Improved calculations of electron capture transitions for decay data and radionuclide metrology

Electron capture properties are crucial to establish the decay schemes of numerous radionuclides. The present modelling aims at improving the theoretical estimates of these decays, which are needed when no measurement is available. Allowed and forbidden unique transitions are calculated on the basis of precise relativistic wave functions of the atomic electrons, determined in previous work. In this context, correcting for atomic effects is of high importance. The two common approaches from Bahcall and Vatai to correct for the overlap and exchange effects have been extended to every subshell in a unified formulation, with the electron occupation precisely taken into account. The shake-up and shake-off effects, which create secondary vacancies, and the influence of the hole due to the capture process, have been considered. Uncertainties are also estimated. Relative capture probabilities and their ratios, including capture-to-positron ratios, have been found to be in good agreement with a selection of precise measurements. This modelling was then applied to the third forbidden unique transition of ⁴⁰K decay, with an update of the recommended values for the branching ratios and the total decay half-life.