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.
Highlights
Excitation spectra of nuclei show a tremendous richness and diversity, going from low energy collective states to giant resonances
The so-called antisymmetrized geminal power (AGP) operators are constructed, projected HFB (PHFB) has a set of killers state, which is the same as the well known number that we classify into particle killers and spin killers
J+2 + J−2 In this work we have introduced the number conserving particle-hole RPA (NCphRPA) following a similar approach presented long ago in quantum chemistry
Summary
Excitation spectra of nuclei show a tremendous richness and diversity, going from low energy collective states to giant resonances. In the small amplitude limit, this means the consistent solution of mean field and RPA equations For superfluid nuclei this has to be generalized to Hartree-FockBogoliubov (HFB) and quasiparticle RPA (QRPA) equations. The restoration of good particle number is technically feasible with modern projection techniques [7, 8] but becomes rather cumbersome on the level of QRPA where one has to project two-quasiparticle states with a subsequent orthogonalization [9]. This might be the reason why only in relatively rare cases it has been applied mainly to β and double-β decays [10, 11]. GCM is generally tailored for large amplitude collective motion and only a few collective coordi-
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