Physics – Nuclear Physics – Nuclear Theory
Scientific paper
1993-05-14
Phys.Rev.C48:1518-1545,1993
Physics
Nuclear Physics
Nuclear Theory
38 pages, RevTeX v3.0, figures available upon request; Caltech Preprint #MAP-159
Scientific paper
10.1103/PhysRevC.48.1518
We present in detail a formulation of the shell model as a path integral and Monte Carlo techniques for its evaluation. The formulation, which linearizes the two-body interaction by an auxiliary field, is quite general, both in the form of the effective `one-body' Hamiltonian and in the choice of ensemble. In particular, we derive formulas for the use of general (beyond monopole) pairing operators, as well as a novel extraction of the canonical (fixed-particle number) ensemble via an activity expansion. We discuss the advantages and disadvantages of the various formulations and ensembles and give several illustrative examples. We also discuss and illustrate calculation of the imaginary-time response function and the extraction, by maximum entropy methods, of the corresponding strength function. Finally, we discuss the "sign-problem" generic to fermion Monte Carlo calculations, and prove that a wide class of interactions are free of this limitation.
Johnson Calvin W.
Koonin Steven E.
Lang G. H.
Ormand Erich W.
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