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NERSC 3 Greenbook

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Ab initio calculations of nuclear systems with realistic forces

J. Carlson (Theory Division, Los Alamos National Laboratory, Los Alamos, NM 87545), J. L. Forest (CEBAF Theory Group, Newport News, VA 23606), V. R. Pandharipande (Department of Physics, University of Illinois, Urbana, IL 61801), S. C. Pieper (Physics Division, Argonne National Laboratory, Argonne, IL 60439), D. G. Ravenhall (Department of Physics, University of Illinois, Urbana, IL 61801), R. Schiavilla ( CEBAF Theory Group, Newport News, VA 23606 and Department of Physics, Old Dominion University, Norfolk, VA 23529), and R. B. Wiringa (Physics Division, Argonne National Laboratory, Argonne, IL 60439).

The long-term goal of this group is to understand the stability, structure, and reactions of nuclei as a consequence of the interactions between individual nucleons. We seek a consistent description of nuclear systems ranging in size from the deuteron to neutron stars using a single Hamiltonian. To achieve this we must develop and refine both the nuclear Hamiltonian and the many-body computational techniques used to compute properties of nuclei from the Hamiltonian.

Realistic nuclear forces, that accurately describe two-nucleon scattering and bound states, are very complicated because they are strongly dependent on the relative orientations of the nucleon spins, positions, and momenta, and on the nuclear isospin (which differentiates between protons and neutrons). We express this by using non-central operators such as tensor and spin-orbit operators, with and with out isospin operators. We have constructed several force models over time; our most recent, the Argonne v₁₈ nucleon-nucleon potential, accurately fits over 4,300 NN scattering data with a $\chi^2$ near 1, but requires eighteen operator components. There is strong evidence for many-nucleon forces and special relativity can also be important. Solving the many-nucleon Schrödinger equation is consequently a very challenging theoretical problem.

Our quantum Monte Carlo (QMC) calculations of light nuclei use sophisticated variational trial functions, and then systematically improve on them with Green's function propagation (GFMC) to approach the true ground state. These calculations are very computer intensive and have always been limited by the available resources. In 1987 we made the first calculations of ⁴He that were accurate to $\sim$1% for the given Hamiltonian. In 1995 such calculations of ⁶Li became possible and at present we can do eight-nucleon systems. Variational cluster Monte Carlo calculations are used for larger closed-shell nuclei, and variational chain summation methods for nuclear and neutron matter. These are necessarily less accurate than the GFMC calculations of light nuclei and we are developing a cluster GFMC method for heavier nuclei.

Our recent progress in both the light and closed-shell nuclei has been made possible by massively-parallel super computers. The programs are written in Fortran-90 and use MPI. Because the kernels cannot be expressed in terms of BLAS's or other standard subroutines, care has been taken to optimize the Fortran for the computers being used; at present this means cache-based machines. The size of the cache is critical for good per-processor speed. Communication rates are very low and with load-balancing we achieve parallel efficiencies better than 95%. Per-processor memory sizes of up to 200 Mbyte are currently used. We use both the IBM SP at Argonne and the Cray T3E at NERSC, and achieve total job speeds of 8 GFLOPS on 64 nodes of the IBM SP (RS6000/593 processors).

Some of our recent results are itemized below; work in all of these areas is continuing.

• QMC has been used to calculate the ground states and many low-lying excited states for all $A \leq 8$ nuclei, demonstrating for the first time the microscopic origin of nuclear shell structure (figure 2).
• Our variational wave functions have been used to explain both elastic and inelastic electromagnetic form factors observed in electron-scattering experiments without the need of effective charges.
• The strong nuclear tensor force has been shown to produce novel toroidal correlations in nuclei (figure 3); several experiments have been proposed to search for these structures.
• The effects of special relativity on nuclear forces and nuclear binding have been studied in the framework of relativistic quantum mechanics for light nuclei.
• QMC has been used to study neutron drops, collections of neutrons bound by an external well, thus providing benchmarks for more schematic methods used to study nuclei far from stability and nuclei in the crusts of neutron stars.
• Studies are in progress for several radiative and weak capture reactions of astrophysical interest, including: ¹H$(p,e^+\nu_e)^2$H, ³He$(p,e^+\nu_e)^4$He, ⁴He$(d,\gamma)^6$Li, and ⁴He(³He$,\gamma)^7$Be.
• The QMC wave functions are being used to study the feasibility of constructing polarized ⁶Li and ⁷Li targets for electron-scattering experiments.

  

Figure 2: Spectra for A=6,8 nuclei. For each nucleus, experimental, Green's function Monte Carlo (GFMC), and variational Monte Carlo (VMC) energies are shown.

  

Figure 3: Constant density surfaces for a polarized deuteron in the $M_d = \pm1$ (left) and M_d = 0 (right) states.

NERSC 3 Greenbook

Next: Grand Challenge on High-Energy Up: High Energy and Nuclear Previous: Lattice Field Theory