Monte Carlo evaluation of path integrals for the nuclear shell model

G. H. Lang, C. W. Johnson, S. E. Koonin, W. E. Ormand

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1518-1545
Number of pages28
JournalPhysical Review C - Nuclear Physics
Volume48
Issue number4
DOIs
StatePublished - 1993

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formulations
evaluation
maximum entropy method
time response
monopoles
fermions
interactions
operators
expansion

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Nuclear and High Energy Physics

Cite this

Monte Carlo evaluation of path integrals for the nuclear shell model. / Lang, G. H.; Johnson, C. W.; Koonin, S. E.; Ormand, W. E.

In: Physical Review C - Nuclear Physics, Vol. 48, No. 4, 1993, p. 1518-1545.

Research output: Contribution to journalArticle

Lang, G. H. ; Johnson, C. W. ; Koonin, S. E. ; Ormand, W. E. / Monte Carlo evaluation of path integrals for the nuclear shell model. In: Physical Review C - Nuclear Physics. 1993 ; Vol. 48, No. 4. pp. 1518-1545.
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