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## 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 

