Effect of an Electric Dipole Moment of the Proton on the Energy Levels of the Hydrogen Atom

The perturbations of the energy levels of the hydrogen atom by a possible electric dipole moment of the proton, $d$, have been obtained. The inhomogeneous equation for the first-order perturbation of the wave functions was solved analytically. The shifts of the energy levels are of the second order in $d$. In particular, there results a decrease of the Lamb shift between the $2S_{\frac{1}{2}}$ and $2P_{\frac{1}{2}}$ levels. By equating this decrease to the maximum allowed by the approximate agreement between the experimental and theoretical values of the Lamb shift, it is concluded that the electric dipole moment of the proton, $d$, must be less than 1.3×${10}^{-13\mathrm{}}$ cm times the charge of the electron. Calculations have also been carried out for the shifts of the energy levels of deuterium produced by a possible electric dipole moment of the deuteron.