Nuclear polarization corrections toμ-datoms in zero-range approximation

Abstract

Nuclear polarization corrections to the $2P$-$2S$ Lamb shift in $\ensuremath{\mu}$-$d$ atoms are developed in order (${\ensuremath{\alpha}}^{5}$), and are shown to agree with a recent calculation. The nuclear physics in the resulting corrections is then evaluated in zero-range approximation. The dominant part of the correction is very simple in form and differs from a recent potential model calculation by less than 1%. It is also demonstrated how the third Zemach moment contribution largely cancels against part of the polarization correction, as it did in $e$-$d$ atoms and does so exactly for pointlike nucleons. This suggests that it may be possible to reduce the uncertainty in the theory (of which nuclear polarization is the largest contributor) to less than 1%.