Nuclear-Polarization Corrections to the Levels of Muonic Atoms

Abstract

It is shown that information about the nuclear electromagnetic-transition vertex derived from experimental inelastic-scattering cross sections for electrons may be used to evaluate the nuclear-polarization (dispersion) corrections to the levels of muonic atoms. A model-independent result is obtained for the contributions of discrete nuclear states. The most important systematic features of nuclear-excitation spectra, the giant-dipole resonance and the quasielastic peak, are considered in detail. The Goldhaber-Teller model is used for the former, and a simple-harmonic-oscillator shell model for the latter. Numerical estimates are obtained for total level shifts of low-lying muon states in nuclei with closed (harmonic-oscillator) proton shells, using closure approximation for the muon. The muon closure energies are considered in detail. It is felt that the results obtained are probably accurate to a factor of 2. The shifts are estimated to be several keV for the $1s$ state in heavy nuclei, and somewhat less (a few tenths to about 1 keV) for the $2s$ and $2p$ states. These shifts are significant in comparison to the present accuracy of measurement of muonic x-ray spectra, and should be considered in calculations to fit nuclear-charge distributions.