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Nuclear Physics

Many-body perturbation methods in a soluble model

Amnon Katz

Published Oct 1, 1960• 15 citations
Publisher
DOI
10.1016/0029-5582(60)90205-4

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Abstract It is shown that a perturbation expansion for projected states proposed earlier satisfies the Schrödinger equation. Modified forms of the series are suggested, and criteria for their convergence are discussed. The method is applied to the ‘Lipkin model' for a two-level many-body problem, which is exactly soluble. The second-order term in the perturbation series is shown to give a good approximation, and is compared with alternative methods. The convergence factor of the series is shown to be better than that of ordinary perturbation theory, which in most cases of this model is divergent.
The exactly soluble R(8) model of Krumlinde and Szyma\ifmmode \acute{n}\else \'{n}\fi{}ski is used as a testing ground for three many-body methods applied to the yrast band: (i) the self-consistent cranking model, (ii) self-consistent cranking plus random-phase approximation, and (iii) variation after projection of particle number. All three methods agree very well with exact results outside of the critical region. The behavior in the critical region is examined in detail.NUCLEAR STRUCTURE Many-body methods, solvable model, high-spin states.