Probing surface quantum flows in deformed pygmy dipole modes

To explore the nature of collective modes in weakly bound nuclei, we have investigated deformation effects and surface flow patterns of isovector dipole modes in a shape-coexisting nucleus, ${}^{40}\mathrm{Mg}$. The calculations were done in a fully self-consistent continuum finite-amplitude quasiparticle random phase approximation in a large deformed spatial mesh. An unexpected result of pygmy and giant dipole modes having disproportionate deformation splittings in strength functions was obtained. Furthermore, the transition current densities demonstrate that the long-sought core-halo oscillation in pygmy resonances is collective and compressional, corresponding to the lowest excitation energy and the simplest quantum flow topology. Our calculations show that surface flow patterns become more complicated as excitation energies increase.

Figure 1

Transition strength functions of isovector dipole resonances in the shape-coexisting nucleus ${}^{40}\mathrm{Mg}$ as a function of excitation energy, calculated with different box sizes. (a) Prolate shape with a box size of 12 fm; (b) prolate shape with a box size of 21 fm; (c) prolate shape with a box size of 27.6 fm; (d) oblate shape with a box size of 27.6 fm.

Figure 2

$K=0$ transition density distributions of pygmy and giant dipole resonances in ${}^{40}\mathrm{Mg}$ with the prolate shape displayed in the cylinder coordinate space as $\delta \rho$($r, z$) for (a) neutrons of PDR, (b) neutrons of GDR, (c) protons of PDR, and (d) protons of GDR.

Figure 3

Neutron transition current density in the cylinder coordinate space, $\delta \vec{j}(r,z,\varphi =0)$, of the PDR in ${}^{40}\mathrm{Mg}$. The color scales denote the logarithm of the current strength and the arrows denote the flow direction. (a) $K=0$ mode of the prolate shape, (b) $K=0$ mode of the oblate shape, (c) $K=1$ mode of the prolate shape, and (d) $K=1$ mode of the oblate shape. The flow boundary lines are given for guiding eyes.

Figure 4

Transition currents similar to Fig. 3, but for (a) the neutron $K=0$ prolate GDR, (b) the neutron $K=1$ oblate GDR, (c) the proton $K=0$ prolate PDR, and (d) the proton $K=0$ prolate GDR.