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Nuclear Physics A

Perturbation theory for projected states in the pairing force model

B. Atalay, D.M. Brink, A. Mann

Published Jan 1, 1974• 10 citations
Publisher
DOI
10.1016/0375-9474(74)90035-9

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The solvable two-level pairing model is used to test two new number-conserving approximations. These approximations are compared with the exact results, with perturbation theory, with the BCS method, and with the projected BCS method of Kerman, Lawson, and Macfarlane. It is found that second-order perturbation theory and one of the tested approximations work rather well for not too high values of the pairing-force strength, while for higher values the other approximation turns out to be quite good.
The BCS and/or Hartree-Fock-Bogoliubov theories are extended by treating the effect of four quasiparticle states perturbatively. The approach is tested on the pairing Hamiltonian, showing that it combines the advantage of standard perturbation theory, valid at low pairing strength, and of nonperturbative approaches breaking the particle number, valid at higher pairing strength. Including the restoration of particle number further improves the description of pairing correlation. In the presented test, the agreement between the exact solution and the combined perturbative plus projection is almost perfect. The proposed method scales friendly when the number of particles increases and provides a simple alternative to other more complicated approaches.