Nuclear Scattering of Electrons and Isotope Shift

Abstract

The volume dependent isotope shift and the elastic scattering of electrons by nuclei are treated by a method with which they can be simply related. The result already obtained by Feshbach that the s-wave scattering due to the finite nuclear size depends only on the volume integral of the potential due to the nuclear charge distribution is derived in a simple manner with a clear indication of the limitations. It is shown that this is then the only information which can be obtained for energies at which only the s-wave scattering is important. The isotope shift is calculated taking into account the distortion of the electronic wave function by the nuclear charge distribution using a non-perturbation method due to Broch and is reduced considerably below that obtained with the simple perturbation method. It is shown by the same method as that used for the electron scattering that the isotope shift depends essentially only on the above volume integral and on its difference between two isotopes. Using the results obtained from the scattering of electrons by Ag and Au by Lyman, Hanson and Scott and assuming that the nuclear radius increases proportionally to A1/3 the isotope shift is brought into considerably better agreement with the experimental data.