A composite bosons minimal basis for the pairing Hamiltonian

The pairing interaction among identical nucleons in a single-particle level is treated in the hamiltonian formalism using even Grassmann variables. A minimal (irreducible) basis having a remarkable symmetry property is set up using composite, commuting variables with a finite index of nilpotency. Ei genvalues and eigenfunctions of given energy, seniority and zero third comp onent of the angular momentum of the pairing hamiltonian are then found. Th e eigenvectors, which cannot be cast solely in terms of composite bosons wi th angular momentum zero and two, are expanded in the minimal basis with co efficients analytically expressed in terms of a generalized hypergeometric function. (C) 2000 Published by Elsevier Science B.V. All rights reserved.