Relativistic finite-nuclear-size corrections to the energy levels in light muonic atoms

We consider higher-order finite-nuclear-size (FNS) contributions to the energy levels of light ordinary and muonic hydrogenlike atoms. Relativistic corrections to the leading FNS term have been known in terms of an integration in coordinate space. The related results are model dependent. In the meantime, if the data on the nuclear structure are obtained from electron-nucleus scattering, it is a representation of the electric charge form factor in momentum space rather than the charge density. An example is the case of a proton as a nucleus. Often the electric form factor is presented in terms of a dispersion integral or a Padé approximation. We present explicit results for such representations for leading finite-nuclear-size higher-order (in $Z\alpha$ and in $Z\alpha m{R}_N$) corrections beyond the leading FNS term.

Figure 1

The third-order perturbation diagram for the logarithmic FNS contribution in (8). The photon lines are for the Coulomb field (with two of the legs related to the extended nucleus and one for the nucleus in the pointlike approximation). The double line is for the Coulomb Green's function of the muon.