# Optimizing phonon space in the phonon-coupling model

## TL;DR

This paper introduces a new phonon selection scheme for the phonon-coupling model, improving computational efficiency and reducing double counting by focusing on phonon-nucleon coupling strengths, and applies it to nuclear resonance studies.

## Contribution

It proposes a novel phonon selection criterion based on coupling strengths, enhancing the phonon-coupling model's accuracy and efficiency.

## Key findings

- Smaller phonon spaces reduce computational cost.
- The new criterion effectively controls cutoff dependence.
- Application to nuclei reveals consistent resonance features.

## Abstract

We present a new scheme to select the most relevant phonons in the phonon-coupling model, named here time-blocking approximation (TBA). The new criterion, based on the phonon-nucleon coupling strengths rather than on $B(EL)$ values, is more selective and thus produces much smaller phonon spaces in TBA. This is beneficial in two respects: first, it curbs down the computational cost, and second, it reduces the danger of double counting in the expansion basis of TBA. We use here TBA in a form where the coupling strength is regularized to keep the given Hartree-Fock ground state stable. The scheme is implemented in an RPA and TBA code based on the Skyrme energy functional. We first explore carefully the cutoff dependence with the new criterion and can work out a natural (optimal) cutoff parameter. Then we use the freshly developed and tested scheme to a survey of giant resonances and low-lying collective states in six doubly magic nuclei looking also on the dependence of the results when varying the Skyrme parametrization.