Modification of nuclear mass formula by considering isospin effects

We propose a semiempirical nuclear mass formula based on the macroscopic-microscopic method in which the isospin and mass dependence of model parameters are investigated with the Skyrme energy density functional. The number of model parameters is considerably reduced compared with the finite range droplet model. The rms deviation with respect to 2149 measured nuclear masses is reduced by 21%, falling to 0.516 MeV. The new magic number $N=16$ in light neutron-rich nuclei and the shape coexistence phenomena for some nuclei have been examined with the model. The shell corrections of superheavy nuclei are also predicted.

Figure 1

(a) Energy of ${}^{16}\mathrm{O}$, ${}^{48}\mathrm{Ca}$, and ${}^{208}\mathrm{Pb}$ with respect to ${\beta }_2$ deformation. Here, the values of $E_0$ are negative. The circles and the solid curves denote the results of SkM* interaction and of a formula $E/E_0=1+b_2{\beta }_2^2$, respectively. (b) The value of $b_2$ obtained with SkM* as a function of mass number.

Figure 2

(a) Energy of ${}^{208}\mathrm{Pb}$ with respect to ${\beta }_2$ and ${\beta }_4$ deformation with Skyrme energy-density functional approach. (b) The value of $b_k$ as a function of mass number. The scattered symbols denote the obtained curvatures of the parabolas with the Skyrme force SkM* for a number of nuclei. The solid curves denote the corresponding results with an empirical formula (6).

Figure 3

(a) Symmetry potential $V_{\mathrm{sym}}$ of nuclear matter with 78 Skyrme forces. (b) The difference between the potential depth of neutrons and of protons as a function of mass asymmetry. The circled curve and the triangled curve denote the results fitted to the calculated results with SLy4 (short red dashes) and SkM* force (small gray squares) for a large number of nuclei, respectively.

Figure 4

(a) Deviations between the calculated nuclear masses from the experimental data. (b) Calculated shell corrections $\Delta E$ of nuclei (crosses). The squares denote the microscopic energy of nuclei with the FRDM model (column $E_{\mathrm{mic}}$ of the table in Ref. [2]).

Figure 5

Potential energy surface $E({\beta }_2,{\beta }_4)$ of ${}^{82}\mathrm{Sr}$.

Figure 6

(a) Shell-correction energies $\Delta E$ of nuclei. The black squares denote the nuclei with microscopic energies of $-(6~7)$ MeV in the FRDM calculations. The straight line passes through the areas with the known heavy magic nuclei. (b) Shell-correction energies of nuclei in the superheavy region. The crosses denote the nearly spherical nuclei (calculated $\left|{\beta }_2\right|⩽0.01$) and the triangles denote the synthesized superheavy nuclei in the “hot” fusion reactions [31, 32].

Figure 7

Deviations of the calculated nuclear masses in this work from the results of FRDM (a) and HFB-17 (b), respectively. The calculated masses with FRDM and HFB-17 are taken from Refs. [2] and [4], respectively. The shades denote the region with deviations smaller than 2 MeV.