a list of references. See also (2005LA03) for commentary and for references concerning the Laget approach in the context of electron scattering. Calculations of the cross section for two-body photodisintegration, reaction (a), for Eγ from threshold to 100 MeV are reported in (2001SC16). Also shown in this reference are the differential cross section at 90° for Eγ from threshold to 40 MeV and angular distributions for Eγ = 60 and 100 MeV. Three different interaction models were used corresponding to three different 3He binding energies. The authors of (2001SC16) note that peak heights of the calculated cross sections are correlated with calculated 3He binding energies with the lower peak heights corresponding to the higher binding energies; see 3H reaction 8 for more on this effect. The calculated cross sections generally follow the trends of the data, but much of the data - including the most recent reported in (2003SH18, 2006NA10) - lies below the calculations as can be seen in Fig. 1 in (2001SC16), Fig. 2 in (2003SH18) and Fig. 12 in (2006NA10), as mentioned above. In a calculation of the angular distribution of photons from proton capture by 2H at Ep = 10.93 MeV, it is shown in (2001SC16) that an excellent fit to the data results from including the E2 component along with the E1 component. The calculation of the fore-aft asymmetry from threshold to about 35 MeV reported in (2001SC16) agrees well with the data, although the data has large uncertainties. Note also that the reference (2001SC16) contains an extensive set of references for experimental papers of 3H and 3He photodisintegration dating back into the 1960s.

Calculations are reported in (2000EF03) for both two- and three-body photodisintegration of both 3H and 3He for Eγ up to 140 MeV. Several interaction models were used and the role of 3N interactions was investigated. It was found that including 3N forces lowers the calculated peak height and raises the calculated cross section at Eγ above 70 MeV. Both the Faddeev method and the Lorentz integral transform method are used in (2002GO24, 2003SK03, 2005SK01) to study the two- and three-body photodisintegrations of 3H and 3He. Studies of the effects of retardation, meson exchange currents using the Siegert theorem and the role of multipoles other than E1 on the transitions are reported in (2002GO24). Note also that (2002GO24) contains a brief discussion of the unretarded E1 transition operator and it is shown there that, for Eγ below about 50 MeV, this approximation is quite accurate. The role of the Δ isobar excitation 3N interaction in nucleon-deuteron capture and in the two- and three-body photodisintegration of 3H and 3He is discussed in (2002YU02, 2004DE11). Using the AGS integral equation method and techniques for handling the Coulomb interaction developed in (2005DE17, 2005DE21, 2005DE39), along with the CD Bonn NN interaction and including the Δ isobar excitation, calculations of the differential cross section for reaction (c) are reported in (2005DE56) for Eγ = 55 and 85 MeV and compared to data from (1991KO16). It was found that the Δ isobar excitation plays only a small role, but including the Coulomb interaction was essential in obtaining a good account of the data.

It is of interest to compare the cross sections for reactions (c) and (d). An experiment that does this is reported in (1994TE07), using polarized photons with energies from 235 MeV to 305 MeV. Fig. 2 of this reference shows that the differential cross section for pn pair emission is larger than that for pp pair emission by factors from about 2 to about 6. The authors of (1994TE07) state the following: "Two-nucleon absorption dominates the pn data, but is suppressed in the pp data. The pp data require the inclusion of three-nucleon absorption to describe the cross section and beam asymmetry over all momenta." The effect that the pn pair emission is larger than the pp pair emission is even more dramatic when the residual particle is essentially a spectator. In Fig. 3 of (1994EM02), the total cross section for pp pair emission with a spectator neutron is shown to drop from about 2 μb at Eγ = 200 MeV to about 1 μb at Eγ = 400 MeV. By contrast, in Fig. 3 of (1994EM01), the total cross section for pn pair emission with a spectator proton is shown to drop from about 60 μb at 200 MeV to about 20 μb at 400 MeV. Both of these reactions have been studied theoretically as reported in (1994WI12, 1995NI07, 1995WI16). The quasi-deuteron model is used for the np pair emission study reported in (1994WI12, 1995NI07).

The quasi-deuteron model as a feature of photodisintegration has been around for many years; see (2002LE05). The reference (1991KO16) also contains references to early evidence of the quasi-deuteron effect. This reference also contains evidence of this effect in the reaction (c) in which coincident n-p pairs are observed. The authors conclude that the quasi-deuteron model holds in the three-body photodisintegration of 3He for Eγ at least as low as 55 MeV. That the Coulomb interaction plays a significant role in reaction (c) can be seen in the Fig. 14 of (2005DE56) where the calculation of the differential cross section with and without the Coulomb is compared with the data of (1991KO16). In another study of reaction (c) reported in (1994EM01) in configurations when one of the protons is essentially a spectator, it was found that the cross section scales with the 2H(γ, p)n cross section, the ratio being 1.24 ± 0.26. Theoretical studies of the data in (1994EM01) using the quasi-deuteron model are reported in (1994WI12) and (1995NI07). See also (1999UM01) for an application of the quasi-deuteron model to both reactions (c) and 4He(γ, pn)2H.

Table 3.20 preview 3.20 (in PDF or PS) lists several references wherein a single outgoing proton is detected. Fig. 1 of (1989DH01) shows a proton spectrum observed at an angle of 23° for Eγ = 278 MeV. A narrow peak is seen in this spectrum at the high proton momentum end corresponding to reaction (a) and a broader peak at lower outgoing proton momentum corresponding to three-body breakup. Also seen in the results reported in (1994RU04) - in which polarized photons are used and both cross sections and cross section asymmetries are measured - is that absorption by two nucleons (the quasi-deuteron effect) is the dominant mechanism in the proton high momentum peak while absorption by three nucleons is also important in the proton momentum region below the narrow peak.

The question of the existence of Δ isobars in the ground state of nuclei in general and 3He in particular has been around for years; see (1987LI1P, 1987ST09, 1993EM02, 2000HU13) and references therein. The Δ isobars are roughly 300 MeV more massive than nucleons. They have spin and isospin of 3/2. Their resonance width is around 120 MeV, which means that they decay in about 5 × 10-24 s and travel no more than a few femtometers before decaying. The dominant decay mode is into a nucleon plus a pion. Two examples are: Δ++ → p + π+ and Δ0 → p + π-. Possible experimental signals indicating the presence of Δ's in the ground state of 3He are discussed in (1987LI1P). One suggestion is that photons of several hundred MeV energy, in favorable kinematic conditions, would produce coincident outgoing p-π+ pairs rather easily by knocking out a doubly charged Δ++ and few or no coincident outgoing p-π- pairs due to the photon's reduced ability to eject an uncharged Δ0. As shown in Table 3.21 preview 3.21 (in PDF or PS), two photodisintegration experiments have been carried out looking for p-π+ and p-π- pairs; see (1993EM02, 2000HU13). The authors of (1993EM02) conclude that the Δ component in the ground state of 3He is less than 2% and the authors of (2000HU13) conclude that it is between about 1.5 ± 0.8 % and 2.6%. The authors of (2000HU13) also note that they were able to identify a kinematical region in which p-π+ pairs were observed but no p-π- pairs were seen, as predicted in (1987LI1P). In a study of 3H and 3He electromagnetic form factors (1987ST09) which includes admixtures of Δ's in the ground state wave functions, percentages of 2.33 and 2.55 were obtained for the Δ isobar component for two different models. Also shown in Fig. 5 of this reference are the momentum distributions of the Δ isobar for the two models.

The highest energy photodisintegration of 3He reported so far is that of reference (2004NI18) in which photons of energies from 350 MeV to 1550 MeV were used and the three-body disintegration, reaction (d), was studied. With the energy of the tagged photon and the energies and momenta of the outgoing protons all measured, the energy and momentum of the neutron were deduced. Different kinematic regions were studied. Studied in particular were the star configuration in which the three particles in the center of mass system have equal energies and their momenta form a 120° triangle and the spectator neutron configuration in which the neutron has a small momentum. At these energies, the theoretical approach used by these authors is that of Laget; see (1988LA31) and other references given in (2004NI18). As discussed in (2004NI18), two-body photodisintegration is the dominant mechanism in the spectator neutron configuration up to about 600 MeV and three-body photodisintegration is dominant in the star configuration as predicted in (1988LA31).

A property of 3He that is obtainable in principle from the photodisintegration cross section is the electric polarizability; αE. By a sum rule, the electric polarizability is directly related to σ-2, which is the energy integral of the photodisintegration cross section divided by the photon energy squared; see (1997EF05), for example. This result requires that the magnetic polarizability is negligible compared to the electric; see (1983FR05). Calculations of αE for 3He using the sum rule with theoretical cross sections have been reported. For example, in (2007PA1E) the value 0.153 fm3 is obtained using a realistic model of 3He and in (1997EF05) values of 0.143 fm3 and 0.151 fm3 are obtained for two different models of 3He. Also reported in (1991GO01) are values of αE from 0.13 fm3 to 0.17 fm3 obtained by evaluating σ-2 using different sets of data for photodisintegration cross sections. By studying deviations from Rutherford scattering of 3He by 208Pb (1991GO01), a value 0.250 ± 0.040 fm3 was obtained for αE. The reason for the difference between the experimental values for αE is unclear; see (1997EF05).

11. (a) 3He(e, e)3He
(b) 3He(e, e'p)2H Qm = -5.4935
(c) 3He(e, e'n)21H Qm = -7.7180

Table 3.22 preview 3.22 (in PDF or PS) lists references for both elastic electron scattering and inclusive inelastic and deep inelastic scattering (DIS) by 3He. Table 3.23 preview 3.23 (in PDF or PS) gives references for the two-body breakup reaction 3He(e, e'p)2H and for the three-body breakup reaction 3He(e, e'p)n1H. Table 3.24 preview 3.24 (in PDF or PS) lists references for the two-body breakup reaction in which the deuteron is observed: 3He(e, e'd)1H. Table 3.25 preview 3.25 (in PDF or PS) lists references in which the three-body breakup reaction is obtained.

A brief history of experimental studies of electron scattering by 3H and 3He is given in the Introduction section of (1994AM07). Of the two targets, 3He was studied more extensively for some time since it is not radioactive.

It has proven to be of value to study the charge and magnetic form factors, Fc and Fm, which can be obtained from the electron elastic scattering cross sections. See (1985JU01), for example, in the context of obtaining the form factors for 3He. These quantities are expressed as functions of q2, the square of the momentum transferred to the target in the scattering process. Two different units are used in the literature for q2, namely fm-2 and (GeV/c)2. The conversion factor is: 1 (GeV/c)2 corresponds to 25.6 fm-2 or 1 fm-2 corresponds to 0.0391 (GeV/c)2. It should be noted that as a unit for q2, (GeV/c)2 is sometimes written as just (GeV)2, as in (2007PE21) and (2007AR1B). The form factors are defined in such a way that both Fc and Fm equal 1 at q2 equal to zero. Figs. 6 and 7 in (1994AM07) show the charge and magnetic form factors for both 3H and 3He. Both form factors for 3He drop rapidly from 1 as a function of q2. The charge form factor has a minimum near q2 = 11 fm-2 and the magnetic form factor has a minimum near q2 = 19 fm-2. The 3H form factors are qualitatively similar to those for 3He; the minima occur at slightly different values of q2. The slopes of the form factors at q2 = 0 can be used to extract charge and magnetic rms radii. Table 2 in (1994AM07) gives these values as rch = 1.959 ± 0.030 fm and rm = 1.965 ± 0.153 fm. For 3H, the corresponding values were similarly determined to be rch = 1.755 ± 0.086 fm and rm = 1.840 ± 0.181 fm. See (1988KI10) for a discussion of the methods and difficulties in deducing rms radii values from form factors.

Since 3H and 3He form an isospin doublet, it is useful to consider the isoscalar and isovector combinations of the form factors of 3H and 3He; see (1992AM04, 1994AM07) for the relationship between the standard form factors and the isoscalar and isovector form factors. As discussed in (1992AM04), meson exchange currents are expected to make a larger contribution to the isovector form factors than to the isoscalar ones. The isoscalar and isovector form factors are shown in Figs. 12 and 13 of (1994AM07). Since both 2H and 4He are isoscalar nuclei, it is of value to compare the A = 3 isoscalar form factor with those of 2H and 4He, as is done in (1994AM07). For example, the position of the minimum in the three cases is about 10 fm-2 for 4He, 12 fm-2 for A = 3 and 20 fm-2 for 2H, which reflects the same ordering of the sizes from smaller to larger of these nuclei.

A general review of quasielastic electron scattering that includes a discussion of response functions of 3H and 3He is reported in (2008BE09). Electron scattering by 3He has been referred to as "a playground to test nuclear dynamics"; see (2004GL08, 2010SI1A). For more on the theoretical description of longitudinal and transverse response functions, including possible relativistic effects, meson exchange currents and pion production threshold effects, see (2004EF01, 2008DE15, 2010EF01) and references therein, as well as (2004GL08, 2010SI1A).

The GDH sum rule is discussed in the 3He Introduction section. As originally developed, it involved the photoabsorption of real photons. Generalizations of this sum rule for virtual photons that are involved in the scattering of electrons have been developed; see (2000KO1Q, 2001DR1A, 2001JI02). Inclusive scattering cross sections of polarized electrons by a polarized 3He target with Ee = 0.862 - 5.058 GeV were reported in (2002AM08, 2005ME03, 2008SL01). The generalized GDH integral and a related Burkhardt-Cottington sum rule were deduced.

12. (a) 3He(μ-, ν)3H Qm = 105.6398
(b) 3He(μ-, ν)2H + n Qm = 99.3825
(c) 3He(μ-, ν)1H + 2n Qm = 97.1580
(d) 3He(μ-, νγ)3H Qm = 105.6398

Muon capture in general is reviewed in (2001ME27); muon capture by 3He is also fairly extensively reviewed there as well. The measured capture rate for reaction (a) is 1496.0 ± 4.0 s-1 (1998AC01). In two theoretical studies of this reaction reported in (2002MA66, 2003VI06), calculated values of 1484 ± 4 s-1 and 1486 ± 8 s-1 were obtained. Different structure models of 3H and 3He were used which gave binding energies close to experimental values. The theoretical values are in good agreement with each other and with the experimental value. A study of reaction (a) is reported in (1993CO05) in which a weighted average of early measurements of the capture rate is 1487 ± 36 s-1. Calculated values of the capture rate are reported in this reference to be 1497 ± 21 s-1 and 1304 s-1 using the elementary particle method and the impulse approximation, respectively. Calculations of analyzing powers for this reaction are reported in (1993CO05, 1996CO30, 2002MA66, 2003VI06). Additional studies of reaction (a) are reported in (1996CO01, 2000GO33, 2002HO09).

A measurement of the VAP for reaction (a) using laser polarized muonic 3He is reported in (1998SO08).

Of the 105.6 MeV released in reaction (a), only 1.9 MeV goes to the recoiling 3H. In contrast, deuterons produced in reaction (b) and protons in (c) are found to have much higher energies; see (1992CU01, 1994KU19, 2004BY01). In (2004BY01) deuteron energies from reaction (b) are measured between 13 MeV and 31 MeV. In the same reference, measurements of the proton energy distribution from reaction (c) between 10 MeV and 49 MeV are reported. By extrapolating to the full range of energies, capture rates for reaction (b) and (c) are obtained. Two different analysis methods were used in each case. For reaction (b), capture rates of 491 ± 125 s-1 and 497 ± 57 s-1 were obtained and for reaction (c), rates of 187 ± 11 s-1 and 190 ± 7 s-1 were obtained. Averaging, using inverse square error weighting, gives 496 ± 52 s-1 for the reaction (b) reaction rate and 189 ± 6 s-1 for the reaction (c) reaction rate. An early calculation of these reaction rates was reported in (1975PH2A) as 414 s-1 and 209 s-1, respectively. A calculation of the sum of these two reaction rates is reported in (1994CO05) as 650 s-1. This compares with the theoretical value of 623 s-1 from (1975PH2A) and 685 ± 52 s-1 obtained by adding the averaged experimental values from (2004BY01).

A study of reaction (b) using the Faddeev equations and realistic NN interactions is reported in (1999SK03).

A theoretical study of reaction (d) is reported in (2002HO09) in which two approaches are compared. In the elementary particle method, 3He and 3H are treated as elementary particles whose internal structures are contained in experimental form factors. In the impulse approximation method, 3He and 3H are treated microscopically. The photon spectrum obtained from both methods is roughly Gaussian shaped, peaked at around 40 MeV. When summed over all photon energies, the calculated capture rate for reaction (d) is of the order of 1 s-1 which is much smaller than the capture rates for reactions (a), (b) and (c).

Adding the capture rates quoted above (1998AC01, 2004BY01) for reactions (a), (b) and (c) and neglecting reaction (d) gives 2181 ± 52 s-1 for the total muon capture rate. Of this total, reaction (a) is 68.6 ± 1.6 %, reaction (b) is 22.7 ± 2.4 % and reaction (c) is 8.7 ± 0.3 %. It is of interest to note that, from calculations reported in (1975PH2A), the corresponding values for these percentages are approximately 70%, 20% and 10%, respectively. These older values, which are quoted in more recent publications (1998AC01, 1999VO23, 2001ME27, 2002MA66, 2003VI06, 2004BY01) are quite consistent with current experimental results.

Another aspect of interest in muon capture by 3He concerns the hyperfine effects. For muonic 3He, the total spin is 0 or 1. It is reported in (1998AC01) that the transition rate between the higher energy spin 0 state and the lower energy spin 1 state is negligibly small. Hence, when the muonic 3He atom is formed, 1/4 have spin 0 and 3/4 have spin 1. A study of the capture rate from each spin state is reported in (1994CO05). Considering reactions (a), (b) and (c), it was found that about 60% comes from the spin 0 state and 40% from the spin 1 state. Since the 3He and 3H wave functions used were fairly simplistic, these results should probably be considered only as estimates.

Additionally, reaction (a) has been used to obtain a value for the pseudoscalar coupling constant, gp. See (1996BO54, 1996JO22, 1998AC01, 1999VO23, 2000GO33, 2001BE16, 2002MA66, 2003TR06).

13. (a) 3He(π±, π±)3He
(b) 3He(π-, π0)3H Qm = 4.5750
(c) 3He(π+, p)1H1H Qm = 132.6345
(d) 3He(π-, p)2n Qm = 131.0698
(e) 3He(π-, n)2H Qm = 133.2944
(f) 3He(π-, π+)3n Qm = -9.2827

A review of pion reactions with 3He and 4He and other nuclei can be found in (2002LE39).

Table 3.26 preview 3.26 (in PDF or PS) gives references related to reaction (a) as well as some related inelastic reactions for the current evaluation period.

In a series of reports, charge symmetry breaking in pion elastic scattering on 3H and 3He was studied by measuring ratios of cross sections - ratios which would equal unity if charge symmetry held; see (1988PI09, 1990NE02, 1991PI03, 1993BR03, 1995BE04, 1995MA32, 1996DH01, 2002BR49). See 3H reaction 10 for more discussion of these results.

When polarized 3He targets became available, asymmetry (Ay) measurements in elastic scattering of pions from polarized 3He were made as reported in (1991LA09, 1994LA09, 1996ES04, 1997ES05). Best agreement between theory and experiment is obtained when the pion-nucleon resonance Δ(1232) is included in the reaction model. Calculations of differential cross sections and analyzing powers for elastic scattering of both π+ and π- by 3He for Eπ = 100, 142, 180 and 256 MeV are reported in (1999ZH14). This reference also displays graphs of differential cross sections and asymmetries collected from several experiments. The agreement with experiment is generally good, except for backward angles. For the asymmetry calculations, it was found that including a D state in the 3He wave function was important for π+ scattering but not for π- scattering.

The spectra of both π+ and π- inelastically scattered by 3He shows a large peak near the quasi-elastic nucleon knock-out energy broadened by nucleon Fermi motion; see Figs. 3 through 9 in (1987KL06). Distorted wave impulse approximation (DWIA) calculations that assume a single pion-nucleon interaction are only in qualitative agreement with data. These authors also studied the reactions 3He(π+, π+'p) and 3He(π-, π-'p) and found that the DWIA calculations agree much better with the data.

A study of reaction (b) is reported in (1999ZH22). The energy of the π- beam was 200 MeV; the 3He target was polarized. The outgoing π0 was detected indirectly by measuring the energies and angles of the two photons into which the π0 decays. The recoiling 3H nucleus was detected in coincidence with the π0. The scattering asymmetry, Ay, was determined for θcm = 60° - 105° and found to be large and negative near 60° and large and positive near 80°. Comparisons are made with calculations with only qualitative agreement.

Studies of the inelastic processes 3He(π+, π0), 3He(π+, π0p), 3He(π-, π0), 3He(π-, π0p) are reported in (1995DO07). The pion beam energy was 245 MeV. The outgoing π0 was detected as discussed above. The results suggest that the 3He(π+, π0p) reaction occurs primarily by a quasi-free pion- nucleon process, but the 3He(π-, π0p) involves more than a single nucleon.

The absorption of π+ by various nuclei, reaction (c), has been a subject of study for some time; see (1993IN01), section 5 of the review in (2002LE39) and references therein. At least two nucleons must be involved in the absorption process since a single free nucleon cannot absorb a pion and conserve energy and momentum. As discussed in (2002LE39), in the early days of pion absorption studies, it was expected that this process would be a way of studying NN correlations. However, the absorption process turned out to involve more than two nucleons to a significant degree. Studies of π+ absorption by 3He have been carried out to separate the two and three nucleon absorption processes; see (1986AN11, 1991WE14, 1996HA04), for example. References for π+ absorption by 3He are given in Table 3.27 preview 3.27 (in PDF or PS).

The total π+ absorption cross section for 2H has a broad resonance with a peak value of about 12 mb for Eπ of about 150 MeV; see Fig. 5 in (1993AR11), or Fig. 4(a) in (1998KA17). The same resonance feature shows up in the total π+ absorption cross section of other nuclei as well; for example, for 3He, see Fig. 4(b) in (1998KA17) and for 12C, see Fig. 2 of (2002LE39) and references therein. Presumably, the resonance is due to the formation of a Δ; π + N → Δ; see (1991GR09), for example. The cross section at the peak in 3He is about 30 mb and for 12C the peak cross section is nearly 200 mb. There is a monotonic increase in the absorption cross section with increasing mass number; see Fig. 3 in (2002LE39) and references therein.

In most of the references in Table 3.27 preview 3.27 (in PDF or PS), the primary concern has been to separate the two nucleon absorption mechanism from that involving three nucleons. See (1989SM03), for example, in which it is shown that the three nucleon absorption percentage of the total cross section increases from about 30% at an incident Eπ = 37 MeV to nearly 50% at Eπ = 500 MeV. Similar results are shown in Fig. 11 in (1991MU01) and in Fig. 10 in (1996HA04).

A measurement of the polarization of the proton emitted in π+ absorption by 3He is reported in (1992MA17). The outgoing protons were selected by kinematical constraints to be those resulting from two nucleon absorption. The results were compared with the theory of (1987NI09) and with proton polarization from π+ absorption by 2H. At 120 MeV, the 3He and 2H results are similar, but not at 250 MeV. The results differ from theory at both energies. See (1993AC01) for a comparison of experimental polarization results for π+ absorption by 2H, 3He and 4He with each other and with theory. Theoretical work related to angular distributions and polarizations of outgoing protons following pion absorption is reported in (2003SC11), which also includes references to earlier work. In both (1993AC01) and (2003SC11), it was found that the polarization data were not well described by a two nucleon absorption mechanism.

The absorption of π- by 3He, reactions (d) and (e), can be studied using either stopped pions or in-flight pions. See Table 3.28 preview 3.28 (in PDF or PS) for references. Results from an experiment with stopped pions in cold, gaseous 3He are reported in (1995GO03). These authors concluded that absorption by two nucleons coupled to zero isospin is the dominant mechanism. The value 4.2 ± 0.6 was obtained for the ratio of the three-body final state decay rate, reaction (d), to the two-body final state, reaction (e). An earlier value for this ratio is 3.6 ± 0.6; see (1995GO03) for references. These authors also concluded that final state interactions play a major role in the decay process.

Table 3.28 preview 3.28 (in PDF or PS) shows that experiments with in-flight pions often have used both π+ and π- beams. Fig. 10 and Table IX in (1996HA04) shows that both the two nucleon and the three nucleon π- absorption cross sections are essentially constant as a function of Eπ- = 37-350 MeV in contrast to π+ absorption which has a resonance feature around 150 MeV. These authors also determined that, for π- absorption, the three nucleon absorption cross section is larger than the two nucleon by an essentially constant factor of about four.

See 3n reaction 4 for more on reaction (f).