Quasi-spin in LS coupling

Abstract

The quasi-spin formalism put forward in the case of jj coupling by Kerman and by Helmers is here extended to the case of LS coupling including isotopic spin. The quasi-spin operators generate the rotation group in eight dimensions of which a six-dimensional rotation sub-group is found to give rise to a classification of states equivalent to the supermultiplet scheme of Wigner. The energy eigenvalues of a charge-independent pairing Hamiltonian are given for the pure configuration ln in terms of the Casimir operators of these two groups.