A characteristic feature of collective and particle-hole excitations in neutron-rich nuclei is that many of them couple to an unbound neutron in continuum single-particle orbits. The continuum random-phase approximation (cRPA) is a powerful many-body method that describes such excitations, and it provides a scheme to evaluate transition strengths from the ground state. In an attempt to apply cRPA to the radiative neutron-capture reaction, we formulate in the present study an extended scheme of cRPA that describes $\gamma$ transitions from the excited states under consideration, which decay to low-lying excited states as well as the ground state. This is achieved by introducing a nonlocal one-body operator which causes transitions to a low-lying excited state, and describing a density-matrix response against this operator. As a demonstration of this new scheme, we perform numerical calculation for dipole, quadrupole, and octupole excitations in ${}^{140}\mathrm{Sn}$, and discuss $E1$ and $E2$ transitions decaying to low-lying $2_{1,2}^{+}$ and $3_1^{-}$ states. The results point to cases where the branching ratio to the low-lying states is larger than or comparable with that to the ground state. We discuss key roles of collectivity and continuum orbits in both initial and final states.

• Received 1 May 2021
• Accepted 17 August 2021

DOI:https://doi.org/10.1103/PhysRevC.104.034305