content_image/348261.jpg content_image/348260.jpg
To take into account the influence of the higher-multipole deformation of nuclei, we inves- tigate the change of energy of a nucleus with respect to a certain set of nuclear deformation parameters with the Skyrme energy density functional approach mentioned previously. In Fig.2 (a), we show the energy of $^{208}$Pb as a function of β$_{2}$ and β$_{4}$ with the Skyrme force SkM*. We find that the influence of nuclear β$_{4}$ deformation on the nuclear energy can be roughly described by a parabola at small deformations. For other higher-multipole defor- mations, the parabola approximation can also be applied for small deformation cases, and the proposed model can be easily extended to consider other higher-multipole deformations. Furthermore, we notice that the curvature of the parabola for a given β$_{k}$ deformation can be approximately described by an empirical formula 

<img src='content_image/348261.jpg'>

which is an extension of the formula (5). In Fig.2(b), we show the mass dependent curvatures of the parabolas. The crosses, the open circles, the solid squares and the triangles denote the obtained curvatures b$_{2}$ , b$_{3}$ , b$_{4}$ and b$_{6}$ of the parabolas with the Skyrme energy density functional approach for a number of nuclei along the β -stability line, respectively. The solid curves denote the corresponding results with the empirical formula (6) taking g$_{1}$ = 0 . 0074 and g$_{2}$ = − 0 . 38. One can see that the curvatures of the parabolas can be reasonably well described by the empirical formula which greatly reduces the computation time for the calculation of deformed nuclei. 

In the microscopic part, the shell correction 

## C. Single-particle Potential in the Microscopic Part 

<img src='content_image/348260.jpg'>

is obtained by the traditional Strutinsky procedure [16] by setting the smoothing parameter γ = 1 . 2 ℏ ω$_{0}$ and the order p = 6 of the Gauss-Hermite polynomials. Where, E$_{sh}$ = E$_{sh}$ ( P ) + E$_{sh}$ ( N ) i.e. sum of the shell energies of protons and neutrons. ℏ ω$_{0}$ = 41 A − 1 / $^{3}$MeV is the mean distance between the gross-shells. In this work, we introduce a scale factor c$_{1}$ to the shell correction. This additional parameter is used to adjust the division of the binding energy between the macroscopic part and the remaining microscopic correction. It is known that a similar scale factor is usually introduced to the liquid-drop part [17] or the shell 

