NERSC 1999 Annual Report

Research Objectives

Quantum Monte Carlo methods for the nuclear shell model allow exact calculations in much larger model spaces than can be treated by conventional methods. The methods are applied to study various properties of medium-mass and heavy nuclei at zero and finite temperature, including level densities, collective properties, pairing, and strength functions.

Computational Approach

We use a representation of the many-body propagator (in imaginary time) in terms of a functional integral over one-body propagators in fluctuating external fields, known as the Hubbard-Stratonovich (HS) transformation. Monte Carlo methods are used to perform the high-dimensional integration. A modification of the Metropolis algorithm, based on Gaussian quadratures, improves the efficiency of the Monte Carlo random walk. Various projection methods are implemented in the HS representation. The calculations are done in the framework of the nuclear shell model.

Accomplishments

Using the Monte Carlo methods in the full fpg_9/2-shell, we have calculated accurate level densities of nuclei in the iron region and found excellent agreement with experiment. We extracted single-particle level density and backshift parameters by fitting the calculated densities to a backshifted Bethe formula, and found new and interesting shell effects in the systematics of these parameters.

We have used a particle-number reprojection method to calculate thermal observables (e.g., level densities) for a series of nuclei using a Monte Carlo sampling for a single nucleus. Level densities of odd-mass and odd-odd nuclei are reliably extracted despite a sign problem. Both the mass and isospin dependence of the experimental level densities are well described without any adjustable parameters. The single-particle level density parameter is found to vary smoothly with mass. The odd-even staggering observed in the calculated backshift parameter follows the experimental data more closely than do empirical formulas.

Significance

The initial applications of these techniques had been severely limited by the sign problem which is generic to fermionic Monte Carlo methods and occurs for all realistic nuclear interactions. We have developed a practical solution to the sign problem in the nuclear case which opens the door to new and interesting realistic calculations in much larger configuration spaces than could be treated previously. Our approach can address a variety of problems in nuclear physics and astrophysics that could not otherwise be solved in full shell calculations. Similar methods might also be useful in other fields in physics that require a non-perturbative approach to the interacting many-body problem.


Right panel: The level density of⁵⁹Co versus excitation energy E_x. The solid circles are the Monte Carlo (MC) results, and the solid line is the experiment. The two insets show the excitation energy and entropy as a function of temperature. The MC level density is well described by the backshifted Fermi gas formula, which is parametrized by the single-particle level density parameter a and the backshift parameter [delta]. Left panels: a and [delta] versus mass number A for cobalt isotopes. The solid circles are obtained from the MC calculations, while the pluses are the experimental values. The MC results follow the experimental data more closely than do empirical formulas (solid lines).

Publications

Y. Alhassid, S. Liu, and H. Nakada, "Particle-number reprojection in the shell model Monte Carlo method: Application to nuclear level densities," Phys. Rev. Lett. 83, 4265 (1999).

Y. Alhassid, "Monte Carlo methods for the nuclear shell model: Recent applications," in Highlights of Modern Nuclear Structure: Proceedings of the 6th International Spring Seminar on Nuclear Physics, edited by Aldo Covello (World Scientific, Singapore, 1999).

H. Nakada and Y. Alhassid, "Microscopic nuclear level densities from Fe to Ge by the shell model Monte Carlo method," Phys. Lett. B 436, 231 (1998).


< Table of Contents	Top ^	Next >