Third-order isotope-shift constants for alkali-metal atoms and ions

We derive expressions for third-order matrix elements of oneand two-particle operators within the framework of relativistic many-body perturbation theory and use these formulas to evaluate specific-mass isotope shifts and isotope field shifts in atoms and ions with one valence electron. Third-order corrections to isotopeshift constants for 3s , 3p , and 3d levels in sodium and sodiumlike ions with Z512–18 and Z526 are given. Applications to 4s , 4p , 3d , and 4d levels in K and 4s , 4p , and 3d levels in Ca are also given. Comparisons are made with previous calculations and with experiment. Including third-order corrections improves the agreement between theoretical and experimental values of the specific-mass isotope-shift constants for the cases considered.