Generalized gauge-space rotations in atomic nuclei: A critical insight

TL;DR

This paper reexamines pairing correlations in nuclei, revealing that alpha correlations behave as a collective mode with a universal pattern, and challenges traditional views on gauge-space moments of inertia.

Contribution

It introduces a new perspective on alpha correlations as a collective mode and critically analyzes the gauge-space moments of inertia, highlighting the impact of macroscopic contributions.

Findings

Alpha correlation energies show universal parabolic trends.

Standard gauge-space moments of inertia are dominated by macroscopic energies.

Removing macroscopic effects reveals negative moments of inertia, indicating Pauli-blocking effects.

Abstract

We critically reexamine the concepts of pairing rotations and moments of inertia in gauge space extracted from experimental binding energies. Our analysis focuses on pairing correlations among like nucleons, neutron-proton pairing, and $\alpha$-type correlations. By investigating $\alpha$ separation energies and binding-energy differences along chains of fixed isospin projection and subtracting macroscopic contributions, we reveal a remarkably smooth and nearly universal behavior in the residual $\alpha$ correlation energy. These results exhibit the parabolic trends characteristic of collective rotations in gauge space. We demonstrate that the standard definition of the gauge-space moment of inertia for like-nucleon pairing is dominated by macroscopic contributions from Coulomb and symmetry energies. Once these are removed, the remaining moment of inertia becomes negative. This suggests that the observed behavior reflects the loss of correlation energy due to Pauli-blocking effect. Our results indicate that $\alpha$ correlations constitute a genuine collective mode associated with quartetting dynamics arising from the coherent coupling of two superfluid components.