Refined theoretical values of field and mass isotope shifts in thallium to extract charge radii of Tl isotopes

Abstract

Electronic factors for the field and mass isotope shifts in the $6p{}^2{P}_{3/2}\to 7s{}^2{S}_{1/2}$ (535 nm), $6p{}^2{P}_{1/2}\to 6d{}^2{D}_{3/2}$ (277 nm) and $6p{}^2{P}_{1/2}\to 7s{}^2{S}_{1/2}$ (378~nm) transitions in the neutral thallium were calculated within the high-order relativistic coupled cluster approach. These factors were used to reinterpret previous experimental isotope shift measurements in terms of charge radii of a wide range of Tl isotopes. Good agreement between theoretical and experimental King-plot parameters was found for the $6p{}^2{P}_{3/2}\to 7s{}^2{S}_{1/2}$ and $6p{}^2{P}_{1/2}\to 6d{}^2{D}_{3/2}$ transitions. It was shown that the value of the specific mass shift factor for the $6p{}^2{P}_{3/2}\to 7s{}^2{S}_{1/2}$ transition is not negligible compared to the value of normal mass shift in contrary to what had been suggested previously. Theoretical uncertainties in mean square charge radii were estimated. They were substantially reduced compared to the previously ascribed ones and amounted to less than 2.6%. The achieved accuracy paves the way to a more reliable comparison of the charge radii trends in the lead region.