Five-Dimensional Quasispin. Exact Solutions of a Pairing Hamiltonian in theJ−TScheme

Abstract

The matrix elements of a charge-independent pairing Hamiltonian spanning several single-particle states have been expressed in terms of the matrix elements of the infinitesimal operators of $R_5$, the rotation group in a five-dimensional space. General algebraic expressions for these matrix elements have been calculated for states with reduced isospin $t=0, \frac{1}{2}, \mathrm{and}, 1$, in a scheme in which both nucleon number $N$ and isospin $T$ are good quantum numbers, making it possible to find exact solutions to the charge-independent pairing Hamiltonian for states with individual level seniorities $v<~2$. Exact solutions are compared with perturbation-theory formulas for some simple models. The results indicate that perturbation theory may be used as a guide to an understanding of the charge-independent pairing interaction in its dependence on $N$ and $T$. For relatively strong pairing and fixed $T$, the dependence on nucleon number $N$ is similar to that for configurations of identical nucleons; while for fixed $N$, the $T$ dependence is given mainly by a term of simple $T(T+1\mathrm{})\mathrm{}$ form.