Atomic masses of nuclei with neutron numbers $N<126$ and proton numbers $Z>82$

In this paper we study atomic masses of the major shells to the northwest of the ${}^{208}\mathrm{Pb}$ nucleus, namely, those with neutron numbers $N<126$ and proton numbers $Z>82$, in terms of neutron-proton interactions. With statistical corrections, we are able to construct mass formulas for nuclei in this region with root-mean-squared deviation close to 30 keV, which is more accurate than all previous efforts. Predicted results of some unaccessible masses are tabulated in the Supplemental Material of this article.

Figure 1

$\delta V_{1n\text{−}1p}$, extracted based on the AME2021 database [3], vs mass number $A$, for nuclei with neutron numbers $N<126$ and proton numbers $Z>82$.

Figure 2

$\mathrm{\Delta }{V}_{1n\text{−}1p}(N,Z)$ versus $\mathrm{\Delta }{V}_{1n\text{−}1p}(N-2,Z-2)$, defined in Eq. (3). The solid straight line in purple is plotted by the optimal value of $\lambda$.

Figure 3

Predicted one- and two-proton separation energies ($S_p$ and $S_{2p}$, in keV) for nuclei with proton number $Z$ from 83 to 93. In each block, the first row corresponds to $S_p$ predicted in this work, the second row corresponds to $S_p$ in Ref. [3], the third row corresponds to $S_{2p}$ predicted in this work, and the fourth row corresponds to $S_{2p}$ in Ref. [3]. The predicted results in this work and experimental data in Ref. [3] are in black and red, respectively. The values in the brackets correspond to uncertainties. The orange solid line plots the proton drip line. We note that the extrapolated results of the ${}^{186}\mathrm{Po}$ nucleus could be problematic, because theoretical $\delta V_{1n\text{−}1p}$ for one of its neighboring nuclei, ${}^{188}\mathrm{Po}$, deviates sizably from experimental data.