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Published October 1, 1993 | public
Journal Article Open

Monte Carlo evaluation of path integrals for the nuclear shell model


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.

Additional Information

©1993 The American Physical Society. Received 12 May 1993. This work was supported in part by the National Science Foundation, Grants No. PHY90-13248 and No. PHY91-15574, and by the DuBridge Foundation (W.E.O.). We are grateful for discussions with P. Vogel and D. Dean and thank B. Girish for his help with the Intel parallel supercomputers.


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