Mean excitation energies in the nuclear muon capture

The parametrization of the total muon capture rates in terms of a mean nuclear excitation energy ${\overline{E}}^{\prime }$, proposed in a recent letter of Christillin, Dellafiore, and Rosa-Clot (CDR), is examined. We show that this parametrization ignores the importance of the allowed transitions in light nuclei and fails to reproduce the experimentally observed trend of the $T_{>}$ giant resonance energy as a function of nuclear mass number. The removal of contributions due to higher multipoles in heavier nuclei aggravates this discrepancy. The failure of ${\overline{E}}^{\prime }$, extracted by CDR, to correspond to physically meaningful nuclear excitation energies in heavier nuclei is attributable to the intrinsic arbitrariness in its definition, and to the oversimplifying assumption of the nuclear Hamiltonian to be a sum of kinetic energy and Wigner potential alone. A first-order improvement of the Primakoff approximation is discussed.