Low-lying dipole resonance in neutron-rich Ne isotopes

Microscopic structure of the low-lying isovector dipole excitation mode in neutron-rich ${}^{26,28,30}\mathrm{Ne}$ is investigated by performing deformed quasiparticle-random-phase-approximation (QRPA) calculations. The particle-hole residual interaction is derived from a Skyrme force through a Landau-Migdal approximation. We obtain the low-lying resonance in ${}^{26}\mathrm{Ne}$ at around 8.6 MeV. It is found that the isovector dipole strength at $E_x<10$ MeV exhausts about 6.0% of the classical Thomas-Reiche-Kuhn dipole sum rule. This excitation mode is composed of several QRPA eigenmodes, one is generated by a $\nu (2s_{1/2}^{-1}2p_{3/2})$ transition dominantly and the other mostly by a $\nu (2s_{1/2}^{-1}2p_{1/2})$ transition. The neutron excitations take place outside of the nuclear surface reflecting the spatially extended structure of the $2s_{1/2}$ wave function. In ${}^{30}\mathrm{Ne}$, the deformation splitting of the giant resonance is large, and the low-lying resonance overlaps with the giant resonance.

Figure 1

Response function for the isoscalar quadrupole operator in ${}^{22}\mathrm{O}$. The transition strengths are smeared by using a Lorentzian function with a width of $\Gamma =0.5$ MeV. The renormalization factors for the QRPA calculation are $f_{\mathrm{ph}}=0.982,f_{\mathrm{pp}}=1.18$. The cutoff energy is 60 MeV.

Figure 2

Cutoff energy dependence of the renormalization factors and the $B(E2\uparrow )$ value for the first $2^{+}$ state in ${}^{22}\mathrm{O}$.

Figure 3

Cutoff energy dependence of the energy centroid of the low-lying dipole resonance in ${}^{26}\mathrm{Ne}$ calculated as $m_1/m_0$ and the fraction of the energy-weighted sum up to 10 MeV.

Figure 4

Response functions for the isovector dipole operator in ${}^{26,28,30}\mathrm{Ne}$. The dotted, dashed, and solid lines correspond to the $K^{\pi }=0^{-},K^{\pi }=1^{-}$, and total responses, respectively. For the $K^{\pi }=1^{-}$ response, the transition strengths for the $K^{\pi }=\pm 1^{-}$ states are summed up. The transition strengths are smeared by using $\Gamma =1$ MeV. The renormalization factors for the QRPA calculation are $f_{\mathrm{ph}}=0.919,0.880,$ and 0.929 for ${}^{26,28,30}\mathrm{Ne}$ and $f_{\mathrm{pp}}=1.225$ for all nuclei.

Figure 5

Isovector dipole transition strengths in ${}^{26}\mathrm{Ne}$ for the $K^{\pi }=0^{-}$ (the upper) and $K^{\pi }=1^{-}$ (the lower) states. Underlying discrete states are shown together with the smeared response functions. The arrow indicates the neutron emission threshold $E_{\mathrm{th}}=6.58$ MeV.

Figure 6

Transition densities in ${}^{26}\mathrm{Ne}$ for the $K^{\pi }=0^{-}$ state at 8.25 MeV (upper panels) and for the $K^{\pi }=1^{-}$ state at 8.76 MeV (lower panels). Solid and dotted lines indicate positive and negative transition densities, and the contour lines are plotted at intervals of $3\times {10}^{-4}$ fm${}^{-3}$. The thick solid lines indicate the neutron and proton half densities, 0.058 and 0.036 fm${}^{-3}$, respectively.

Figure 7

Same as Fig. 6, for the unperturbed transition density of $\nu [211]1/2\to [310]1/2$ excitation.

Figure 8

Energy-weighted sum of the isovector dipole strength function. The solid and the dotted lines are calculations with the energy cutoff at 60 and 30 MeV. The horizontal lines show the classical TRK and the RPA sum rule including the enhancement factor, $m_1=m_1^{\mathrm{cl}}(1+\kappa )$. Here $\kappa =0.32$ for the SkM* interaction in ${}^{26}\mathrm{Ne}$.

Figure 9

Same as Fig. 5 but for ${}^{28}\mathrm{Ne}$ and ${}^{30}\mathrm{Ne}$. The arrows indicate the neutron emission threshold $E_{\mathrm{th}}=4.44$ and 4.51 MeV.

Figure 10

Same as Fig. 6 but for the $K^{\pi }=0^{-}$ state at 8.1 MeV and for the $K^{\pi }=1^{-}$ state at 6.7 MeV in ${}^{30}\mathrm{Ne}$.