Systematization of β<SUP>+</SUP>-decaying atomic nuclei: Interrelation between half-life, mass, energy and size

Abstract

We propose a novel systematization of positron-decaying atomic nuclei, for which we first focus on determining the kinetic energy of the most energetic positron at the moment it is emitted from the nucleus. We find that this energy is inversely proportional to the number of nucleons A making up the nucleus. Further on, for A > 60, we figure out that the measured kinetic energy of positrons detected in the laboratory turns out to be substantially less than what one would classically expect based on the electrical interaction between the nucleus and the positron, starting from the moment the latter gets emitted. We particularly disclose that the initial kinetic energy of the positron escaping from the nucleus can be formally negative at A > 60, which indicates that the positron in question is not released from the classically conceived nuclear surface, but from much above the said surface. This requires the need to involve the quantum mechanical properties of the system composed of "the nucleus and the positron". Finally, we show how the half-life, mass, kinetic energy and size involved in positron-decay are interrelated in a way already established through Yarman's approach (YA) for polyatomic molecules and alpha-decaying nuclei.