GLYPH<s45>GLYPH<s48>GLYPH<s46>GLYPH<s52> GLYPH<s45>GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s48>GLYPH<s46>GLYPH<s52> GLYPH<s48>GLYPH<s46>GLYPH<s57>GLYPH<s55> GLYPH<s48>GLYPH<s46>GLYPH<s57>GLYPH<s56> GLYPH<s48>GLYPH<s46>GLYPH<s57>GLYPH<s57> GLYPH<s49>GLYPH<s46>GLYPH<s48>GLYPH<s48> GLYPH<s48> GLYPH<s49>GLYPH<s48>GLYPH<s48> GLYPH<s50>GLYPH<s48>GLYPH<s48> GLYPH<s51>GLYPH<s48>GLYPH<s48> GLYPH<s45> GLYPH<s48>GLYPH<s46>GLYPH<s50> GLYPH<s45> GLYPH<s48>GLYPH<s46>GLYPH<s49> GLYPH<s48>GLYPH<s46>GLYPH<s48> GLYPH<s32> GLYPH<s32>GLYPH<s83>GLYPH<s107> GLYPH<s77>GLYPH<s42>GLYPH<s32>GLYPH<s32> GLYPH<s32>GLYPH<s49>GLYPH<s43>GLYPH<s32>GLYPH<s98> GLYPH<s50> GLYPH<s50> GLYPH<s50> GLYPH<s32> GLYPH<s69> GLYPH<s47> GLYPH<s69> GLYPH<s48> GLYPH<s50> GLYPH<s50> GLYPH<s48> GLYPH<s56> GLYPH<s80>GLYPH<s98> GLYPH<s52> GLYPH<s56> GLYPH<s67>GLYPH<s97> GLYPH<s49> GLYPH<s54> GLYPH<s79> GLYPH<s40>GLYPH<s97>GLYPH<s41> GLYPH<s98> GLYPH<s50> GLYPH<s65> GLYPH<s40>GLYPH<s98>GLYPH<s41> FIG. 1: (Color online) (a) Energy of $^{16}$O, $^{48}$Ca and $^{208}$Pb with respect to β$_{2}$ 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$_{2}$β 2 $_{2}$, respectively. (b) The value of b$_{2}$ obtained with SkM* as a function of mass number. B. Influence of Nuclear Deformation on the Macroscopic Energy For the deformation of nuclei, we only consider axially-deformed cases. In this work, only β$_{2}$ and β$_{4}$ deformations of nuclei are taken into account. We first investigated the energy of a nucleus with respect to a β$_{2}$ deformation based on the Skyrme energy density functional together with the extended Thomas-Fermi approximation (ETF) [7, 8]. The procedure is as follows: The total energy of a nucleus can be expressed as the integral over the Skyrme energy density functional H ( r ) [15]. Given a density functional ρ ( r ), one can calculate the corresponding energy via E = ∫ H [ ρ ( r )] d r under the ETF approximation. We first obtain the binding energy E$_{0}$ and the spherical Woods-Saxon density distributions of a nucleus with the approach in [8]. Then, with the same procedure we calculate the energy E ( β$_{2}$ ) of the nucleus with a quadrupole deformed Woods-Saxon density distribution of the nucleus in which the central density and the surface diffuseness remained unchanged. Fig.1(a) shows the calculated energy of $^{16}$O, $^{48}$Ca and $^{208}$Pb as a function of β$_{2}$ deformation with the SkM* interaction [15] (denoted by circles). The solid curves denote the results of a formula E/E$_{0}$ = 1 + b$_{2}$β 2 in which the value of b$_{2}$ is obtained by fitting the open circles. One can 5