Lithium transition energies and isotope shifts:QEDrecoil corrections

Abstract

A QED recoil correction of order $(\ensuremath{\mu}/M){\ensuremath{\alpha}}^{5}{\mathrm{mc}}^{2}$ recently derived by Pachucki [J. Phys. B 31, 5123 (1998)] is evaluated for lithium in the ${1s}^{2}{2s}^{2}{S}_{1/2},$ ${1s}^{2}{3s}^{2}{S}_{1/2},$ and ${1s}^{2}{2p}^{2}P$ states, and its contribution to the isotope shift is calculated. The new term is shown to be equivalent to the recoil term included in our previous work in a hydrogenic approximation. Total energies are calculated for each of the states in question, including screening corrections to the Bethe logarithm estimated from the two-particle parent states. The results for the total transition frequencies are shown to be in good agreement with experiment, but there are surprisingly large discrepancies between theory and experiment for the isotope shift in the fine structure splitting (SIS) for the ${1s}^{2}{2p}^{2}P$ state. The ionization potential of ${}^{7}\mathrm{Li}$ is calculated to be $43487.1520(40){\mathrm{cm}}^{\ensuremath{-}1}.$ The estimated accuracy is about the same as the experimental value. A recent measurement of the ${}^{7}\mathrm{Li}{--}^{6}\mathrm{Li}$ isotope shift for the ${2}^{2}{P}_{1/2}\ensuremath{-}{2}^{2}{S}_{1/2}$ transition determines the difference of the squares of the nuclear radii to be $0.84(6){\mathrm{fm}}^{2},$ which is a factor of 4 more accurate than the value $0.79(25){\mathrm{fm}}^{2}$ derived from nuclear scattering data.