Pairing correlations studied in the two-level model

Abstract

We study the pairing energy in the ground state of a system of N particles occupying a symmetric two-level model space with a level degeneracy A. Assuming a pairing Hamiltonian, we calculate the energies of the projected BCS states, using the exact, the Kamlah, and the Lipkin-Nogami particle number projection methods. We And that conclusions regarding the quality of the B.C.S. approximation as well as various approximate projection methods, drawn from studying the N=A case alone, are not valid in the more general N g 0 case when the pairing interaction is weak.

Superdeformed rotational bands in the mercury region. A cranked Skyrme-Hartree-Fock-Bogoliubov study

“…(See the recent studies of model systems without [40,41] and with rotation [42], and the references cited therein. )…”

Implementation of a variational approach to approximate particle number projection with effective forces

“…This failure being, probably, the cause of the slow convergence rate found in some cases. It is important to notice that this happens in the strong pairing regime, this behavior was not observed in earlier investigations [5,9] probably because the considered model was too simplistic.…”

“…In refs. [5,9] the same restriction was made to solve the SCK2 equations. The general expression of δh 2 and the specific one for the Gogny force can be found in ref.…”

“…Since exact particle number projection (PNP) is very time consuming for non-separable interactions, the approximation most widely used is the LipkinNogami (LN) [1][2][3][4] one, just because of simplicity. The LN prescription can be derived in several ways [5], one transparent derivation [6,7] can be obtained in terms of the Kamlah [8] expansion to second order. Here one sees that the basic assumptions are : first, to have a well pair-correlated system (i.e.…”

“…Zheng, Sprung and Flocard [5], using a very simple model space of two levels discussed the LN and SCK2 approximation to particle number projection. The force used in the calculations was a monopole pairing which intensity G could be varied in order to simulate different pairing regimes.…”