# Number conserving particle-hole RPA for superfluid nuclei

## TL;DR

This paper introduces a number conserving particle-hole RPA method for superfluid nuclei, which smoothly describes collective excitations across the superfluid transition, improving upon traditional RPA approaches.

## Contribution

It develops a novel number conserving particle-hole RPA formalism based on antisymmetric geminal powers, bridging the normal and superfluid phases seamlessly.

## Key findings

- Excitations evolve smoothly across the phase transition.
- The method aligns closely with exact results in a minimal model.
- It avoids the basis change required by traditional RPA methods.

## Abstract

We present a number conserving particle-hole RPA theory for collective excitations in the transition from normal to superfluid nuclei. The method derives from an RPA theory developed long ago in quantum chemistry using antisymmetric geminal powers, or equivalently number projected HFB states, as reference states. We show within a minimal model of pairing plus monopole interactions that the number conserving particle-hole RPA excitations evolve smoothly across the superfluid phase transition close to the exact results, contrary to particle-hole RPA in the normal phase and quasiparticle RPA in the superfluid phase that require a change of basis at the broken symmetry point. The new formalism can be applied in a straightforward manner to study particle-hole excitations on top of a number projected HFB state.