Lithium isotope shifts as a measure of nuclear size

Abstract

The isotope shifts for $2{}^{2}{P}_{J}$\char21{}$2{}^{2}S$ and $3{}^{2}S$\char21{}$2{}^{2}S$ transition energies in lithium are calculated variationally in Hylleraas coordinates, including nonrelativistic, relativistic, and QED terms up to $O(\ensuremath{\mu}/M),$ $O(\ensuremath{\mu}{/M)}^{2},$ $O({\ensuremath{\alpha}}^{2}\ensuremath{\mu}/M),$ and $O({\ensuremath{\alpha}}^{3}\ensuremath{\mu}/M)$ atomic units, and the lowest-order finite nuclear size correction. With high-precision isotope shift measurements, our results can potentially yield a precise determination of the nuclear charge radius for different isotopes of lithium, and especially for the exotic ${}^{11}$Li ``halo'' isotope. For the case of ${}^{7}\mathrm{Li}$-${}^{6}\mathrm{Li},$ using the nuclear charge radii from nuclear scattering data, our calculated isotope shifts for the $2{}^{2}{P}_{1/2}$\char21{}$2{}^{2}S,$ $2{}^{2}{P}_{3/2}$\char21{}$2{}^{2}S,$ and $3{}^{2}S$\char21{}$2{}^{2}S$ transitions are $10534.31(61)(6)$ MHz, $10534.70(61)(6)$ MHz, and $11454.31(39)(5)$ MHz, respectively, where the first brackets indicate the uncertainties due to the nuclear charge radii, and the second brackets indicate the computational uncertainties. The experimental isotope shifts are inconsistent with each other and with theory for these transitions.