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Physical Review C

Particle-hole interactions and vibrational states

Richard R. Chasman

Published May 1, 1974• 0 citations
Publisher

Abstract

A method is presented for the treatment of particle-hole residual interactions that is both simple and extremely accurate. This method is compared with the random-phase approximation, Tamm-Dancoff approximation, and other approximations in the schematic model of Brown and the monopole model of Lipkin, Meshkov, and Glick.
DOI
10.1103/physrevc.9.1795

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Abstract The Agassi model (Agassi 1968 Nucl. Phys. A 116 49) is a schematic two-level model that involves pairing and monopole–monopole interactions. It is, therefore, an extension of the well known Lipkin–Meshkov–Glick model (Lipkin et al 1965 Nucl. Phys. 62 188). In this paper we review the algebraic formulation of an extension of the Agassi model as well as its bosonic realization through the Schwinger representation. Moreover, a mean-field approximation for the model is presented and its phase diagram discussed. Finally, a 1/ j analysis, with j proportional to the degeneracy of each level, is worked out to obtain the thermodynamic limit of the ground state energy and some order parameters from the exact Hamiltonian diagonalization for finite— j .