On the distribution law in locally rapidly fluctuating fields which are steady when averaged over a sufficient time interval

Abstract

Thomas(1) and later Fermi(2) have attempted to determine the time average electrical potential around the nucleus of a heavy atom. They treat the electrons as if they formed an ideal degenerate Fermi gas which becomes statistically distributed in the steady field due to the nucleus plus the locally rapidly fluctuating field due to the electrons themselves. This method is apparently fully justified and it is hard to see, at first, why the numerical solutions given by the above writers turn out to be so roughly approximate, especially for heavy atoms with many electrons. The following investigation purports to show that the roughness of the method is due to the unjustified, except for approximation purposes, use of the statistical distribution law of an ideal gas in a steady field in the case where the field is steady only when averaged over a sufficiently long time interval and is locally fluctuating.