Monte Carlo evaluation of path integrals for the nuclear shell model

Journal Article · Fri Oct 01 00:00:00 EDT 1993 · Physical Review, C (Nuclear Physics); (United States)

DOI:https://doi.org/10.1103/PhysRevC.48.1518· OSTI ID:6393245

Lang, G H; Johnson, C W; Koonin, S E; Ormand, W E ^[1]

---

1. W. K. Kellogg Radiation Laboratory, 106-38, California Institute of Technology, Pasadena, California 91125 (United States)

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.

• OSTI ID: 6393245
• Journal Information: Physical Review, C (Nuclear Physics); (United States), Vol. 48:4; ISSN 0556-2813
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
FEYNMAN PATH INTEGRAL
MONTE CARLO METHOD
SHELL MODELS
EXTRACTION
FERMIONS
MANY-BODY PROBLEM
RESPONSE FUNCTIONS
STRENGTH FUNCTIONS
CALCULATION METHODS
FUNCTIONS
INTEGRALS
MATHEMATICAL MODELS
NUCLEAR MODELS
SEPARATION PROCESSES
663120* - Nuclear Structure Models & Methods- (1992-)