Ab-initio study of the effects of pressure and chemistry on the electron-capture radioactive decay constants of 7Be, 22Na and 40K

Using state-of-the-art ab-initio computations, we find that pressure and chemical environment have a small effect on the electron-capture component of the decay constants of isotopes of ⁷Be, ²²Na and ⁴⁰K. As expected, ⁷Be shows the greatest amount of change with ~ 0.1-0.2% increase in the decay constant at 25 GPa as a metal, chloride or oxide. In their metallic forms, ²²Na and ⁴⁰K show an increase of 0.06% and 0.025% change, respectively, at 25 GPa. Upon further compression, potassium and sodium undergo an s-to-d electronic transition of their valence electron, causing a significant change in the charge density at the nucleus. Our results suggest that the effect of pressure and chemistry on ⁴⁰K, combined with the opposing effects of high temperatures, will have little, discernible effect on the heat production in the deep Earth as our predicted changes are smaller than the uncertainties in the total decay constant for ⁴⁰K.