Nuclear mass parabola and its applications

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