Relativistic correction to the dipole polarizability of a hydrogenic ion

The first relativistic correction of orderα ² to the dipole polarizability of a hydrogenic ion has been investigated by using mean excitation energy of the ion within the second-order perturbation theory. The density-dependent mean excitation energy is estimated via Bethe theory for the stopping cross section for a moving point charge interacting with the hydrogenic ion. In this approach only the unperturbed Dirac wavefunctions are required to evaluate the appropriate matrix elements. The first relativistic correction turns out to be − (13/12)(αZ)². This has the correct sign and is within 5% of the exact result which is −(28/27)(αZ)².