Internal Diamagnetic Fields

Abstract

In the precise molecular beam experiments of Rabi and his collaborators, it is necessary to know the value at the nucleus of the magnetic field produced by the diamagnetism of the atomic electrons. This has been calculated on the basis of the Fermi-Thomas model, and checked for a number of atoms by use of the available Hartree calculations. The statistical treatment gives for ratio of induced to external field $0.319\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}{Z}^{\frac{4}{3}}$, while the numerical coefficient on the basis of the Hartree model is lower by 19 percent at $Z=19$ and by 12 percent at $Z=80$. The effect is equivalent to a reduction of the nuclear $g$ value by a factor of ($1\ensuremath{-}0.319\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}{Z}^{\frac{4}{3}}$), and in this form, the correction may be applied in the calculation of hyperfine structure of heavy atoms. The influence of the diamagnetic fields on an orbital electron has also been considered, and it is shown that it is equivalent to a reduction in the $g$ value of an outer $s$ electron by an amount of just the same order of magnitude as the relativistic correction calculated by Margenau.