Microscopic description of pair transfer between two superfluid Fermi systems: combining phase-space averaging and combinatorial techniques

TL;DR

This paper introduces the Phase-Space combinatorial (PSC) method to efficiently calculate pair transfer probabilities in superfluid Fermi systems, accounting for gauge-angle effects through phase-space averaging and combinatorics.

Contribution

The novel PSC approach combines phase-space averaging with combinatorial techniques to estimate pair transfer probabilities using only mean-field calculations.

Findings

PSC method accurately predicts one-pair transfer probabilities.

Significant differences observed in two-pair transfer predictions.

Best suited for identical superfluid nuclei collisions.

Abstract

In a mean-field description of superfluidity, particle number and gauge angle are treated as quasi-classical conjugated variables. This level of description was recently used to describe nuclear reactions around the Coulomb barrier. Important effects of the relative gauge angle between two identical superfluid nuclei (symmetric collisions) on transfer probabilities and fusion barrier have been uncovered. A theory making contact with experiments should at least average over different initial relative gauge-angles. In the present work, we propose a new approach to obtain the multiple pair transfer probabilities between superfluid systems. This method, called Phase-Space combinatorial (PSC) technique, relies both on phase-space averaging and combinatorial arguments to infer the full pair transfer probability distribution at the cost of multiple mean-field calculations only. After benchmarking this approach in a schematic model, we apply it to the collision $^{20}$O+$^{20}$O at various energies below the Coulomb barrier. The predictions for one pair transfer are similar to results obtained with an approximated projection method whereas significant differences are found for two pairs transfer. Finally, we investigated the applicability of the PSC method to the contact between non-identical superfluid systems. [...] The applicability of the PSC method to asymmetric nuclear collisions is investigated for the $^{14}$O+$^{20}$O collision and it turns out that unrealistically small single- and multiple-pair transfer probabilities are obtained. [...] We conclude that the best ground for probing gauge-angle effects in nuclear reaction and/or for applying the proposed PSC approach on pair transfer is the collisions of identical open-shell spherical nuclei.