l - th / 9 81 20 31 v 1 1 0 D ec 1 99 8 Monte Carlo methods and applications for the nuclear shell model

The shell-model Monte Carlo (SMMC) technique transforms the traditional nuclear shell-model problem into a path-integral over auxiliary fields. We describe below the method and its applications to four physics issues: calculations of sd-pf-shell nuclei, a discussion of electron-capture rates in pf-shell nuclei, exploration of pairing correlations in unstable nuclei, and level densities in rare earth systems. Studies of nuclei far from stability have long been a goal of nuclear science. Nuclei on either side of the stability region, either neutron-rich or deficient, are being produced at new radioactive beam facilities across the world. At these facilities, and with the help of advances in nuclear many-body theory, the community will address many of the key physics issues including: mapping of the neutron and proton drip lines, thus exploring the limits of stability; understanding effects of the continuum on weakly bound nuclear systems; understanding the nature of shell gap modifications in very neutron-rich systems; determining nuclear properties needed for astrophysics; investigating deformation, spin, and pairing properties of systems far from stability; and analyzing microscopically unusual shapes in unstable nuclei. The range and diversity of nuclear behavior, as indicated in the above list of ongoing and planned experimental investigations, have naturally engendered a host of theoretical models. Short of a complete solution to the many-nucleon problem, the interacting shell model is widely regarded as the most broadly capable description of low-energy nuclear structure, and the one most directly traceable to the fundamental many-body problem. Difficult though it may be, solving the shell-model problem is of fundamental importance to our understanding of the correlations found in nuclei. One avenue of research during the past few years has been in the area of the nuclear shell model solved not by diagonalization, but by integration. In what follows,