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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: ³n, ³H, ³He and ³Li. Of these, only ³H and ³He are known with certainty to possess bound states. Studies of the reaction ¹H(⁶He, α)³H reported in (1994AL54, 2003RO13) have suggested the possibility of a resonance in ³H at about 7 MeV above the ground state; see ³H 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: ³n, ³H, ³He, ³Li. 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 ³He section, the beta decay process ³H(β^-)³He is given first.

1) Basic issues:

(a) The Gerasimov-Drell-Hearn (GDH) sum rule relates an energy weighted integral over the spin-dependent 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 ³He targets, it has become possible to test this sum rule - as well as a generalized form that allows for virtual photons - for ³He and the neutron (2001GI06, 2001WE07, 2002AM08). See the ³He section for more on the GDH sum rule, anomalous magnetic moments and polarized ³He targets. Related to the GDH sum rule is the forward spin polarizability, γ₀. 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 γ₀ for ²H 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 ³H and ³He; the binding energy of ³H is greater than that of ³He by almost 764 keV of which about 85% is due to the effect of the Coulomb interaction between the two protons in ³He. See (2005FR02, 2006MI33) and the introduction of the ³He 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 ³H and ³He; see (2002BR49, 2002KU36) and references therein. Details on these reactions are discussed in ³H reaction 10 and ³He 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 ³H 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: AV₁₄ (1984WI05), NijmI, NijmII, Reid93 (all three are presented in (1994ST08)), AV₁₈ (1995WI02) and CD-Bonn (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 ³H and ³He 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 ³H or ³He 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 non-local NN potential:

Both many-body and relativistic effects can introduce non-local 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 non-local. The CD-Bonn interaction mentioned above falls into this category to a certain extent. In addition, see (1996MA09, 1998DO13, 1999DO35, 2000DO23, 2003DO05, 2004DO05, 2008DO06).

4) Non-local, separable potential from inverse scattering methods:

Using J-matrix inverse scattering techniques, a separable, non-local nucleon-nucleon 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 ³H and ³He 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 ²H, ³H, ³He and ⁴He.

5) Dressed bag model of the NN interaction:

This approach treats the short and intermediate parts of the NN interaction as a six-quark 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 n-p radiative capture, see (2003KA56).

6) NNN potentials:

Three-body 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 Tucson-Melbourne (1995ST12, 2001CO13). The ³H and ³He binding energy discrepancy referred to above can be resolved by including a three-body force. This is illustrated in (2003NO01) where the binding energies of ³H and ³He are calculated using the AV₁₈ two-body interaction and the Urbana IX three-body interaction. A three-body force has also been obtained in the dressed-bag model; see (2004KU05). For a discussion of the three nucleon force in the context of neutron-deuteron and proton-deuteron 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 AV₁₈ 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 AV₁₈ and CD-Bonn 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 ³H and ³He to constrain low energy constants. Low energy constants for the ChPT formulation of the NNN interaction are also obtained in (2009GA23), using ³H and ³He binding energies and the ft value for the beta decay of ³H. Chiral symmetry and ChPT also demonstrated that the Tucson-Melbourne three-body 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 spin-dependent 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 ³H, 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 ³H was studied using the coordinate Faddeev approach and several realistic NN interactions. In another Faddeev approach to ³H and ³He 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 Alt-Grassberger-Sandhas (AGS) method; see (2008DE1D, 2009DE02) and references therein. See (2001CA44) for an application of the AGS approach to neutron-deuteron 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 proton-deuteron 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 ³H, both with and without a three-body force, are quoted. See also (1998WI10), where calculations of the ground state properties of ³H are included along with several other light nuclei. In (2008MA50), the method is applied to calculations of the magnetic moments of ³H and ³He as well as the isoscalar and isovector combinations of these nuclei and to magnetic moments and M1 transitions of other light nuclei.

(d) The no-core 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 ³H and ³He. A calculation of the binding energy of ³H (and ⁴He) using this method with a three-body interaction from effective field theory is reported in (2007NA30). Recent developments and applications of the method are reviewed in (2009NA13). A variation of the no-core shell model method is discussed in (2004ZH11) where a calculation of the binding energy of ³H is used as a test case. Related to the no-core shell model is the no-core full configuration method; see (2009MA02) which includes calculations of ³H and ³He binding energies.

(e) A variational approach using the dressed-bag model NN and NNN interactions as well as Coulomb and charge symmetry breaking effects has been applied to calculations of the ground states of ³H and ³He; 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 ³He reaction 10 for more details. See (2000EF03) for calculations of the photodisintegration of ³H and ³He and (2006GA39) for the photodisintegration of ⁴He using the LIT method.

(g) Additional theoretical studies that use ³H and ³He as test cases are an improved variational wave function method (2009US02) and a global vector representation of the angular motion method (1998VA1P, 2008SU1B).

1988GI03		B.F. Gibson and B.H.J. McKeller, The three-body force in the trinucleons
1988WE20		H.R. Weller and D.R. Lehman, Manifestations of the D state in light nuclei
1990EI01		A.M. Eiro and F.D. Santos, Non-spherical components of light nuclei
1990LE24		D.R. Lehman, Evidence for and explication of the D state in few-nucleon systems
1990MI1D		G.A. Miller, B.M.K. Nefkens and I. Slaus, Charge symmetry, quarks and mesons
1992GI04		B.F. Gibson, The trinucleons: physical observables and model properties
1993FR11		J.L. Friar et al., Triton calculations with the new Nijmegan potentials
1993FR18		J.L. Friar, Three-nucleon forces and the three-nucleon systems
1993WU08		Y. Wu, S. Ishikawa and T. Sasakawa, Three-nucleon bound states: detailed calculations of 3H and 3He
1996FR1E		J.L. Friar and G.L. Payne, Proton-deuteron scattering and reactions, Chapter 2 in Coulomb Interactions in Nuclear
		and Atomic Few-Body Collisions, edited by Frank S. Levin and David A. Micha, 1996
1996GL05		W. Glockle et al., The three-nucleon continuum: achievements, challenges and applications
1998CA29		J. Carlson and R. Schiavilla, Structure and dynamics of few-nucleon systems
2000BE39		P.F. Bedaque, H.-W. Hammer and U. van Kolck, Effective theory of the triton
2000FR1C		J.L. Friar, Twenty-five years of progress in the three-nucleon problem
2001SI39		I. Sick, Elastic electron scattering from light nuclei
2002BA15		B.R. Barrett et al., Ab initio large-basis no-core shell model and its application to light nuclei
2002BA65		B.R. Barrett, P. Navratil and J.P. Vary, Large-basis no-core shell model
2002FR21		J.L. Friar, The structure of light nuclei and its effect on precise atomic measurements
2002GL1F		W. Glockle, Three-nucleon scattering
2004GL08		W. Glockle et al., Electron scattering on 3He - A playground to test nuclear dynamics
2005VI05		M. Viviani et al., New developments in the study of few-nucleon systems
2006HE17		K. Helbing, The Gerasimov-Drell-Hearn sum rule
2006MI33		G.A. Miller, A.K. Opper and E.J. Stephenson, Charge Symmetry Breaking and QCD
2006WE03		C. Weinheimer, Neutrino mass from triton decay
2007EF1A		V.D. Efros, et al., The Lorentz Integral Transform (LIT) method and its applications to perturbation-induced reactions
2007SA59		H. Sakai, Three-nucleon forces studied by nucleon-deuteron scattering
2008DE1D		A. Deltuva, A.C. Fonseca, and P.U. Sauer, Nuclear many-body scattering calculations with the Coulomb interaction
2008KI08		A. Kievsky et al., A high-precision variational approach to three- and four-nucleon bound and zero-energy scattering states
2008OT03		E.W. Otten and C. Weinheimer, Neutrino mass limit from tritium β decay
2009EP1A		E. Epelbaum, H.-W. Hammer and Ulf-G. MeiBner, Modern theory of nuclear forces
2009LE1D		W. Leidemann, Few-nucleon physics

E		bombarding energy in the laboratory system; subscripts p, d, t, π refer to protons, deuterons, tritons, pions, etc.;
Ecm		energy in the cm system;
Qm		reaction energy;
Sn(Sp)		neutron(proton) separation energy;
σ(θ)		differential cross section;
σtot		total cross section;
P(θ)		polarization;
Ay(θ)		vector analyzing power; VAP;
TAP		tensor analyzing power;
Jπ		spin and parity;
μ		magnetic moment;
μN		nuclear magneton;
ann		neutron-neutron scattering length;
apn		proton-neutron scattering length;
and		neutron-deutron scattering length;
apd		proton-deutron scattering length;
rch		rms charge radius;
rm		rms magnetic radius;
DWBA		Distorted Wave Born Approximation;
FSI		final state interaction;
QFS		quasifree scattering.
		If not specified otherwise, energies are given in MeV.