Continuum particle-vibration coupling method in coordinate-space representation for finite nuclei

TL;DR

This paper introduces a continuum particle-vibration coupling formalism in coordinate space for finite nuclei, enabling accurate treatment of resonant states and continuum effects in nuclear structure calculations.

Contribution

It presents a self-consistent, microscopic PVC model using zero-range interactions that properly incorporates the continuum, improving upon traditional discrete models.

Findings

Successfully applied to $^{40}$Ca, $^{208}$Pb, and $^{24}$O

Demonstrates improved description of resonant states in continuum

Provides insights into weakly-bound nuclei like $^{24}$O

Abstract

In this paper we present a new formalism to implement the nuclear particle-vibration coupling (PVC) model. The key issue is the proper treatment of the continuum, that is allowed by the coordinate space representation. Our formalism, based on the use of zero-range interactions like the Skyrme forces, is microscopic and fully self-consistent. We apply it to the case of neutron single-particle states in $^{40}$Ca, $^{208}$Pb and $^{24}$O. The first two cases are meant to illustrate the comparison with the usual (i.e., discrete) PVC model. However, we stress that the present approach allows to calculate properly the effect of PVC on resonant states. We compare our results with those from experiments in which the particle transfer in the continuum region has been attempted. The latter case, namely $^{24}$O, is chosen as an example of a weakly-bound system. Such a nucleus, being double-magic and not displaying collective low-lying vibrational excitations, is characterized by quite pure neutron single-particle states around the Fermi surface.