Large-amplitude $Q_n$-$Q_p$ collectivity in the neutron-rich oxygen isotope ${}^{20}\mathrm{O}$

By means of HFB calculations with independent constraints on axial neutron and proton quadrupole moments ${\widehat{Q}}_n$ and ${\widehat{Q}}_p$, we investigate the large amplitude isoscalar and isovector deformation properties of the neutron-rich isotope ${}^{20}\mathrm{O}$. Using the particle-number and angular-momentum projected generator coordinate method, we analyze the collective dynamics in the $\{\langle {\widehat{Q}}_n\rangle ,\langle {\widehat{Q}}_p\rangle \}$ plane. The parametrization SLy4 of the Skyrme interaction is used for all calculations in connection with a density-dependent zero-range pairing interaction. Our results show that already for this moderately neutron-rich nucleus the transition moments are modified when independent neutron and proton collective dynamics are allowed.

Figure 1

Particle-number projected energy curve obtained with a single constraint on the mass quadrupole moment (left) and the corresponding path in the plane of proton and neutron quadrupole deformation (right). The dotted line in the right panel corresponds to the line of equal proton and neutron deformation ${\beta }_{2,n}={\beta }_{2,p}$.

Figure 2

Neutron (top) and proton (bottom) single-particle energies (in MeV) versus mass quadrupole deformation (bottom horizontal scales) and mass quadrupole moment (top horizontal scale). Solid (dotted) lines correspond to positive (negative) parity states. The dashed lines represent the Fermi energies of protons and neutrons, respectively.

Figure 3

Particle-number projected mean-field (solid curve) and particle-number and angular-momentum projected deformation energy curves of ${}^{20}\mathrm{O}$ as a function of the mass quadrupole deformation.

Figure 4

Contour lines of the angular-momentum and particle-particle number projected deformation energy surface of ${}^{20}\mathrm{O}$ (in MeV) as a function of the neutron and proton deformation ${\beta }_{2,q},q=n,p$. The right and upper axes show the corresponding proton and neutron quadrupole moments $Q_q,q=n,p$. The upper panel shows the surface for $J=0$, the lower panel for $J=2$. The solid line in both panels represents the line of equal proton and neutron deformation ${\beta }_{2,p}={\beta }_{2,n}$, the dotted line the isoscalar path followed when a single constraint on the mass quadrupole moment ${\widehat{Q}}_t$ is applied.

Figure 5

GCM wave functions of the $0^{+}$ ground state and the lowest $J=2$ state of ${}^{20}\mathrm{O}$ for a collective motion restricted to one dimension, plotted versus the mass quadrupole deformation ${\beta }_{2,t}$.