Comparison of computed energy levels of light nuclei with experimental (green) values. The blue lines are computed without a three-nucleon potential and fail to reproduce experiment. The red lines have a modern three-nucleon potential. The A = 9 calculations shown here are the first ab initio calculations of nine-body nuclei and were made on NERSC's IBM SP.

Steven Pieper, Argonne National Laboratory

Research Objectives
This project uses Green's function (GFMC) and variational (VMC) Monte Carlo (generically known as quantum Monte Carlo) methods to compute ground-state and low-lying excited state expectation values of energies, densities, structure functions, astrophysical reaction rates, etc., for light nuclei and neutron drops. Realistic two- and three-nucleon potentials are used. We are developing new computational techniques, optimizing them for different computer architectures, and improving the nuclear Hamiltonian used in the calculations. An area of increasing interest is the use of our wave functions to compute reaction rates of astrophysical interest.

Computational Approach
This project uses variational and Green's function Monte Carlo methods. The variational wave function contains noncentral 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.

The Quantum Monte Carlo methods work very efficiently on parallel processors. We use MPI and see speed-up efficiencies better than 97% for up to 512 CPUs on NERSC's IBM SP. The program has achieved 100 Gflops on the SP.

Accomplishments
This year we finished our study of new three-nucleon potential terms. Our previous work had demonstrated that the Hamilto-nian that has been used successfully for more than a decade in studies of s-shell nucleon is inadequate in the p-shell. Some of the possible new potential terms, whose forms are derived from meson-exchange arguments, result in considerable additional complications in the Green's function propagator. We have developed potential models that reproduce all of the known stable or narrow-width levels of up to nine-body nuclei with an average error of only 300 keV.

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% for the binding energies. The resulting wave functions can be used to compute properties measured at electron and hadron scattering facilities (in particular Jefferson Labora-tory), and to compute astrophysical reaction rates, many of which cannot be measured in the laboratory.

Publications
R. B. Wiringa, Steven C. Pieper, J. Carlson, and V. R. Pandharipande, "Quantum Monte Carlo calculations of A = 8 nuclei," Phys. Rev. C 62, 14001 (2000).

D. Van Neck, M. Waroquier, A. E. L. Dieperink, S. C. Pieper, and V. R. Pandharipande, "Center-of-mass effects on the quasi-hole spectroscopic factors in the ¹⁶O(e,e' p) reaction," Phys. Rev. C 57, 2308 (1998).

B. S. Pudliner, V. R. Pandharipande, J. Carlson, S. C. Pieper, and R. B. Wiringa, "Quantum Monte Carlo calculations of nuclei with A < 7," Phys. Rev. C 56, 1720 (1997).

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