Shell Model Calculation of the β- and β+ Partial Half-Lives of 54Mn and Other Unique Second Forbidden β Decays

Abstract

The nucleus 54Mn, observed in cosmic rays, decays there dominantly by the β- branch with an unknown rate. The branching ratio of its β+ decay was determined recently. We use the shell model with only a minimal truncation and calculate both β+ and β- decay rates. Good agreement for the β+ branch suggests that the calculated partial half-life of the β- decay, 4.94×10^5 yr, should be reliable. However, this half-life is noticeably shorter than the range 1–2×10^6 yr indicated by the fit based on the 54Mn abundance in cosmic rays. We also evaluate other known unique second forbidden β decays from the p and sd shells and show that the shell model can describe them with reasonable accuracy as well.