Weizsäcker-Skyrme-type nuclear mass formula incorporating two combinatorial radial basis function prescriptions and their application

Within the improved Weizs\"acker-Skyrme (WS)-type nuclear mass formulas, we systematically calculated one-nucleon and two-nucleon separated energy, \ensuremath{\alpha}-decay and \ensuremath{\beta}-decay energies, and the odd-even staggering (OES) of nuclear binding energies. As a result, the root-mean-square (rms) deviations of 2267 nuclei within the new improved WS-type mass formula are dropped from 493 to 167 keV, where 2267 nuclei are extracted from the atomic mass evaluation of 2012. Simultaneously, all the rms deviations of one-nucleon and two-nucleon separation energies and decay energies ${Q}_{\ensuremath{\alpha}},{Q}_{{\ensuremath{\beta}}^{\ensuremath{-}}},{Q}_{{\ensuremath{\beta}}^{+}}$, and ${Q}_{\mathrm{EC}}$ for more than 3000 nuclei are cut down by about 100--400 keV. Further, some basic physical observations of 988 boundary nuclei are predicted for providing reference to experiments. Finally, the overall neutron OESs and proton OESs have been systemically investigated and the residual error satisfies a normal distribution. The pairing gaps ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{n}}$ and ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{p}}$ of the isotopes of O, Ca, Ni, Zr, Sn, Gd, Qs, Pb, Pa, Ds and the isotonic magic chains of $N=28,50,82,126$ and even-even nuclei are also studied with dramatic improvements obtained. Especially, the rms of ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{n}}$ and ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{p}}$ in these nuclei have been reduced by about 200 keV. The above physical quantities show important information for nuclear charts and the features of nuclear structure.