Many-body perturbation theory was applied to calculate the specific mass shift of the (4s4p) ${}_{}{}^1{}_{}{}^{}$,3P states in Ca relative to the 4s ground state of ${\mathrm{Ca}}^{+}$. The interaction between each valence electron and the core was treated in the same way as the level isotope shifts in the alkali metals in earlier work. The strong correlation between the two valence electrons in neutral Ca was treated self-consistently by iterative solution of the pair equation describing their interaction and its effect on the specific mass shift was evaluated in the same way as for helium. However, also the correlation between the pair of valence electrons and the core is important. All second-order and a large number of third- (and higher-) order diagrams of this type were included, but certain important third-order diagrams could not yet be evaluated. Our final results, -31 and -1533 MHz, respectively, for the 4 ${}_{}{}^1{}_{}{}^{}P$ and 4 ${}_{}{}^3{}_{}{}^{}P$ states between ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, show only a qualitative agreement with the experimental values, -120(9) and -1116(8) MHz. This is not surprising, in view of the many competing effects with contributions larger than the final value. The remaining discrepancies are consistent with the expected size of the neglected diagrams and illustrate the importance of the core-valence correlation.

• Received 25 June 1984

DOI:https://doi.org/10.1103/PhysRevA.31.58