# Generalized Seniority on Deformed Single-Particle Basis

## TL;DR

This paper extends a fast computational scheme for generalized seniority from spherical to deformed single-particle bases, enabling efficient analysis of deformed nuclei like Gd-158 with realistic interactions.

## Contribution

The work redesigns the generalized seniority scheme for deformed bases and demonstrates its effectiveness in truncating the deformed shell model for heavy nuclei.

## Key findings

- Accurately computes low-lying intrinsic states with up to four broken pairs.
- States converge well to exact solutions, validating the scheme.
- Ground state resembles a coherent pair condensate, with pairs breaking at higher energies.

## Abstract

Recently we proposed [62] a fast computing scheme for generalized seniority on spherical single-particle basis. This work redesigns the scheme to make it applicable to deformed single-particle basis. The algorithm is applied to the rare-earth nucleus $^{158}_{~64}$Gd$_{94}$ for intrinsic (body-fixed frame) neutron excitations under the low-momentum {\emph{NN}} interaction $V_{{\rm{low}}-k}$. By allowing as many as four broken pairs, we compute the lowest $300$ intrinsic states of several multipolarity. These states converge well to the exact ones, showing generalized seniority is very effective in truncating the deformed shell model. Under realistic interactions, the picture remains approximately valid that the ground state is a coherent pair condensate, and the pairs gradually break up as excitation energy increases.