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

We derive expressions for third-order matrix elements of one- and 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 isotope-shift constants for 3s, 3p, and 3d levels in sodium and sodiumlike ions with Z=12–18 and Z=26 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.