Exact and approximate solutions of the nuclear pairing problem

H.C. Pradhan, Yukihisa Nogami, J. Law

Feng Pan, Jerry Paul Draayer

Vladimir Zelevinsky, Alexander Volya

Volya, A, B. ALEX BROWN, Zelevinsky, V

A method is developed for exact treatment of the general pairing problem in a finite Fermi-system. The method is based on SU(2) quasispin algebras that are present in the problem. We show examples of practical applications of the method and its comparison with approximate treatments.

HERVÉ MOLIQUE, J. Dudek

In this article we present a method to parametrise the exact solutions to the nuclear pairing problem, for realistic large-scale many-body spaces. This new approach allows for rapid and quite accurate estimates of the pairing influence on the excitation energies of the nucleus, treated in the standard mean-field approximation.

HERVÉ MOLIQUE, J. Dudek

A comparison of different seniority zero solutions to the picket-fence model for the nuclear pairing hamiltonian problem is performed. These solutions are calculated, in the normal regime, within the self-consistent Random Phase Approximation (SCRPA) and various simplifications of this formalism, and also with the Tamm-Dancoff approach in the particle-particle-hole-hole channel (pphh-TDA). The latter formalism represents a first approximation to the earlier developped so-called P-Symmetric Many-Body method (PSY-MB). In the superfluid regime, the solutions are compared with the BCS results. By comparing the results with the exact ones, obtained by the Richardson method, it is shown that the PSY-MB method provides a powerful tool in solving the problem with good accuracy both in the normal and the superfluid regime, for single-particle space sizes adapted to typical nuclear structure calculations.