Skyrme interactions and the total muon capture rate in 16O

Abstract

A sum rule technique which systematically improves the usual closure approximation has been used to study the total muon capture rate in oxygen. To apply this method the energy-weighted moments m 0, m 1, m 2, m 3 for vector, axial vector and pseudoscalar excitations are calculated with different density-dependent effective interactions. These include standard Skyrme forces as well as new parametrizations developed recently for self-consistent RPA calculations. The v/ c corrections to the capture rate are evaluated consistently by calculating the corresponding moments m' 0, m' 1. Although the velocity dependence of the Skyrme interactions leads to a considerable reduction of total rates compared to the rates of the independent particle model, the results are still 10–60% higher than the experimental value. Similar discrepancies in photoabsorption sum rules indicate the need for ground-state correlations.