Continuum random-phase approximation for (n,\gamma) reactions on neutron-rich nuclei: collective effects and resonances

We formulate a microscopic theory to calculate cross section of the radiative neutron capture reaction on neutron-rich nuclei using the continuum random-phase approximation (cRPA) to the time-dependent density functional theory (TDDFT). With an intension of applying to the r-process, for which the statistical reaction model may not be appropriate, we describe the transition between a initial state of incident neutron and a final state of the gamma decay by means of a single many-body framework of the cRPA-TDDFT. With the cRPA approach, it is possible to describe various excitation modes present in the $(n,\gamma)$ reaction, including soft dipole excitation, the giant resonances as well as non-collective excitations and the single-particle resonances. Furthermore, it enables us to describe the $(n,\gamma)$ reaction where the final states of the gamma transition are low-lying surface vibrational states. We demonstrate the theory by performing numerical calculation for the reaction $^{139}{\rm Sn} (n,\gamma) ^{140}{\rm Sn}$. We discuss various new features which are beyond the single-particle model; presence of narrow and wide resonances originating from non-collective and collective excitations and roles of low-lying quadrupole and octupole vibrational states.