Number-conserving shell-model calculations for nickel and tin isotopes

The broken-pair approximation (BPA), introduced as a number-conserving approximation to the lowest-seniority shell model (LSSM), is applied to the nickel and tin isotopes. The shell-model interactions used are microscopically derived from the Tabakin potential and the Yale-Shakin reaction matrix or phenomenologically determined (by the Argonne group) through a shell-model-fit procedure. The results are compared with those of standard quasiparticle calculations (QTD) and, when possible, of the exact shell model (ESM) and of the LSSM. It is found that the BPA and the QTD can give essentially different results. Comparison with the LSSM and the ESM indicates that the BPA is a much more reliable approximation than the QTD.