Numerical Value of the Lamb Shift

Abstract

The average excitation potential of the $2s$ state of hydrogen which occurs in the Lamb shift, is calculated numerically and found to be 16.646\ifmmode\pm\else\textpm\fi{}0.007 Ry. This gives a theoretical value of 1051.41\ifmmode\pm\else\textpm\fi{}0.15 megacycles for the Lamb shift, compared with the latest experimental value of 1062\ifmmode\pm\else\textpm\fi{}5. It is not known whether the discrepancy of 10 Mc can be explained by relativistic effects. Simple analytical approximations are discussed which make plausible the high value of the average excitation potential and give a good approximate value for it.