Mirror nuclei constraint in nuclear mass formula

The macroscopic-microscopic mass formula is further improved by considering mirror nuclei constraint. The rms deviation with respect to 2149 measured nuclear masses is reduced to $0.441$ MeV. The shell corrections, the deformations of nuclei, the neutron and proton drip lines, and the shell gaps are also investigated to test the model. The rms deviation of $\alpha$-decay energies of 46 superheavy nuclei is reduced to $0.263$ MeV. The predicted central position of the superheavy island could lie around $N=176~178$ and $Z=116~120$ according to the shell corrections of nuclei.

Figure 1

(a) Shell-correction difference $\Delta E^{\prime }-\Delta E$ in pairs of mirror nuclei. The squares and the open circles denote the results without and with the $E_{\mathrm{sh}}^{\prime }$ term being taken into account, respectively. The balls denote the experimental values of $(E_B-E_C)-(E_B^{\prime }-E_C^{\prime })$ between mirror nuclei with the Coulomb energy form in Ref. [5]. (b) Deviations of the calculated nuclear masses from the experimental data [8]. The squares and the crosses denote the results of WS and WS*, respectively. The solid curve denote the results of an empirical formula, ${\Delta }_T=-0.7[\cos (2\pi \frac{N}{16})+\cos (2\pi \frac{N}{20})]A^{-1/3}$, which will be discussed later.

Figure 2

(a) Contour plot of shell corrections of nuclei with WS*. The dot-dashed line passes through the areas with the known heavy magic nuclei. (b) Shell corrections of nuclei as a function of neutron number. The crosses and the squares denote the results of WS and WS*, respectively.

Figure 3

(a) Contour plot of quadrupole deformation $\left|{\beta }_2\right|$ of nuclei with WS*. (b) ${\beta }_4$ and (c) ${\beta }_6$ of nuclei as a function of neutron number, respectively.

Figure 4

Deviations of calculated nuclear masses in this work from the results of other models. The calculated masses with FRDM and HFB-17 are taken from Refs. [6] and [10], respectively.

Figure 5

Smooth drip lines from different mass formulas. The crosses denote the measured nuclei. The solid-squared line denote the neutron drip line of nuclei $A\to \infty$ with $I=-\frac{1}{2}\frac{a_v}{a_{\mathrm{sym}}}$ and taking $a_v=-16$ MeV and $a_{\mathrm{sym}}=32$ MeV. The open-squared and the solid-circled curve denote the smooth $\beta$-stability line from FRDM and WS* calculations, respectively.

Figure 6

Shell gap calculated with different models. The dashed, dot-dashed, and solid curve denote the results of HFB-17, FRDM, and WS*, respectively. The squared curve denote the experimental data.

Figure 7

Fission barriers of some superheavy nuclei. The solid-circled curve denote the calculated fission barriers of superheavy nuclei in Ref. [13]. The open-circled curve and the crosses denote the values of $-\Delta E$ with WS and WS*, respectively. The dashed line denotes the position $N=184$.