d $E_{\mathrm{th}}=4.44$ and 4.51 MeV. []{data-label="28Ne_strength"}](fig8-2.eps "fig:")

The central panel in Fig. \[response\] shows the response function in $^{28}$Ne. In the low-energy region, we can see a two-bump structure at around 7 and 8 MeV. Because the deformation is small as in $^{26}$Ne, we cannot see a splitting of the giant resonance. In Fig. \[28Ne\_strength\], we show the low-energy part of the strength functions. In the $K^{\pi}=0^{-}$ states, there is a prominent peak at 8.1 MeV with a strength of 0.098 $e^{2}$fm$^{2}$. The strength distribution is fragmented for the $K^{\pi}=1^{-}$ mode, but correspondingly, we can see an eigenmode at 8.9 MeV with the largest transition strength of 0.058 $e^{2}$fm$^{2}$.

We show in Table \[28Ne\_0-\] the QRPA amplitude for the $K^{\pi}=0^{-}$ state at 8.14 MeV in $^{28}$Ne. The main component is the neutron two-quasiparticle excitation of $\nu([310]1/2 \otimes [211]1/2)$ corresponding to $\nu(2s^{-1}_{1/2}2p_{3/2})$. Two quasiparticle excitations of (b) and (c) in Table \[28Ne\_0-\] correspond to $\nu(1d^{-1}_{5/2}1f_{7/2})$, and (d): $\nu(2s^{-1}_{1/2}1f_{7/2})$, (e) and (f): $\nu(1d^{-1}_{3/2}2p_{3/2})$, (g): $\nu(1d^{-1}_{3/2}1f_{7/2})$, (h) and (i): $\nu(1d^{-1}_{5/2}2p_{3/2})$, and (j): $\nu(1d^{-1}_{5/2}2p_{1/2})$ excitations, respectively. The proton excitation of $\pi(1p_{1/2}\otimes 1d_{5/2})$ has an appreciable contribution as in $^{26}$Ne.

  ----- --------------- --------------- ------------------------ -------------------------------------------- ----------------------
                                         $E_{\alpha}+E_{\beta}$                                                $Q_{10,\alpha\beta}$
           $\alpha$         $\beta$              (MeV)            $X_{\alpha \beta}^{2}-Y_{\alpha\beta}^{2}$      ($e\cdot$ fm)
   (a)   $\nu[310]1/2$   $\nu[211]1/2$            8.27                              0.569                            $-0.303$
   (b)   $\nu[330]1/2$   $\nu[220]1/2$            11.2                              0.055      