Continuum quasiparticle random-phase approximation for $(n,\gamma)$ reactions on neutron-rich nuclei: collectivity and resonances in low-energy cross section

Abstract

We formulate a microscopic theory to calculate cross section of the radiative neutron capture on neutron-rich nuclei using the continuum quasiparticle random-phase approximation. This formulation is designed to be applied to neutron-rich nuclei around the $r$-process path, for which the compound nuclear model may not be appropriate. It takes into account effects of various excitation modes such as the soft dipole excitation, the giant resonances, and the quasiparticle resonance in addition to the surface vibrations such as quadrupole and octupole modes. We perform numerical calculations to demonstrate new features of the present theory, employing reactions $^{89}{\rm Ge}(n,\gamma)^{90}{\rm Ge}$ and $^{91}{\rm Zn}(n,\gamma)^{92}{\rm Zn}$ with $E1$ transitions populating the ground state, collective $2^{+}_{1}$ and $3^{-}_{1}$ states in $ ^{90}{\rm Ge}$ and $^{92}{\rm Zn}$. With these examples, we discuss enhanced resonance contributions in the $(n,\gamma)$ reaction at low energy, which originate from the quasiparticle resonance and the pygmy quadrupole resonance located just above the one neutron separation energy, and from combination with the low-lying octupole vibrational state.