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 ch...

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Bibliographic Details
Published in:Physical review. C, Nuclear physics Nuclear physics, 1993-10, Vol.48 (4), p.1518-1545
Main Authors: Lang, GH, Johnson, CW, Koonin, SE, Ormand, WE
Format: Article
Language:English
Subjects:
CALCULATION METHODS
EXTRACTION
FERMIONS
FEYNMAN PATH INTEGRAL
FUNCTIONS
INTEGRALS
MANY-BODY PROBLEM
MATHEMATICAL MODELS
MONTE CARLO METHOD
NUCLEAR MODELS
NUCLEAR PHYSICS AND RADIATION PHYSICS
RESPONSE FUNCTIONS
SEPARATION PROCESSES 663120 > Nuclear Structure Models & Methods-- (1992-)
SHELL MODELS
STRENGTH FUNCTIONS
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Summary: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.
ISSN:0556-2813
1089-490X
DOI:10.1103/physrevc.48.1518