On the description of two-particle transfer in superfluid systems

TL;DR

This paper compares exact pair transfer probabilities in superfluid systems with approximations like ppRPA and QRPA, highlighting QRPA's overestimation near phase transitions and proposing a projection-based method for improvement.

Contribution

It introduces a projection-based method that improves pair transfer probability calculations in superfluid systems over traditional QRPA.

Findings

QRPA overestimates transfer probabilities near phase transition

Projection method improves accuracy of pair transfer predictions

Exact results are provided for Richardson model with different level spacings

Abstract

Exact results of pair transfer probabilities for the Richardson model with equidistant or random level spacing are presented. The results are then compared either to particle-particle random phase approximation (ppRPA) in the normal phase or quasi-particle random phase approximation (QRPA) in the superfluid phase. We show that both ppRPA and QRPA are globally well reproducing the exact case although some differences are seen in the superfluid case. In particular the QRPA overestimates the pair transfer probabilities to excited states in the vicinity of the normal-superfluid phase transition, which might explain the difficult in detecting collective pairing phenomena as for example the Giant Pairing Vibration. The shortcoming of QRPA can be traced back to the breaking of particle number that is used to incorporate pairing. A method, based on direct diagonalization of the Hamiltonian in the space of two quasi-particle projected onto good particle number is shown to improve the description of pair transfer probabilities in superfluid systems.