A sum rule approach to total muon capture rates

Abstract The total muon capture rate is expanded in terms of sum rules and the convergence of such an expansion is analyzed. It results that the energy-weighted and the inverse-energy-weighted sum rules provide an accurate estimate for the total rate in agreement with a complete RPA calculation through the response function. The static polarizability of the isovector dipole mode turns out to be the relevant quantity to determine the total muon capture rate, in light and medium nuclei.