# Pairing and deformation effects in nuclear excitation spectra

## TL;DR

This study examines how pairing interactions and nuclear deformation influence various nuclear excitation modes using QRPA with Skyrme functional, revealing negligible particle-particle channel effects and distinctive deformation splitting features.

## Contribution

It provides a detailed analysis of pairing and deformation effects on nuclear excitations, highlighting the minimal role of the pp-channel and differences between volume and surface pairing.

## Key findings

- Particle-particle channel effects are negligible for most excitations.
- Differences between volume and surface pairing are small, except for peak heights.
- The $K^{ ext{pi}}=1^-$ branch dominates in low-energy pygmy and toroidal modes.

## Abstract

We investigate effects of pairing and of quadrupole deformation on two sorts of nuclear excitations,$\gamma$-vibrational $K^{\pi}=2^+$ states and dipole resonances (isovector dipole, pygmy, compression, toroidal). The analysis is performed within the quasiparticle random-phase approximation (QRPA) based on the Skyrme energy functional using the Skyrme parametrization SLy6. Particular attention is paid to i) the role of the particle-particle (pp) channel in the residual interaction of QRPA, ii) comparison of volume pairing (VP) and surface pairing (SP), iii) peculiarities of deformation splitting in the various resonances. We find that the impact of the pp-channel on the considered excitations is negligible. This conclusion applies also to any other excitation except for the $K^{\pi}=0^+$ states. Furthermore, the difference between VP and SP is found small (with exception of peak height in the toroidal mode). In the low-energy isovector dipole (pygmy) and isoscalar toroidal modes, the branch $K^{\pi}=1^-$ is shown to dominate over $K^{\pi}=0^-$ one in the range of excitation energy $E <$ 8--10 MeV. The effect becomes impressive for the toroidal resonance whose low-energy part is concentrated in a high peak of almost pure $K^{\pi}=1^-$ nature. This peculiarity may be used as a fingerprint of the toroidal mode in future experiments. The interplay between pygmy, toroidal and compression resonances is discussed, the interpretation of the observed isoscalar giant dipole resonance is partly revised.