Nuclear rotation in the continuum

Background: Atomic nuclei often exhibit collective rotational-like behavior in highly excited states, well above the particle emission threshold. What determines the existence of collective motion in the continuum region is not fully understood.

Purpose: In this work, by studying the collective rotation of the positive-parity deformed configurations of the one-neutron halo nucleus ${}^{11}\mathrm{Be}$, we assess different mechanisms that stabilize collective behavior beyond the limits of particle stability.

Method: To solve a particle-plus-core problem, we employ a nonadiabatic coupled-channel formalism and the Berggren single-particle ensemble, which explicitly contains bound states, narrow resonances, and the scattering continuum. We study the valence-neutron density in the intrinsic rotor frame to assess the validity of the adiabatic approach as the excitation energy increases.

Results: We demonstrate that collective rotation of the ground band of ${}^{11}\mathrm{Be}$ is stabilized by (i) the fact that the $\ell =0$ one-neutron decay channel is closed, and (ii) the angular momentum alignment, which increases the parentage of high-$\ell$ components at high spins; both effects act in concert to decrease decay widths of ground-state band members. This is not the case for higher-lying states of ${}^{11}\mathrm{Be}$, where the $\ell =0$ neutron-decay channel is open and often dominates.

Conclusion: We demonstrate that long-lived collective states can exist at high excitation energy in weakly bound neutron drip-line nuclei such as ${}^{11}\mathrm{Be}$.

Figure 1

Calculated yrast bands of ${}^{11}\mathrm{Be}$ with $J\le 13/2$ with signature $r=-i$ (squares) and $r=+i$ (triangles) compared to the experimental ground-state band of ${}^{10}\mathrm{Be}$ core (horizontal dashed lines). Some excited (yrare) states of ${}^{11}\mathrm{Be}$ are marked by stars.

Figure 2

Partial densities ${\rho }_{JK}\left(\mathit{r}\right)$ (in ${10}^{-2} {\mathrm{fm}}^{-3}$) with $K=1/2$ for the three first ground-state band members of ${}^{11}\mathrm{Be}$ in panels (b)–(d), and for selected states of the unfavored $r=i$ band (in ${10}^{-3}$ ${\mathrm{fm}}^{-3}$) in panels (e) $J=7/2,K=5/2$ and (f) $J=15/2,K=3/2$. The adiabatic limit ($I\to \infty$) is shown in panel (a).

Figure 3

Contribution from different partial waves $\left(\ell j\right)$ to the norms (top) and widths ${\mathrm{\Gamma }}_{\ell j}={\sum }_{j_r}{\mathrm{\Gamma }}_{\ell j{j}_r}$ (bottom) of different states of the ground-state band of ${}^{11}\mathrm{Be}$ (left) and yrare states (right). The total widths are marked by stars.

Figure 4

Partial wave contribution to the width of the ${7/2}^{+}$ yrast state of ${}^{11}\mathrm{Be}$. Continuous and dashed lines correspond to the full- and pole-space calculations, respectively. The total width is indicated with dotted line in both cases.