Continuum random-phase approximation for (n,γ) reactions on neutron-rich nuclei: Collective effects and resonances

Abstract

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 intention 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 $\ensuremath{\gamma}$ 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 $(n,\ensuremath{\gamma})$ reaction, including soft dipole excitation, the giant resonances, as well as noncollective excitations and the single-particle resonances. Furthermore, it enables us to describe the $(n,\ensuremath{\gamma})$ reaction where the the final states of the $\ensuremath{\gamma}$ transition are low-lying surface vibrational states. We demonstrate the theory by performing numerical calculation for the reaction $^{139}\mathrm{Sn}(n,\ensuremath{\gamma})^{140}\mathrm{Sn}$. We discuss various new features which are beyond the single-particle model: the presence of narrow and wide resonances originating from noncollective and collective excitations and roles of low-lying quadrupole and octupole vibrational states.