
A = 3 Introduction (2010PU04)The present evaluation summarizes the research that has been published on the A = 3 systems since the previous evaluations (1975FI08, 1987TI07). There are four A = 3 systems to consider: ^{3}n, ^{3}H, ^{3}He and ^{3}Li. Of these, only ^{3}H and ^{3}He are known with certainty to possess bound states. Studies of the reaction ^{1}H(^{6}He, α)^{3}H reported in (1994AL54, 2003RO13) have suggested the possibility of a resonance in ^{3}H at about 7 MeV above the ground state; see ^{3}H reaction 2. In the two previous evaluations, the material was presented in the framework of a discussion of the energy levels of the A = 3 systems. This same approach has proven to be a useful means of presenting large amounts of data for A > 3 systems. Also, the desire to discover and study resonances has motivated both experimental and theoretical research in the A = 3 systems. The same approach is followed in this review. Except in rare instances, references to papers published prior to and included in either the 1975 or the 1987 evaluation are not included here. The present review includes material that appeared in the National Nuclear Data Center (NNDC) Nuclear Science References (NSR) database through December 31, 2009. In a few instances, references to articles not appearing in the Nuclear Science References are included. A few references with a 2010 publication date have been included; however, systematic searches later than 2009 have not been performed. As in earlier reviews for A = 3, data tabulations and/or graphs of scattering and reaction cross sections have not been included in this evaluation. The database EXFOR/CSISRS contains a vast collection of experimental reaction data for incident neutrons, charged particles and photons. The material is separated into the four systems: ^{3}n, ^{3}H, ^{3}He, ^{3}Li. The ordering of the reactions follows that of the previous evaluations, for the most part. For historical reasons associated with Evaluated Nuclear Structure Data File (ENSDF), in the ^{3}He section, the beta decay process ^{3}H(β^{})^{3}He is given first.
1) Basic issues: (a) The GerasimovDrellHearn (GDH) sum rule relates an energy weighted integral over the spindependent photoabsorption cross sections of a particle to its ground state anomalous magnetic moment; see the reviews (2004DR12, 2008DR1A). It is derived using basic principles of invariance, causality and unitarity and relates a static property of a particle's ground state with aspects of its dynamical spectrum. The GDH sum rule was first tested experimentally for protons (2000TH04, 2001AH03, 2004DU17). However, by using polarized ^{3}He targets, it has become possible to test this sum rule  as well as a generalized form that allows for virtual photons  for ^{3}He and the neutron (2001GI06, 2001WE07, 2002AM08). See the ^{3}He section for more on the GDH sum rule, anomalous magnetic moments and polarized ^{3}He targets. Related to the GDH sum rule is the forward spin polarizability, γ_{0}. In this case, however, the integrand contains the photon energy to the inverse third power rather than to the inverse first power as in the GDH sum rule; see (2009WE1A) and references therein. Calculations of both the GDH sum rule and γ_{0} for ^{2}H are reported in (2004CH58, 2004JI03). (b) Charge symmetry breaking (CSB), or isospin violation, as currently understood, is due to the down quark having a slightly greater mass than the up quark and to electromagnetic effects; see Tables 1.1 and 1.2 in (1990MI1D) as well as (2006MI33) and references therein. Recent advances in effective field theory have been used to include CSB into NN and NNN interactions; see (2000VA26, 2003FR20, 2005FR02, 2006MI33). More references on effective field theory are given below. CSB shows up in the binding energy difference of ^{3}H and ^{3}He; the binding energy of ^{3}H is greater than that of ^{3}He by almost 764 keV of which about 85% is due to the effect of the Coulomb interaction between the two protons in ^{3}He. See (2005FR02, 2006MI33) and the introduction of the ^{3}He section for more details on the origins of the remaining 15%. CSB has also been studied in the context of elastic scattering of π^{+} and π^{} from ^{3}H and ^{3}He; see (2002BR49, 2002KU36) and references therein. Details on these reactions are discussed in ^{3}H reaction 10 and ^{3}He reaction 13. More general than charge symmetry and charge symmetry breaking is the subject of charge independence and charge independence breaking (CIB). A study of CIB and the role of mixing of T = 3/2 states with T = 1/2 states in ^{3}H and related reactions is reported in (1991WI06). 2) Realistic NN potentials: Several phenomenological NN interactions have been developed that include the correct long range one pion exchange tail, yield essentially perfect descriptions of pp and np phase shifts and the properties of the deuteron and in some cases include charge dependent aspects. Some that are frequently used in A = 3 applications are: AV_{14} (1984WI05), NijmI, NijmII, Reid93 (all three are presented in (1994ST08)), AV_{18} (1995WI02) and CDBonn (1996MA09, 2001MA07). Details of various NN interactions along with comparisons of calculated results can be found in (1998CA29). Calculations using these potentials for A = 3 systems are in (1993FR11, 2000VI05, 2003NO01, 2004KU12). However, when the binding energy of ^{3}H and ^{3}He are calculated using these NN interactions, it is found that the predictions underbind these nuclei by about 10%. This result has been known for some time and is illustrated in (2002GL1F). However, this discrepancy is not as bad as it first sounds. Since the binding energy of ^{3}H or ^{3}He is the sum of the kinetic energy of around 40 MeV and a negative potential energy of about 48 MeV, an error of only 1 or 2 % in the potential energies can give an error of 10% in the binding energies. 3) Partially nonlocal NN potential: Both manybody and relativistic effects can introduce nonlocal aspects into NN interactions, especially at short distances. There have been several studies which treat the long range part of the NN interaction as local and the short range part as nonlocal. The CDBonn interaction mentioned above falls into this category to a certain extent. In addition, see (1996MA09, 1998DO13, 1999DO35, 2000DO23, 2003DO05, 2004DO05, 2008DO06). 4) Nonlocal, separable potential from inverse scattering methods: Using Jmatrix inverse scattering techniques, a separable, nonlocal nucleonnucleon interaction, called JISP, has been obtained and used in calculations related to the structure of light nuclei, including mass 3; see (2004SH41, 2009MA02, 2009SH02) and references therein. Note: The reference (2004SH41) was reproduced and updated in (2008AL1C). Calculations of the binding energies of ^{3}H and ^{3}He using various interactions, including JISP, are compared in (2005SH33). See also (2007SH27, 2009MA02). The JISP interaction was used in (2006BA57) to calculate the photoabsorption cross sections of ^{2}H, ^{3}H, ^{3}He and ^{4}He. 5) Dressed bag model of the NN interaction: This approach treats the short and intermediate parts of the NN interaction as a sixquark bag surrounded by one or more meson fields; see (2001KU14, 2001KU16). For applications to scattering phase shifts and deuteron properties, see (2002KU14) and for an application to np radiative capture, see (2003KA56). 6) NNN potentials: Threebody forces have been studied for decades. A brief discussion of the physical origin of these interactions is given in (1998CA29). The reference (1999FR02) contains a listing of several of these forces with original references. Two of these NNN interactions that have continued to be used in recent calculations  sometimes in modified form  are Urbana IX (1995PU05, 2003NO01) and TucsonMelbourne (1995ST12, 2001CO13). The ^{3}H and ^{3}He binding energy discrepancy referred to above can be resolved by including a threebody force. This is illustrated in (2003NO01) where the binding energies of ^{3}H and ^{3}He are calculated using the AV_{18} twobody interaction and the Urbana IX threebody interaction. A threebody force has also been obtained in the dressedbag model; see (2004KU05). For a discussion of the three nucleon force in the context of neutrondeuteron and protondeuteron scattering, see (2007SA38, 2007SA59). Section 1 of (2008KI08) contains a discussion and extensive list of references on nucleon interactions in general and the three nucleon interaction in particular from a historical perspective. A comparative study of three different NNN interactions combined with the AV_{18} NN interaction is reported in (2010KI05). 7) Effective field theory: This topic also goes by the names chiral effective field theory and chiral perturbation theory (ChPT). A brief history of this theory along with relevant references is given in (2003EN09). Work reported in this reference shows that calculations of the properties of the deuteron using an NN interaction obtained from fourth order ChPT compare favorably with those using AV_{18} and CDBonn NN interactions and with experiment. Third order ChPT has been used to produce an NNN interaction (2002EP03, 2007NA30). A brief introduction to this topic can be found in (1998VA04). A comprehensive review of the theory can be found in (2002BE90). See also (1995BE72). Some references in which ChPT has been applied to A = 3 systems are (2002EP02, 2002EP03, 2004GL05, 2006PL09, 2007HA42). The reference (2007NA16) contains a useful introduction to ChPT and uses the binding energies of ^{3}H and ^{3}He to constrain low energy constants. Low energy constants for the ChPT formulation of the NNN interaction are also obtained in (2009GA23), using ^{3}H and ^{3}He binding energies and the ft value for the beta decay of ^{3}H. Chiral symmetry and ChPT also demonstrated that the TucsonMelbourne threebody interaction needed to be modified; see (1999FR02, 2001CO13, 2001KA34). See also (2006RA33) for a study of parity violation using effective field theory. See also (2004CH58, 2004JI03) for calculations of the GDH sum rule and spindependent polarizabilities using effective field theory. See (2009EP1A) for a review of the application of effective field theory to the interaction of nucleons based on quantum chromodynamics. 8) Renormalization group methods: Techniques using the Renormalization Group in general and the Similarity Renormalization Group in particular have been used to separate lower momentum, longer range components of the NN interaction from the higher momentum, shorter range components; see (2003BO28, 2005SC13, 2007BO20, 2007JE02, 2008BO07) and references therein. The review (2007JE02) has a discussion of the role of the Renormalization Group in effective field theory applications. The reference ( 2008BO07) reports on shell model calculations of light nuclei, including ^{3}H, using an NN interaction produced from effective field theory modified by the Similarity Renormalization Group. See also (2008DE04). 9) Dynamical and structural calculations: Several methods have been used to calculate bound and continuum states in A = 3 systems. Some of the best know are described next. (a) The Faddeev approach has a long history as discussed in (1993WU08, 1996GL05). Both coordinate space and momentum space Faddeev methods are outlined in (1998CA29). Both methods are used and results compared in (1990FR13) where n + d scattering is studied and in (1995FR11) where n + d breakup amplitudes are calculated. In (1993FR11), the ground state of ^{3}H was studied using the coordinate Faddeev approach and several realistic NN interactions. In another Faddeev approach to ^{3}H and ^{3}He ground states, the interacting pair is treated in coordinate space and the spectator particle is treated in momentum space; see (1981SA04, 1993WU08). Equivalent to the continuum Faddeev approach is the AltGrassbergerSandhas (AGS) method; see (2008DE1D, 2009DE02) and references therein. See (2001CA44) for an application of the AGS approach to neutrondeuteron scattering. Using the AGS approach, the Coulomb interaction can be taken into account by using a screening technique. See (2006DE26, 2009DE47) for an application of the AGS method to protondeuteron scattering. New formulations of the Faddeev equations which contain applications to A = 3 processes are presented in (2008WI10, 2010GL04). (b) The hyperspherical harmonic basis method (1993KI02, 1994KI14, 1995KI10, 1998CA29, 2004KI16) comes in several different forms. It can treat the Coulomb force exactly, produces results in agreement with Faddeev calculations (2003NO01) and has been extended to the A = 4 systems (2005VI02, 2005VI05). For a detailed discussion of the hyperspherical harmonic method including an application to the bound and zero energy scattering states of three and four nucleon systems, see (2008KI08). See also (2009LE1D) for a discussion of the method and some applications to three body systems. (c) The Green's function Monte Carlo method has been applied mostly to systems with A > 3. The method is described in (1998CA29) where the results of a binding energy calculation of ^{3}H, both with and without a threebody force, are quoted. See also (1998WI10), where calculations of the ground state properties of ^{3}H are included along with several other light nuclei. In (2008MA50), the method is applied to calculations of the magnetic moments of ^{3}H and ^{3}He as well as the isoscalar and isovector combinations of these nuclei and to magnetic moments and M1 transitions of other light nuclei. (d) The nocore shell model approach has been applied to systems with A ≥ 3. A summary of the method is given in (2002BA65) along with results of binding energy calculations of ^{3}H and ^{3}He. A calculation of the binding energy of ^{3}H (and ^{4}He) using this method with a threebody interaction from effective field theory is reported in (2007NA30). Recent developments and applications of the method are reviewed in (2009NA13). A variation of the nocore shell model method is discussed in (2004ZH11) where a calculation of the binding energy of ^{3}H is used as a test case. Related to the nocore shell model is the nocore full configuration method; see (2009MA02) which includes calculations of ^{3}H and ^{3}He binding energies. (e) A variational approach using the dressedbag model NN and NNN interactions as well as Coulomb and charge symmetry breaking effects has been applied to calculations of the ground states of ^{3}H and ^{3}He; see (2004KU05, 2004KU06). (f) A totally different approach, called the Lorentz Integral Transform (LIT) method, has been developed that enables matrix elements involving unbound states to be calculated without calculating the continuum wave functions. See (2007EF1A) for a review of the method and ^{3}He reaction 10 for more details. See (2000EF03) for calculations of the photodisintegration of ^{3}H and ^{3}He and (2006GA39) for the photodisintegration of ^{4}He using the LIT method. (g) Additional theoretical studies that use ^{3}H and ^{3}He as test cases are an improved variational wave function method (2009US02) and a global vector representation of the angular motion method (1998VA1P, 2008SU1B).
