Temperature Dependence of the Lamb Shift

The temperature-dependent correction to the Lamb shift of a single-electron atom exposed to black-body radiation at temperature

T

is considered. At room temperatures, the correction for

Z > 1

is dominated by a shift, not considered before, of the

2 s_{\frac{1}{2}}

level, involving

2 p_{\frac{3}{2}}

as an intermediate state, and is given by

\frac{π α^{3} Z^{2} {(kT)}^{2}}{8 m}

. This competes with another shift

\approx \frac{x {(kT)}^{4}}{Z^{4} {(α m)}^{3}}

discussed by Walsh, where

x

is a purely numerical but remarkably large coefficient of order 300.

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