Correlations and Total Muon Capture Rates

Abstract

The total muon capture rate for s-wave muons can be accounted for by the Primakoff expression which gives the dependence of this rate on the mass number A and the proton number Z of the absorbing nucleus. The expression is a simple three parameter phenomenological formulae which accurately describes these rates from light weight nuclei to heavy nuclei. These parameters relate to the isospin structure of the squared isovector operator which appears in a sum rule approach to such rates. A microscopic analysis of the parameters appearing in the capture rate expression is presented in the light of recent developments concerning photonuclear reactions. A shell model analysis is given and it is found that the predictions of the unperturbed shell model and also Hartree-Fock theory are in complete disagreement with the data. Considerable improvement is obtained when long range correlations are included in the ground state wave function of the absorbing nucleus.