Some convergence properties of the perturbation series for the effective nuclear interaction:: The stability of results under double partitioning in mass-18 nuclei

Abstract

The Bloch-Horowitz-Brandow (BHB) expansion for the effective interaction in mass-18 nuclei is evaluated by the method of double partitioning. That is, the BHB expansion for the effective interaction is divided into two calculations for the purpose of approximating separately the high- and low-energy (long- and short-range, respectively) effects so as to improve the approximation of each. This is done by approximating a high-energy effective interaction (for a larger, or “outer”, model space) and then using that for the potential in terms of which the low-energy BHB expansion (for a smaller, or “inner”, model space: the sd shell) is evaluated. The size of the outer model space is 4 h ̷ Ω larger than the smaller. The results, by comparision with earlier works by Barrett, show a trend that suggests that the (intermediate-range) tensor force is being poorly accounted for and as a result the convergence of the intermediate-excitation sums is poor, a finding similar to that found by Vary, Sauer and Wong. The convergence of the order-by-order sum, however, seems to be improved as the outer model space is enlarged. The suggestion is made that the use of a better approximation, if one can be found, to the effective interaction for the outer model space (appropriate for including the effects of the tensor force) might improve the intermediate excitation convergence.