Pair-transfer probability in open- and closed-shell Sn isotopes

TL;DR

This paper investigates two-nucleon transfer probabilities in Sn isotopes, analyzing improvements in theoretical approximations and the impact of particle number restoration, surface effects, and canonical basis formulations on transfer probability calculations.

Contribution

It introduces refined methods for estimating transfer probabilities, including particle number projection and surface effect analysis, enhancing understanding of pairing correlations in Sn isotopes.

Findings

Improved treatment enhances transfer probability near magic numbers.

Particle number projection compensates for approximation errors in mid-shell regions.

Surface effects influence transfer probabilities through single-particle occupancy fragmentation.

Abstract

Approximations made to estimate two-nucleon transfer probabilities in ground-state to ground-state transitions and physical interpretation of these probabilities are discussed. Probabilities are often calculated by approximating both ground states, of the initial nucleus A and of the final nucleus A\pm 2 by the same quasiparticle vacuum. We analyze two improvements of this approach. First, the effect of using two different ground states with average numbers of particles A and A\pm2 is quantified. Second, by using projection techniques, the role of particle number restoration is analyzed. Our analysis shows that the improved treatment plays a role close to magicity, leading to an enhancement of the pair-transfer probability. In mid-shell regions, part of the error made by approximating the initial and final ground states by a single vacuum is compensated by projecting onto good particle number. Surface effects are analyzed by using pairing interactions with a different volume-to-surface mixing. Finally, a simple expression of the pair-transfer probability is given in terms of occupation probabilities in the canonical basis. We show that, in the canonical basis formulation, surface effects which are visible in the transfer probability are related to the fragmentation of single-particle occupancies close to the Fermi energy. This provides a complementary interpretation with respect to the standard quasiparticle representation where surface effects are generated by the integrated radial profiles of the contributing wave functions.