Session 1: NN and many-body interactions: chiral perturbation theory; effective interactions
[J. Arrington, K. De Jager, C. Elster, R. Gilman, R. Holt, R. Machleidt, D. Phillips, A.
Schwenk, R. Wiringa]
16-17 October 2006, Washington, DC
The study of nucleon-nucleon (NN) and many-nucleon (mN) interactions has benefited from a close interplay of theory and experiment for many years. NN and mN interactions are the building blocks of our understanding of nuclear structure and low-energy nuclear reactions. Experiments provide the data to construct nuclear interactions, and test the limits of their accuracy and applicability. Data from elastic NN scattering are essentiallycomplete and a number of very precise NN potential models have been constructed.
However, data at higher energies is less extensive, andtheoretical models in the inelastic regime are severely deficient.mN interactions are a topic of great present interest; they are expectedon theoretical grounds and there is strong empirical evidence for themfrom mN scattering and nuclear structure. Additional three- and four-nucleon scattering data, particularly polarization data, are highly desirable; data on very neutron-rich nuclei from exotic beam sources are crucial for unraveling the isospin dependence of mN forces.
New theoretical approaches to nuclear interactions are being pursued using chiral perturbation theory and renormalization group methods, to construct models with consistent
NN and mN forces and current operators, and to find better effective interactions for heavier systems. Additional charge-independence-breaking and parity-violating terms in the interaction are being studied both theoretically and experimentally. There is also a major opportunity to extend our understanding of hyperon-nucleon interactions in the next few years. Present experiments indicate that hadronic degrees of freedom work well down to scales of 1 fm at low-energy and momentum transfers; future experiments at
JLab will continue to test these limits. The first attempts to connect aspects of NN and mN interactions with lattice QCD are now being made. Finally, there are interesting connections that can be made between halo nuclei, dilute neutron matterand other manybody systems such as cold atoms that exhibit "universal" behavior. These topics are all discussed in more detail below.
NN data of sufficient quality exist to allow a phase-shift analysis (PSA) upto 3000 MeV for pp scattering, but only to 800 MeV for np data. The 1993 Nijmegen PSA demonstrated that elastic NN data up to Elab=350 MeV can be represented at the chi**2/dof=1 level of accuracy. This led to a number of "high-precision" (HP) potentials, such as NijmI,
NijmII, AV18, and CD-Bonn, which set the foundation for the tremendous progress in ab initiocalculations of nuclear structure in the last decade. Additional data taken at IUCF and other places since 1993, have increased the elastic database by ~50% while definitely resolving the issue of pion-nucleon coupling strength.

The HP potentials can be adjusted to fit this added data as demonstrated by the latest version of the CD-Bonn potential. The HP potentials have similar long-range behavior, but differ in detail at shorter ranges, reflecting the non-unique character of NN potentials.
Many-body calculations of nuclear structure and reactions with these models often give similar results, demonstrating considerable convergence in our understanding. The remaining differences give a good estimate of uncertainties, e.g., in predicted reaction rates.
Models of NN forces in the inelastic regime are much more primitive. While not an issue for nuclear structure, realistic descriptions of nuclear reactions at intermediate and high energy could be of considerable benefit in a number of fields, such as the N* program at
JLab and medium-energy heavy-ion scattering.
The theoretical description of NN forces for a long time has been based on mesonexchange theory (MET). However, NN potentials have usually depended on a fair amount of phenomenology to reach HP status. A valuable new theoretical approach is chiral perturbation theory (chiPT), which isbased on the symmetries (and symmetrybreaking) of quantum chromodynamics (QCD). The chiPT uses "power counting" to make a systematic expansion in momentum and chiral-symmetry breaking. NN potentials are constructed at increasing levels of sophistication, from lowest order (LO) to successively higher levels. At N3LO (next-to-next-to-next-to-leading order) it ispossible to fit the elastic NN data at about the same level of accuracy as the HP potentials, as demonstrated by the Idaho potential, while reducing the number of fit parameters from about 40 to 24.
Both MET and chiPT predict the existence of many-nucleon forces. Three-nucleon (3N) forces have been modeled in MET for a long time as a means of including the effect of non-nucleonic degrees of freedom, e.g., low-lying nucleon resonances. In chiPT, 3N forces appear at N2LO, 4N forces at N3LO, etc., which are predicted to be successively weaker as the order increases. In practice, 3N forces such as Fujita-Miyazawa, Tucson-
Melbourne, Brazil, and Urbana provide additional binding and increase the spin-orbit splitting between states in light nuclei, which are under-predicted by the HP potentials.
The 3N forces can contribute in both T=1/2 and T=3/2 triples. Experimental studies of extremely neutron-rich light nuclei, such as the recent determinations of charge radii in helium and lithium isotopes using exotic beam sources, are a particularly effective means of studying this isospin dependence. This is an important ingredient for a number of astrophysical contexts, such as heavy-element nucleosynthesis and neutron stars.
The situation for multi-nucleon scattering is less clear. Comparisonsbetween highquality Nd scattering data and very precise calculations by the Bochum-Krakow and Pisa groups show that iterated HP and N2LO chiPT potentials explain much of the cross section data. However, a variety of polarizeddata, at even very low energies, show significant deviations. There is fairly little spread between the HP potentials; addition of present 3N force models improve the agreement with data in many cases, but worsen it in others. However, Nd scattering and A=3 bound states probe only the T=1/2 component of 3N forces; to test the T=3/2 component n-t or p-3He scattering is needed.

There is a need for additional three- and four-nucleon data, at both lowand intermediate energies and for both elastic scattering and break-upreactions. We note with dismay that the experimental facilities that provide such data are disappearing, just at a time when the theoretical studies are making significant progress. There is clearly much room for improvement in the 3N potentials; new potentials such as the Illinois modelsand chiPT at the N3LO level give hope of further progress. This will be a major frontier for the next decade.
Another major goal is to translate as much of our newfound knowledge of NN and mN interactions into effective interactions for heavier systems, e.g., replacing Skyrme-type models with finite-range interactions connectedto NN scattering, and helping the search for a "universal" energy-density functional. Present potentials are used as input to ab initio calculations of light nuclei, including Green's function Monte Carlo, no-core shell model, and coupled cluster methods. Some of these calculations can be extended tolarger systems, but it will be some time before heavy nuclei can beevaluated at this level. Part of the difficulty is the strong repulsive core of typical HP potentials. One method to ameliorate this problem is the Vlowk approach, which employs renormalization-group ideas to formulate softer versions of existing potentials, characterized by a variable cutoff that represents a resolution scale. Transformations that maintain low-energy observables are made and dependence on the cutoff tested in many-body calculations. At low-resolution scales there is evidence that 3N potentials become perturbative, which can greatly simplify many-body calculations. Other unitary transformation methods, such as Jmatrixinverse scattering potentials, are exploring the freedom to alter off-shell NN potential behavior to fit nuclear binding energies.
Additional features of NN and mN interactions are becoming more accessible as the basic theoretical features are refined and ever more precise data are gathered. The chargedependence (CD) and charge-symmetry-breaking (CSB) parts of the strong interaction trace back to the mass and charges ofthe component up and down quarks. Part of the CD, which is clearly seen in differences between np and pp scattering in S-waves, and may be detectablein P-waves, is due to the difference in neutral and charged pion masses. However, the microscopic origin of CSB is less clear and is limited bythe small amount of nn scattering data. These terms are the source forthe Nolen-Schiffer anomaly and control isospin-mixing in nuclei, which isan important background term for various experimental symmetry tests. There is also a small parity-violating part to the NN interaction. New experiments in progress at LANSCE and NIST and planned for the SNS should provide important constraints on current parameterizations of this force.
Calculations of nuclear structure and reactions require electroweakoperators beyond the one-body impulse approximation. In particular, meson-exchange currents and nucleon resonances can make important andmeasurable contributions to nuclear electromagnetic moments, structurefunctions, transition form factors, and weak decays. Two-body
(andhigher) operators can be constructed with MET or chiPT that are consistent with the
NN and 3N interactions. Notable recent applications are precisedeterminations of np radiative capture at Big Bang energies and pp weak capture at solar energies. These reac-

tions are difficult or impossible to measure in the laboratory, so reliable theory with good error estimates is essential.
Hyperon-nucleon (HN) interactions are an important related subject. There is very little
Lambda-N scattering data, but a moderate amount of dataon hypernuclear ground and excited states. A broad program to study the spectroscopy of hypernuclei is being established at JLab, and initialexperiments on nuclei like 9Be, 12C, and 16O, have achieved significantlyimproved energy resolution relative to earlier studies with pion or kaon beams. The electron-induced hypernuclear spectroscopy provides complementary information with a different isospin selectivity character. This program willprovide much needed information on the Lambda-N interaction. Theoretically, HN interactions have many similarities but also many differences with NN interactions: no one-pion-exchange in Lambda-N, but one-kaon-exchange; important two-pion-exchange with the excitation of an intermediate Sigma; and HNN forces that may be relatively more important than 3N forces, depending on whether Sigmas are kept explicitly. Better HN forces would help us understand the role of hyperonic degreesof freedom in high-density matter, e.g., compact stars.
The validity of using hadronic degrees of freedom has been tested inelastic electron scattering on the deuteron; indications are that a hadronicdescription works well down to scales of 1 fm at low-energy transfers. Corresponding experiments on 3He and 4He are planned in the near future, which should provide a further test. However, there is evidence of thescaling predicted by quark counting rules and a failure of the hadronic description at large energy and momentum transfers, as seen in deuteron photodisintegration. Additional experiments are probing the boundary between hadronic and quark degrees of freedom at lower momentum transfer, through measurements of the
Coulomb sum rule on a range of nuclei and polarization transfer in proton knockout from
4He.
NN and mN potentials are effective forces representing the highlynonpertubative lowenergy regime of QCD. Initial attempts at calculatingNN scattering in lattice QCD have been made with encouraging results. It will be interesting to see what developments will be possible along these lines in the next few years. Certain observables in nuclei are correlated with one another for reasons that are independent of the details of the force.
These "universal" relations, e.g. the Tjon line and the scaling of low-energy 3N scattering with the binding energy, can be understood using a systematic expansion about the limit where NN scattering lengths are infinite. Possible applications include dilute neutron matter in supernovae and neutron stars. The physics is closely related to other subjects such as cold atoms, where the scattering lengths are also large compared to the range of the interaction.