Empirical formulas for nucleon separation energies

In this paper, we reexamine the formulas of one-nucleon separation energies proposed and studied by Vogt [Phys. Lett. B 517, 255 (2001)] and by Bao [Phys. Rev. C. 87, 044313 (2013)], by considering the parities for both neutron number and proton number, and more sophisticated treatments of the shell effect and the fourth-order correction of the symmetry energy. The root-mean-squared deviation (RMSD) is 272 keV for one-neutron separation energy ${S}_{n}$ and 301 keV for one-proton separation energy ${S}_{p}$, in comparison with experimental data compiled in the AME2016 database, for nuclei with mass number $Ag40$. With corrections of the radial basis function method, the RMSD is reduced to 147 and 151 keV for ${S}_{n}$ and ${S}_{p}$, respectively. We demonstrate, by numerical experiments of extrapolation from earlier versions of the AME databases to the AME2016 database, that our new formulas are very competitive in predicting one-nucleon separation energies as well as binding energies.