Computational Nuclear Theory

Volker E. Oberacker and A. Sait Umar, Vanderbilt University

Research Objectives

Describe theoretically the structure of atomic nuclei far from the stability line. Study the dynamics of nuclear fission, in particular viscosity of nuclear matter, via prompt muon-induced fission. Simulate relativistic heavy-ion collisions in a (3+1) dimensional classical string model.

Computational Approach

In the nuclear structure project, we solve a set of self-consistent Schršdinger equations (HF + BCS / HFB) on a 2D lattice (axial symmetry) using the Cray J90; high accuracy is achieved by utilizing the Galerkin method with B-Splines. In the muon-induced fission project, we implement the time-dependent Dirac equation on a 3D Cartesian lattice using the B-Spline collocation method on the C90 and J90. The classical string calculations in (3+1) dimensions are solved using Monte Carlo techniques on the J90.

Accomplishments

The main challenge for the theory of exotic nuclei near the proton or neutron drip lines is that the outermost nucleons are weakly bound (implying a large spatial distribution) and that these states are strongly coupled to the particle continuum. For these reasons, the traditional basis-expansion methods fail to converge. We overcome these problems by representing the nuclear Hamiltonian on a lattice. We have achieved high accuracy (on a moderate-size lattice) in calculating nuclear observables with the B-Spline Galerkin method.

Significance

The nuclear quantum many-particle problem represents a numerical challenge. Our mean-field nuclear structure calculations are carried out in connection with current and future experiments at DOE facilities such as the Oak Ridge Holifield Radioactive Ion Beam Facility (HRIBF) accelerator and the proposed ISOL (Isotope Separation On-Line) facility. The classical string model simulations provide the theoretical background for experiments to be carried out at Brookhaven's Relativistic Heavy-Ion Collider (RHIC).

Publications

D. R. Kegley, V. E. Oberacker, M. R. Strayer, A. S. Umar, and J. C. Wells, "Basis spline collocation method for solving the Schroedinger equation in axially symmetric systems," J. Comp. Phys. 128, 197 (1996).

V. E. Oberacker et al., "Prompt muon-induced fission," in Proceedings of the International Conference on Fission and Properties of Neutron-Rich Nuclei (World Scientific, Teaneck, NJ, 1998).

D. E. Malov, A. S. Umar, and D. J. Ernst, "Hadronic structure functions as distributions of classical strings," Phys. Rev. C (submitted, 1998).