Generalized Seniority and the Surface Delta Interaction

It is shown that the surface delta interaction (SDI), which can be defined as a delta interaction $\delta \left({\Omega }_{12}\right)$ in the angles of the interacting particles (with the additional assumption that all radial integrals are equal), provides a very simple coupling scheme for configurations of identical particles (i.e., maximum isospin) involving degenerate mixed orbits. This scheme, a generalization of the well-known seniority scheme, can be conveniently expressed in terms of "quasispin." It is shown that the SDI is a sum of a term which is a scalar with respect to quasispins and a term which is proportional to the number of particles. The well-known pairing interaction, like the SDI, is diagonal with respect to quasispin but is not a quasispin scalar. Thus for configurations of an even number of identical particles in mixed degenerate orbits coupled by an SDI, the ground-state energy of the seniority zero ground state varies linearly with the number of particles. We can also apply the BCS method and express the excited states in terms of quasiparticle configurations. For identical nucleons in degenerate orbits coupled by an SDI, we obtain the exact energies of the ground-state and low-lying levels.