A composite bosons minimal basis for the pairing Hamiltonian

Abstract

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. Eigenvalues and eigenfunctions of given energy, seniority and zero third component of the angular momentum of the pairing hamiltonian are then found. The eigenvectors, which cannot be cast solely in terms of composite bosons with angular momentum zero and two, are expanded in the minimal basis with coefficients analytically expressed in terms of a generalized hypergeometric function.

15 pages, LateX, 1 Postscript figure

References in corpus (3)

• Bosonization and even Grassmann variables
• A free action for pions as quark composites
• The quark-composites approach to QCD: The nucleon-pion interaction

Cited by in corpus (5)

• On the analytic solution of the pairing problem: one pair in many levels
• The Goldstone bosons in the pairing Hamiltonian: the path integral approach
• The many levels pairing Hamiltonian for two pairs
• The pairing Hamiltonian for one pair of identical nucleons bound in a potential well
• Bosonization of the pairing Hamiltonian