For Sets of β+Decaying Radioisotopes of the Same Element, the Highest Initial Kinetic Energy of the Emitted Positron Falls Off Straightly With Increasing Atomic Mass Number a

Abstract

Earlier, we had presented a systematization of beta+-decaying nuclei,1 where the interrelation between the decay half-life T and the highest initial kinetic energy epsilon of the positron at the instant it is emitted (if the neutrino energy is assumed to be zero) was transcribed through the formula T similar to 1/epsilon. Herein, we reveal that the highest initial kinetic energy epsilon linearly decreases with respect to the increasing atomic mass number A for each of the given sets of beta+-decaying radioisotopes of the same element. This, combined with the foregoing relationship, means a more stable beta+-decaying nucleus, or the same, a longer decay half-life with respect to increasing A. All this, in turn, leads, as a first approximation, to an easily memorizable expression of the rate of change Delta T/T of the half-life versus the change Delta A in the form of Delta T/T similar to Delta A. Using this relationship, and putting aside possible anomalies, one can predict within an acceptable accuracy the half-lives of beta+-decaying nuclei that could not be measured until now.