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

Within the improved Weizsäcker-Skyrme (WS)-type nuclear mass formulas, we systematically calculated one-nucleon and two-nucleon separated energy, α-decay and β-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 $Q_{\alpha },Q_{{\beta }^{-}},Q_{{\beta }^{+}}$, 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 ${\mathrm{\Delta }}_{\mathrm{n}}$ and ${\mathrm{\Delta }}_{\mathrm{p}}$ 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 ${\mathrm{\Delta }}_{\mathrm{n}}$ and ${\mathrm{\Delta }}_{\mathrm{p}}$ 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.

Figure 1

(a) Differences between the calculated nuclear binding energies and the experimental ones of Set I as functions of mass number $A$, and distributions of those differences (b),(c),(d) for three models. The best fitted Gaussian distributions are also shown with blue lines, and the corresponding parameters are listed in Table 3.

Figure 2

(a) Contour map of the differences between the calculated binding energies with WS-LZ and the experimental ones of Set II group as a function of neutron number and proton number. (b) Similar to (a) but with the calculation extracted from the WS-LZ1 model. (c) Similar to (a) but with the calculation extracted from the WS-LZ2 model.

Figure 3

Contour maps of the calculated one-nucleon and two-nucleon separated energies—$S_{\mathrm{n}},S_{2\mathrm{n}},S_{\mathrm{p}}$, and $S_{2\mathrm{p}}$—and decay energies—$Q_{\alpha },Q_{{\beta }^{-}},Q_{{\beta }^{+}}$, and $Q_{\mathrm{EC}}$—of Set III group as a function of neutron number and proton number. The horizontal and vertical dotted lines denote neutron and proton magic numbers.

Figure 4

Distributions of deviations between experimental and calculated OES pairing gaps both obtained from Eq. (12). ${\mathrm{\Delta }}_{\mathrm{n}}$ $\left({\mathrm{\Delta }}_{\mathrm{p}}\right)$ obtained from WS-LZ (a), WS-LZ1 (b), WS-LZ2 (c) formulas are shown in the top (bottom) panels. The best fitted Gaussian distributions are also shown with blue lines, and the corresponding parameters are listed in Table 7.

Figure 5

The neutron OESs of ten isotopes (a)–(j) as functions of neutron number. Black spheres present the results from experimental data, and red stars denote the calculation of WS-LZ2. The results extracted from the calculation of WS-LZ1 are represented by open upward-pointing triangles and those of WS-LZ1 are represented by open downward-pointing triangles.

Figure 6

The same as Fig. 5 but for the proton OESs of four magic isotones $N=28,50,82,126$. Blue spheres and magenta stars donate the pairing gap of experiment and WS-LZ2.

Figure 7

Contours plot of neutron OESs in 764 even-even nuclei calculated with experiment (a), WS-LZ (b), WS-LZ1 (c), and WS-LZ2 (d).