GFMC calculations of nine- and ten-body nuclei using just the AV18 NN potential and AV18 + Illinois-4 NNN potential. The negative-parity A = 10 results are preliminary. Note that a three-nucleon potential is necessary to obtain the correct 10B ground state.

Steven Pieper, Robert Wiringa, and Bogdan Mihalia, Argonne National Laboratory

Research Objectives
Our goal is to compute ground-state and low-lying excited-state expectation values of energies, densities, structure functions, astrophysical reaction rates, etc., for light nuclei, neutron drops, and nucleonic matter, using a Hamiltonian that also provides an excellent description of nucleon-nucleon scattering. Such a "standard nuclear model" can then be used, for example, to compute low-energy astrophysical reactions which cannot be experimentally measured.

Computational Approach
This project uses variational (VMC) and Green's function (GFMC) Monte Carlo and coupled-cluster [exp(S)] methods. The variational wave function contains non-central two- and three-body correlations corresponding to the operator structure of the potentials. The GFMC systematically improves these wave functions to give the exact (within statistical errors) energy for the given Hamiltonian. We have demonstrated the reliability of constrained path methods for overcoming the well-known Fermion sign problem. Our Monte Carlo methods are limited to light nuclei; for heavier systems we use the coupled-cluster method. The present implementation of the exp(S) method for finite nuclei is carried out in configuration space. We have shown that we can choose a large enough configuration space in order to achieve convergence despite the relatively hard core of the NN interaction.

Accomplishments
We made our first calculations of nine- and ten-nucleon systems, the only calculations of such nuclei that use realistic two- and three-nucleon interactions and achieve a reliability of 1-2%. Our ¹⁰B calculations show that one must have a three-nucleon potential to correctly predict the ground-state spin of 3⁺. Using just realistic two-nucleon potentials gives a ground-state spin of 1⁺. We are now making the first calculations of bound unnatural parity states in A = 10 nuclei; these calculations are significantly more complicated than those for the normal parity states. We are also studying the development of nuclear structure in these nuclei as the two-nucleon potential evolves from more simple schematic models to a fully realistic interaction.

For heavier nuclei, we have continued the study of ground-state properties in the p-shell using exp(S). We are in the process of carrying out calculations for the spin-isospin saturated nuclei ¹²C, ¹⁴C, ¹⁴O, and ¹⁶O. We are also in the process of making exp(S) calculations of Yrast states in neighboring nuclei, and calculating observables of interest to Jefferson Lab, such as the magnetic form factors for ¹⁵N and ¹³C.

Significance
One of the principal goals of nuclear physics is to explain the properties and reactions of nuclei in terms of interacting nucleons (protons and neutrons). There are two fundamental aspects to this problem: (1) determining the interactions between nucleons, and (2) given the interactions (i.e., the Hamiltonian), making accurate calculations of many-nucleon systems. We work in both areas and have made the only calculations of six- through ten-nucleon systems that use realistic interactions and that are accurate to 1-2% for the binding energies. The resulting wave functions can be used to compute properties measured at electron and hadron scattering facilities (in particular JLab), and to compute astrophysical reaction rates, many of which cannot be measured in the laboratory.

Publications
S. C. Pieper, V. R. Pandharipande, R. B. Wiringa, and J. Carlson, "Realistic models of pion-exchange three-nucleon interactions," Phys. Rev. C 64, 014001 (2001).

R. B. Wiringa, S. C. Pieper, J. Carlson, and V. R. Pandharipande, "Quantum Monte Carlo calculations of A = 8 nuclei," Phys. Rev. C 62, 014001 (2000).

K. M. Nollett, R. B. Wiringa, and R. Schiavilla, "Six-body calculation of the a-deuteron radiative capture cross section," Phys. Rev. C 63, 024003 (2001).

http://www.phy.anl.gov/theory/research/forces.html