Muon capture on nuclei: random phase approximation evaluation versus data for 6 $\le$ Z $\le$ 94 nuclei

Abstract

We use the random phase approximation to systematically describe the total muon capture rates on all nuclei where they have been measured. We reproduce the experimental values on these nuclei to better than 15% accuracy using the free nucleon weak form factors and residual interactions with a mild $A$ dependency. The isospin dependence and the effects associated with shell closures are fairly well reproduced as well. However, the calculated rates for the same residual interactions would be significantly lower than the data if the in-medium quenching of the axial-vector coupling constant is employed to other than the true Gamow-Teller amplitudes. Our calculation thus suggests that no quenching is needed in the description of semileptonic weak processes involving higher multipole transitions and momentum transfer $\sim m_{\mu}$, with obvious importance to analogous weak processes.