Generalized broken pair approximation: A viable alternative to the shell model for sphercal nuclei

The broken pair approximation (BPA) and its generalized version, developed as a useful approximation to the shell model and an improvement over the number projected quasiparticle method, can be applied in practice to most of the spherical nuclei. The BPA configuration space includes for an even number of identical valence nucleons all the seniority (ν) two components while it contains all configurations with ν < 4 except ν = 4 proton components and ν = 4 neutron components for the nonidentical (even-even) valence nucleons. Various expressions for the physical quantities like the matrix elements of the Hamiltonian, transition rates, etc., are expressed in a simple and coherent form involving the overlaps between the BPA states which are ideal for numerical computation. The validity of BPA has been demonstrated for identical (N = 50 even A nuclei) as well as for nonidentical (even Zr-isotopes) systems through an excellent agreement obtained between the BPA results and the corresponding shell model results. The BPA calculations have also been carried out for even Zr-, Mo-, and Ru-isotopes using phenomenological as well as realistic (Sussex) interaction matrix elements. The results reproduce well both the observed energy systematics and the electromagnetic transition rates. The effects of the truncation of the valence space have been examined in detail. The success of the present analysis paves the way for the application of the BPA to many more cases.