Isotope Shift in the X-Ray Spectra of Heavy Elements

Isotope shifts in the x-ray levels due to the nuclear volume effect have been calculated for three different nuclear potentials by using first-order perturbation theory with the relativistic wave functions in a Coulomb field. In order to correct for the error made in using first-order perturbation theory, the exact relativistic wave function was obtained for one of the potentials. The screening effects of the atomic electrons are taken into account by comparing the value of the wave function at the nuclear radius in a Fermi-Thomas field with that in a Coulomb field. An upper limit is obtained on contributions to the isotope shift due to the change in screening of the other atomic electrons when a $K$ or $L$ shell electron is removed or replaced. The results for isotope shift in Mo and U are one-half and one-twentieth, respectively, of the experimental resolution of Rogosa and Schwarz.