interaction is taken to have a zero-range, density- and momentum-dependent form [@Cha97], i.e., $$\begin{aligned}
V_{12}(\mathbf{R},\mathbf{r}) &=&t_{0}(1+x_{0}P_{\sigma })\delta (\mathbf{r})
\notag \\
&+&\frac{1}{6}t_{3}(1+x_{3}P_{\sigma })\rho ^{\sigma }(\mathbf{R})\delta (\mathbf{r})  \notag \\
&+&\frac{1}{2}t_{1}(1+x_{1}P_{\sigma })(\mathbf{K}^{^{\prime }2}\delta (\mathbf{r})+\delta (\mathbf{r})\mathbf{K}^{2})  \notag \\
&+&t_{2}(1+x_{2}P_{\sigma })\mathbf{K}^{^{\prime }}\cdot \delta (\mathbf{r})\mathbf{K}  \notag \\
&\mathbf{+}&iW_{0}(\mathbf{\sigma }_{1}+\mathbf{\sigma }_{2})\cdot \lbrack
\mathbf{K}^{^{\prime }}\times \delta (\mathbf{r})\mathbf{K]},  \label{V12Sky}\end{aligned}$$with $\mathbf{r}=\mathbf{r}_{1}-\mathbf{r}_{2}$ and $\mathbf{R}=(\mathbf{r}_{1}+\mathbf{r}_{2})/2$. In the above expression, the relative momentum operators $\mathbf{K}=(\mathbf{\nabla }_{1}-\mathbf{\nabla }_{2})/2i$ and $\mathbf{K}^{\prime }=-(\mathbf{\nabla }_{1}-\mathbf{\nabla }_{2})/2i$ act on the wave function on the right and left, respectively. The quantities $P_{\sigma }$ and $\sigma _{i}$ denote, respectively, the spin exchange operator and Pauli spin matrices. The $\sigma $, $t_{0}-t_{3}$, $x_{0}-x_{3}$ are the $9$ Skyrme interaction parameters which can be expressed analytically in terms of $9$ macroscopic quantities $\rho _{0}$, $E_{0}(\rho
_{0})$, the incompressibility $K_{0}$, the isoscalar effective mass $m_{s,0}^{\ast }$, the isovector effective mass $m_{v,0}^{\ast }$, $E_{\text{\textrm{sym}}}({\rho _{0}})$, $L$, the gradient coefficient $G_{S}$, and the symmetry-gradient coefficient $G_{V}$ [@Che10; @Che11b], i.e., $$\begin{aligned}
t{_{0}} &=&4\alpha /(3{\rho _{0}}) \\
x{_{0}} &=&3(y-1)E_{\text{\textrm{sym}}}^{\mathrm{loc}}({\rho _{0}})/\alpha
-1/2 \\
t{_{3}} &=&16\beta /\left[ {\rho _{0}}^{\gamma }(\gamma +1)\right] \\
x{_{3}} &=&-3y(\gamma +1)E_{\text{\textrm{sym}}}^{\mathrm{loc}}({\rho _{0}})/(2\beta )-1/2 \\
t_{1} &=&20C/\left[ 9{\rho _{0}(}k_{\mathrm{F}}^{0})^{2}\right] +8G_{S}/3 \\
t_{2} &=&\frac{4(25C-18D)}{9{\rho _{0}(}k_{\mathrm{F}}^{0})^{2}}-\frac{8(G_{S}+2G_{V})}{3} \\
x_{1} &=&\left[ 12G_{V}-4G_{S}-\frac{6D}{{\rho _{0}(}k_{\mathrm{F}}^{0})^{2}}\right] /(3t_{1}) \\
x_{2} &=&\left[ 20G_{V}+4G_{S}-\frac{5(16C-18D)}{3{\rho _{0}(}k_{\mathrm{F}}^{0})^{2}}\right] /(3t_{2}) \\
