Exact solution of the pairing problem in the LST scheme

Abstract

Exact solutions for the pairing interaction problem in the LST scheme are formulated in terms of the matrix elements of pair creation and annihilation operators for pairs coupled to zero orbital angular momentum. General expressions are given for these matrix elements for states with seniority [nu] = 0 and 1. This makes it possible to study an orbital pairing interaction with different spin singlet and triplet strengths acting in mixed configurations of several single-particle levels. The mathematical formulation of the problem is based on the eight-dimensional quasispin group which is broken down according to the decomposition O(8) [superset or implies] O(6) [superset or implies] [O(3) x O(3)], where O(6) corresponds to the usual Wigner supermultiplet symmetry group. A sample calculation for a simple two-level configuration, and states with [nu]1 = [nu]2 = 0, nucleon numbers of 4, 6, 8, 10, shows (i) that the pairing interaction is very effective compared with the single-particle excitations, and (ii) that it tends to make more stable those states built from the largest possible number of [alpha]-like grouping of 4 particles.