Linear Dependence of Electron-Decay Maximum Energy on the Mass Number A Along Isotopic Chains For Z<47

TL;DR

This study reveals a linear relationship between maximum electron-decay energy and mass number A along isotopic chains for Z<47, with separate trends for even-A and odd-A isotopes, providing a systematic parameterization.

Contribution

We present a novel, highly accurate linear model describing electron-decay energy dependence on A for isotopic chains, systematically tabulated across elements with Z<47.

Findings

Decay energy follows two linear trends for even-A and odd-A isotopes.

Coefficients of determination are typically almost unity, indicating excellent fit.

Provides a compact empirical parameterization not previously tabulated.

Abstract

We investigate the systematics of the maximum Electron-decay energy E as a function of the mass number A along isotopic chains with a fixed proton number across Z<47. By making use of the available curated nuclear data, we find that, for each fixed Z, the decay energy can be described to excellent accuracy by a linear dependence on A, provided that even-A and odd-A isotopes are treated separately. This yields two straight-line trends for each element, which are characterized by the slope and intercept parameters that can be systematically tabulated across the studied range. The corresponding fits are remarkably accurate, where the coefficients of determination are typically almost unity. Such an element-by-element empirical regularity does not appear to have been previously tabulated in a compact systematic form in the nuclear physics literature. We hence provide a simple and compact parameterization of Electron-decay energetics along isotopic chains with respect to our stated scope, whereby the approach at hand may prove useful for the analysis of decay-energy evolution, behavioral classification, and preliminary estimates of Electron-decay properties. The broader theoretical motivation that initially led us to search for such a regularity is discussed only after the confirmation of our results through experimental data is established.