Specific mass shifts in Li and K calculated using many-body perturbation theory

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Abstract
Recently, experimental isotope shifts have become available for individual levels of Li and K. The authors have used many-body perturbation theory to calculate all first- and second-order contributions to the specific mass shifts. The correlation effects were obtained by numerical solution of inhomogeneous radial 'pair equations'. For the lowest s, p and d states of Li the authors results were 962, -3273 and -2 MHz compared with the experimental results of 1111(6), -3608(11) and 0(6) MHz, respectively. As in the authors earlier hyperfine structure calculations, the need to include higher-order effects is more pronounced for K, especially for the strongly perturbed d states. Adding the lowest-order correlation effects to the results obtained with a self-consistent treatment of the change in the core orbitals due to the valence electron gave satisfactory agreement for the 4s and 4p states in K, -53 and -30 MHz, respectively, compared with the experimental data, -61(2) and -28(2) MHz. The 5d state shows a larger discrepancy, the theoretical shift being -22 MHz compared with the experimental result-53(8)MHz, emphasising the need to include higher-order correlation effects.