Nuclear mass parabola and its applications

TL;DR

This paper introduces a novel method to determine key parameters of the nuclear isobaric mass parabola using double beta decay energies, effectively removing pairing energy effects and providing insights into Coulomb and symmetry energy coefficients.

Contribution

It presents a new approach to extract the mass parabola parameters from decay energies, improving accuracy by eliminating pairing energy influences.

Findings

Parameters $Z_A$ and $b_A$ obtained for 251 A values.

Coulomb energy coefficient $a_c$ determined as 0.6910 MeV.

Symmetry energy coefficient related to $b_A$ and $Z_A$.

Abstract

We propose a method to extract the properties of the isobaric mass parabola based on the total double $\beta$ decay energies of isobaric nuclei. Two important parameters of the mass parabola, the location of the most $\beta$-stable nuclei $Z_{A}$ and the curvature parameter $b_{A}$, are obtained for 251 A values based on the total double $\beta$ decay energies of nuclei compiled in AME2016 database.The advantage of this approach is that we can remove the pairing energy term $P_{A}$ caused by odd-even variation, and the mass excess $M(A,Z_{A})$ of the most stable nuclide for mass number $A$ in the performance process, which are used in the mass parabolic fitting method. The Coulomb energy coefficient $a_{c}=0.6910$ MeV is determined by the mass difference relation of mirror nuclei, and the symmetry energy coefficient is also studied by the relation $a_{\rm sym}(A)=0.25b_{A}Z_{A}$.