\text{\ }\sigma &=&\gamma -1  \label{SkySigma}\end{aligned}$$where $k_{\mathrm{F}}^{0}=(1.5\pi ^{2}{\rho _{0}})^{1/3}$, $E_{\text{\textrm{sym}}}^{\mathrm{loc}}({\rho _{0}})=E_{\text{\textrm{sym}}}({\rho _{0}})-E_{\text{\textrm{sym}}}^{\mathrm{kin}}({\rho _{0}})-D$, and the parameters $C$, $D$, $\alpha $, $\beta $, $\gamma $, and $y$ are defined as [@Che09] $$\begin{aligned}
C &=&\frac{m-m_{s,0}^{\ast }}{m_{s,0}^{\ast }}E_{\mathrm{kin}}^{0} \\
D &=&\frac{5}{9}E_{\mathrm{kin}}^{0}\left( 4\frac{m}{m_{s,0}^{\ast }}-3\frac{m}{m_{v,0}^{\ast }}-1\right) \\
\alpha &=&-\frac{4}{3}E_{\mathrm{kin}}^{0}-\frac{10}{3}C-\frac{2}{3}(E_{\mathrm{kin}}^{0}-3E_{0}(\rho _{0})-2C)  \notag \\
&&\times \frac{K_{0}+2E_{\mathrm{kin}}^{0}-10C}{K_{0}+9E_{0}(\rho _{0})-E_{\mathrm{kin}}^{0}-4C} \\
\beta &=&(\frac{E_{\mathrm{kin}}^{0}}{3}-E_{0}(\rho _{0})-\frac{2}{3}C)
\notag \\
&&\times \frac{K_{0}-9E_{0}(\rho _{0})+5E_{\mathrm{kin}}^{0}-16C}{K_{0}+9E_{0}(\rho _{0})-E_{\mathrm{kin}}^{0}-4C} \\
\gamma &=&\frac{K_{0}+2E_{\mathrm{kin}}^{0}-10C}{3E_{\mathrm{kin}}^{0}-9E_{0}(\rho _{0})-6C}. \\
y &=&\frac{L-3E_{\text{\textrm{sym}}}({\rho _{0}})+E_{\text{\textrm{\ sym}}}^{\mathrm{kin}}({\rho _{0}})-2D}{3(\gamma -1)E_{\text{ \textrm{sym}}}^{\mathrm{loc}}({\rho _{0}})}\end{aligned}$$with $E_{\mathrm{kin}}^{0}=\frac{3\hbar ^{2}}{10m}\left( \frac{3\pi ^{2}}{2}\right) ^{2/3}\rho _{0}^{2/3}$ and $E_{\text{\textrm{sym}}}^{\mathrm{kin}}({\rho _{0}})=\frac{\hbar ^{2}}{6m}\left( \frac{3\pi ^{2}}{2}{\rho _{0}}\right) ^{2/3}$. In the above, the isoscalar effective mass $m_{s,0}^{\ast }$ is the nucleon effective mass in symmetric nuclear matter at its saturation density ${\rho _{0}}$ while the isovector effective mass $m_{v,0}^{\ast }$ corresponds to the proton (neutron) effective mass in pure neutron (proton) matter at baryon number density ${\rho _{0}}$ (See, e.g., Refs. [Cha97,Che09]{}). Furthermore, $G_{S}$ and $G_{V}$ are respectively the gradient and symmetry-gradient coefficients in the interaction part of the binding energies for finite nuclei defined as $$E_{\mathrm{grad}}=G_{S}(\nabla \rho )^{2}/(2{\rho )}-G_{V}\left[ \nabla
(\rho _{n}-\rho _{p})\right] ^{2}/(2{\rho )}.$$

HF + continuum-RPA calculations
-------------------------------

Since the energy of the giant monopole resonance is above the single particle continuum threshold, a proper calculation should, in principle, involve 