Electron-Nuclear Potential Fields from Hyperfine Structure

Theoretical predictions for the effects of nuclear size on hyperfine structure are compared with experimental data. New data show that isotope shifts of $\mathrm{ns}$ levels in Tl III are proportional to ${\psi }^2\mathrm{}\left(0\right)\mathrm{}$ as predicted. The fractional change in nuclear radius for the addition of two neutrons, determined from $s$ electron shifts in Hg II, Tl III, Pb IV, is the same for the three elements. Köhler's results for Tl II are consistent with those for Tl III when allowance is made for the mutual screening of the valence electrons.

Corrections for the approximation of the perturbation method and for screening of inner electrons by the valence electron are considered and found to be appreciable. Even after applying the corrections, the fractional change in nuclear radius is smaller than expected if the charge is uniformly distributed throughout the nucleus and the volume is proportional to the mass.

Values of nuclear magnetic moments of thallium deduced from hyperfine structure measurements are compared with those measured by radiofrequency induction and found to be 15 percent lower. This discrepancy is removed by the correction for finite nuclear size assuming either a uniform charge distribution or a concentration of charge toward the surface of the nucleus. Thus both the isotope shift and the magnetic effect indicate that the electron-nuclear potential is consistent with a charge distribution of this form and that the non-electrical forces between electrons and nuclei are relatively small.