LINEAR DEPENDENCE OF β ˗-DECAY MAXIMUM ENERGY E ON THE MASS NUMBER A WITHIN THE SAME ELEMENT ACROSS Z<47

Abstract

We investigate the systematics of β⁻-decay maximum energy E versus the mass number A, along isotopic chains with Z<47. Using evaluated nuclear data, we find that for any fixed 𝑍, the decay energy exhibits an excellent linear dependence on the mass number 𝐴, with separate straight-line trends for even-A and odd-A isotopes. This empirical regularity, surprisingly unreported in the literature, provides a simple and accurate parameterization of β⁻- decay energetics. The theoretical motivation for the emergence of such linearity is supplied by the Universal Matter Architecture (UMA) framework rooted to Yarman's Approach (YA), which predicts that nuclear binding variations with A along a fixed-𝑍 isotopic chain should produce nearly uniform shifts in β-decay energies. The resulting linear fits yield intercept (p) and slope (q) parameters that can be tabulated for all elements with Z<47, and which in turn allow a compact description of decay-energy evolution across isotopes. The remarkable accuracy of these linear relations −quantified through their 𝑅2coefficients− indicates that the trend is robust and may offer a practical basis for analyzing or estimating β⁻-decay properties in isotopic chains, all the more so since the E values used here are available with a precision of about 0.1%, if not even better.