# From bare to renormalized order parameter in gauge space: structure and reactions

## TL;DR

This paper explains how symmetry restoration in gauge space underpins accurate calculations of two-nucleon transfer reactions, highlighting the role of pairing interactions and the dominance of successive transfer in nuclear structure.

## Contribution

It introduces a new understanding of the link between symmetry restoration and reaction calculations, emphasizing the emergence of a physical sum rule in nuclear pairing phenomena.

## Key findings

- Restoration of gauge symmetry explains transfer reaction accuracy.
- Successive transfer dominates Cooper pair tunneling.
- Emergent sum rule connects structure and reactions.

## Abstract

The physical reason why one can calculate with similar accuracy, as compared to the experimental data, the absolute cross section associated with two-nucleon transfer processes between members of pairing rotational bands, making use of simple BCS (constant matrix elements) or of many-body (Nambu-Gorkov (NG), nuclear field theory (NFT)) spectroscopic amplitudes, is not immediately obvious. Restoration of spontaneous symmetry breaking and associated emergent generalised rigidity in gauge space provides the answer, and points to a new emergence: a physical sum rule resulting from the intertwining of structure and reaction processes and closely connected with the central role induced pairing interaction plays in structure together with the fact that successive transfer dominates Cooper pair tunnelling.