Quadrupole and octupole collectivity and cluster structures in neon isotopes

The lowest positive- and negative-parity bands of ${}^{20}\mathrm{Ne}$ and neutron-rich even-even Ne isotopes are investigated using a theoretical framework based on energy density functionals. Starting from a self-consistent relativistic Hartree-Bogoliubov calculation of axially symmetric and reflection-asymmetric deformation energy surfaces, the collective symmetry-conserving states are built using projection techniques and the generator coordinate method. Overall a good agreement with the experimental excitation energies and transition rates is obtained. In particular, the model provides an accurate description of the excitation spectra and transition probabilities in ${}^{20}\mathrm{Ne}$. The contribution of cluster configurations to the low-energy states is discussed, as well as the transitional character of the ground state. The analysis is extended to ${}^{22}\mathrm{Ne}$ and the shape-coexisting isotope ${}^{24}\mathrm{Ne}$, and to the drip-line nuclei ${}^{32}\mathrm{Ne}$ and ${}^{34}\mathrm{Ne}$. The role of valence neutrons in the formation of molecular-type bonds between clusters is discussed.

Figure 1

Self-consistent RHB binding energies of even-even ${}^{20–34}\mathrm{Ne}$ isotopes, in the ${\beta }_2-{\beta }_3$ plane. For each nucleus, energies are normalized with respect to the corresponding absolute minimum. Dashed contours are separated by $2\mathrm{MeV}$.

Figure 2

Angular momentum- and parity-projected energy surfaces of even-even ${}^{20–34}\mathrm{Ne}$ isotopes, for spin and parity $J^{\pi }=0^{+}$ in the ${\beta }_2–{\beta }_3$ plane. For each nucleus, energies are normalized with respect to the binding energy of the corresponding absolute minimum. Dashed contours are separated by $2\mathrm{MeV}$. See text for the explanation of symbols.

Figure 3

Same as in the caption to Fig. 2, but for spin and parity $J^{\pi }=2^{+}$.

Figure 4

Angular momentum- and parity-projected energy surfaces of even-even ${}^{20–34}\mathrm{Ne}$ isotopes, for spin and parity $J^{\pi }=1^{-}$ in the ${\beta }_2-{\beta }_3$ plane. For each nucleus, energies are normalized with respect to the binding energy of the corresponding $0^{+}$ minimum. Dashed contours are separated by $2\mathrm{MeV}$. See text for the explanation of symbols.

Figure 5

Same as in the caption to Fig. 4, but for spin and parity $J^{\pi }=3^{-}$.

Figure 6

Two-neutron separation energies of ${}^{22–34}\mathrm{Ne}$ isotopes. The RHB values obtained on the mean-field level (squares), and results of the full angular momentum- and parity-projected GCM calculation (triangles), are compared to the available data [37].

Figure 7

Amplitudes of collective wave functions squared $|g({\beta }_2,{\beta }_3){|}^2$ of the ground states of ${}^{20-34}\mathrm{Ne}$ isotopes. Dashed contours in the ${\beta }_2-{\beta }_3$ plane successively denote a $10\%$ decrease starting from the largest value of the amplitude.

Figure 8

Deformation parameters ${\beta }_2$ (left panel (a)) and ${\beta }_3$ (right panel (b)) that correspond to RHB mean-field minima of ${}^{20-34}\mathrm{Ne}$, in comparison with the expectation values $\langle {\beta }_2\rangle$ and $\langle \left|{\beta }_3\right|\rangle$ in the corresponding angular momentum- and parity-projected GCM ground states. The deformations obtained by taking the expectation values over only prolate (triangle left) and only oblate (triangle right) configurations, as well as their respective contributions, are also shown.

Figure 9

Calculated excitation energies of the states $2_1^{+}$ and $4_1^{+}$ [left panel (a)] and the transition probabilities $B(E2;2_1^{+}\to 0_1^{+})$ [right panel (b)] in the even-even ${}^{20–34}\mathrm{Ne}$ isotopes, compared with the available experimental data [41].

Figure 10

Theoretical low-energy excitation spectrum of ${}^{20}\mathrm{Ne}$ compared with available data. The calculated $E2$ transition probabilities within the bands (red color, in $e^2{\mathrm{fm}}^4)$, and $E3$ transition probabilities between the bands (blue color, in $e^2{\mathrm{fm}}^6)$ are also shown. Results obtained with two other beyond mean-field models [17, 20] are also shown for comparison. See text for details.

Figure 11

Amplitudes of collective wave functions squared $|g({\beta }_2,{\beta }_3){|}^2$ of the low-energy levels of ${}^{20}\mathrm{Ne}$. Dashed contours in the ${\beta }_2-{\beta }_3$ plane successively denote a $10\%$ decrease starting from the largest value of the amplitude.

Figure 12

Characteristic intrinsic nucleon densities of states of the ground-state band and the $K^{\pi }=0^{-}$ band in ${}^{20}\mathrm{Ne}$. See text for description.

Figure 13

Calculated low-energy spectra of ${}^{22,24}\mathrm{Ne}$ (left panel) and ${}^{32,34}\mathrm{Ne}$ (right panel). The $E2$ reduced transition probabilities within the bands (red color, in $e^2{\mathrm{fm}}^4)$ and $E3$ transition probabilities between the bands (blue color, in $e^2{\mathrm{fm}}^6)$ are also shown.

Figure 14

Characteristic intrinsic nucleon densities of the ground state and the $K^{\pi }=0_1^{-}$ bandhead in ${}^{22}\mathrm{Ne}$. Total nucleon densities (lower panel) and valence neutrons densities (upper panel) are shown.

Figure 15

Same as in the caption to Fig. 14, but for ${}^{24}\mathrm{Ne}$.