Effective interactions for light nuclei: an effective (field theory) approach

One of the central open problems in nuclear physics is the construction of effective interactions suitable for many-body calculations. We discuss a recently developed approach to this problem, where one starts with an effective field theory containing only fermion fields and formulated directly in a no-core shell-model space. We present applications to light nuclei and to systems of a few atoms in a harmonic-oscillator trap. Future applications and extensions, as well as challenges, are also considered

Effective Theory for Trapped Few-Fermion Systems

We apply the general principles of effective field theories to the construction of effective interactions suitable for few- and many-body calculations in a no-core shell model framework. We calculate the spectrum of systems with three and four two-component fermions in a harmonic trap. In the unitary limit, we find that three-particle results are within 10% of known semi-analytical values even in small model spaces. The method is very general, and can be readily extended to other regimes, more particles, different species (e.g., protons and neutrons in nuclear physics), or more-component fermions (as well as bosons). As an illustration, we present calculations of the lowest-energy three-fermion states away from the unitary limit and find a possible inversion of parity in the ground state in the limit of trap size large compared to the scattering length. Furthermore, we investigate the lowest positive-parity states for four fermions, although we are limited by the dimensions we can currently handle in this case.Comment: 8 pages, 5 figure

Two and Three Nucleons in a Trap and the Continuum Limit

We describe systems of two and three nucleons trapped in a harmonic-oscillator potential with interactions from the pionless effective field theory up to next-to-leading order (NLO). We construct the two-nucleon interaction using two-nucleon scattering information. We calculate the trapped levels in the three-nucleon system with isospin $T=1/2$ and determine the three-nucleon force needed for stability of the triton. We extract neutron-deuteron phase shifts, and show that the quartet scattering length is in good agreement with experimental data.Comment: 19 pages, 15 figure

Nucleon-Nucleon Scattering from Effective Field Theory

We perform a nonperturbative calculation of the 1S0 NN scattering amplitude using an effective field theory (EFT) expansion. The expansion we advocate is a modification of what has been used previously; it is no a chiral expansion in powers of the pion mass. We use dimensional regularization throughout and the MS-bar subtraction scheme; our final result depends only on physical observables. We show that the EFT expansion of the quantity |p|cot delta(p) converges at momenta much greater than the scale that characterizes the derivative expansion of the EFT Lagrangian. Our conclusions are optimistic about the applicability of an EFT approach to the quantitative study of nuclear matter.Comment: Revised discussion of power counting in the EFT expansion. Tex file uses harvmac, epsf macros, 35 pages with 9 postscript figure

Three and Four Harmonically Trapped Particles in an Effective Field Theory Framework

We study systems of few two-component fermions interacting via short-range interactions within a harmonic-oscillator trap. The dominant interactions, which are two-body, are organized according to the number of derivatives and defined in a two-body truncated model space made from a bound-state basis. Leading-order (LO) interactions are solved for exactly using the formalism of the No-Core Shell Model, whereas corrections are treated as many-body perturbations. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. We present results at unitarity for three- and four-fermion systems, which show excellent agreement with the exact solution (for the three-body problem) and results obtained by others methods (in the four-body case). We also present results for finite scattering lengths and non-zero range of the interaction, including (at positive scattering length) observation of a change in the structure of the three-body ground state and extraction of the atom-dimer scattering length.Comment: 18 pages, 10 figure

Electric Dipole Moments of Light Nuclei From Chiral Effective Field Theory

We set up the framework for the calculation of electric dipole moments (EDMs) of light nuclei using the systematic expansion provided by chiral effective field theory (EFT). We take into account parity (P) and time-reversal (T) violation which, at the quark-gluon level, originates from the QCD vacuum angle and dimension-six operators capturing physics beyond the Standard Model. We argue that EDMs of light nuclei can be expressed in terms of six low-energy constants that appear in the P- and T-violating nuclear potential and electric current. As examples, we calculate the EDMs of the deuteron, the triton, and 3He in leading order in the EFT expansion

Charge-Symmetry-Breaking Three-Nucleon Forces

Leading-order three-nucleon forces that violate isospin symmetry are calculated in Chiral Perturbation Theory. The effect of the charge-symmetry-breaking three-nucleon force is investigated in the trinucleon systems using Faddeev calculations. We find that the contribution of this force to the 3He - 3H binding-energy difference is approximately 5 keV.Comment: 14 pages, 3 figure

Charge-Independence Breaking in the Two-Pion-Exchange Nucleon-Nucleon Force

Charge-independence breaking due to the pion-mass difference in the (chiral) two-pion-exchange nucleon-nucleon force is investigated. A general argument based on symmetries is presented that relates the charge-symmetric part of that force to the proton-proton case. The static potential linear in that mass difference is worked out as an explicit example by means of Feynman diagrams, and this confirms the general argument.Comment: 10 pages, latex, 1 figure -- epsfig.sty required -- To appear in Phys. Rev.

The AyA_y Puzzle and the Nuclear Force

The nucleon-deuteron analyzing power $A_y$ in elastic nucleon-deuteron scattering poses a longstanding puzzle. At energies $E_{lab}$ below approximately 30 MeV $A_y$ cannot be described by any realistic NN force. The inclusion of existing three-nucleon forces does not improve the situation. Because of recent questions about the $^3P_J$ NN phases, we examine whether reasonable changes in the NN force can resolve the puzzle. In order to do this we investigate the effect on the $^3P_J$ waves produced by changes in different parts of the potential (viz., the central force, tensor force, etc.), as well as on the 2-body observables and on $A_y$. We find that it is not possible with reasonable changes in the NN potential to increase the 3-body $A_y$ and at the same time to keep the 2-body observables unchanged. We therefore conclude that the $A_y$ puzzle is likely to be solved by new three-nucleon forces, such as those of spin-orbit type, which have not yet been taken into account.Comment: 35 pages in REVTeX, 1 figure in postscript and 3 figures in PiCTe

The spin-dependent nd scattering length - a proposed high-accuracy measurement

The understanding of few-nucleon systems at low energies is essential, e.g. for accurate predictions of element abundances in big-bang and stellar fusion. Novel effective field theories, taking only nucleons, or nucleons and pions as explicit degrees of freedom, provide a systematic approach, permitting an estimate of theoretical uncertainties. Basic constants parameterising the short range physics are derived from only a handful of experimental values. The doublet neutron scattering length a_2 of the deuteron is particularly sensitive to a three-nucleon contact interaction, but experimentally known with only 6% accuracy. It can be deduced from the two experimentally accessible parameters of the nd scattering length. We plan to measure the poorly known "incoherent" nd scattering length a_{i,d} with 10^{-3} accuracy, using a Ramsey apparatus for pseudomagnetic precession with a cold polarised neutron beam at PSI. A polarised target containing both deuterons and protons will permit a measurement relative to the incoherent np scattering length, which is know experimentally with an accuracy of 2.4\times 10^{-4}.Comment: 5 pages LaTeX2e, 1 .eps figure. To be published in Nucl. Inst. Methods A as part of the Proceedings of the 9th International Workshop on Polarized Solid Targets and Techniques in Bad Honnef (Germany), 27th - 29th October 200