round 6 and 7 MeV are consistent between the two calculations. The energy-weighted sum ($1.867\times10^{4}$MeV$\cdot$fm$^{4}$) overestimates by about 13.9% the EWSR value ($1.638\times 10^{4}$MeV$\cdot$fm$^{4}$). The overshooting of the EWSR for the isoscalar quadrupole mode in the LM approximation was pointed out in Ref [@miz07].

![image](fig3.eps)

\[results\]Results and Discussion
=================================

                                               $^{26}$Ne     $^{28}$Ne     $^{30}$Ne
  ------------------------------------------- ------------ ------------- -------------
             $\lambda_{\nu}$ (MeV)              $-4.60$       $-3.06$       $-2.90$
             $\lambda_{\pi}$ (MeV)              $-14.8$       $-17.0$       $-19.9$
               $\beta_{2}^{\nu}$                  0.08         0.12          0.32
               $\beta_{2}^{\pi}$                  0.14         0.20          0.39
     $\langle \Delta_{\nu} \rangle$ (MeV)      0.0 (0.70)   1.27 (1.24)   1.34 (1.30)
     $\langle \Delta_{\pi} \rangle$ (MeV)         1.04         0.87           0.0
   $\sqrt{\langle r^{2} \rangle_{\nu}}$ (fm)      3.20         3.35          3.53
   $\sqrt{\langle r^{2} \rangle_{\pi}}$ (fm)      2.93         2.98          3.08

  : Ground state properties of $^{26,28,30}$Ne obtained by the deformed HFB calculation with the SkM\* interaction and the surface-type pairing interaction. Chemical potentials, deformations, average pairing gaps and root-mean-square radii for neutrons and protons are listed. []{data-label="GS"}

We now discuss the properties of $^{26,28,30}$Ne nuclei calculated with the SkM\* interaction. We summarize in Table \[GS\] the ground state properties of these Ne isotopes obtained by solving Eq. (\[eq:HFB1\]). The ground state is slightly deformed in $^{26}$Ne and $^{28}$Ne, and we obtain a well-deformed ground state for $^{30}$Ne. The values in parentheses are experimental pairing gaps extracted by the three-point mass difference formula [@sat98] using the experimental binding e