COMPARISON OF THE EFFECTIVE INTERACTION TO VARIOUS ORDERS IN DIFFERENT MASS REGIONS

The convergence of the perturbation expansion for the effective intera ction to be used in shell-model calculations is investigated as a func tion of the mass number A, from A = 4 to A = 208. As the mass number i ncreases, there are more intermediate states to sum over in each highe r-order diagram which contributes to the effective interaction. Togeth er with the fact that the energy denominators in each diagram are smal ler for larger mass numbers, these two effects could largely enhance h igher-order contributions to the effective interaction, thereby deteri orating the order-by-order convergence of the effective interaction. T his effect is counterbalanced by the short range of the nucleon-nucleo n interaction, which implies that its matrix elements are weaker for v alence single-particle states in 'large' nuclei with large mass number as compared to those in light nuclei. These effects are examined by c omparing various mean values of the matrix elements. It turns out that the contributions from higher-order terms remain fairly stable as the mass number increases from A = 4 to A = 208. The implications for nuc lear structure calculations are discussed.