# Consistency of two different approaches to determine the strength of a pairing residual interaction in the rare-earth region

## TL;DR

This study compares two independent methods for determining pairing residual interaction strengths in rare-earth nuclei, finding consistent results and supporting the use of moments of inertia and odd-even staggering as measures of nuclear pairing correlations.

## Contribution

It introduces a dual-approach analysis using mass staggering and moments of inertia to accurately determine pairing interaction strengths in rare-earth nuclei.

## Key findings

- Both methods yield consistent pairing strength values (~0.1% for neutrons, ~0.2% for protons).
- Traditional fits based on BCS gaps differ significantly from those based on moments of inertia.
- Results support moments of inertia and odd-even staggering as effective measures of nuclear pairing correlations.

## Abstract

Two fits of the pairing residual interaction in the rare-earth region are independently performed. One is made on the odd-even staggering of masses by comparing measured and explicitly calculated three-point binding-energy differences centered on odd-even nuclei. Another deals with the moments of inertia of the first 2+ states of well deformed even-even nuclei upon comparing experimental data with the results of Inglis-Belyaev moments (supplemented by a crude estimate of the so-called Thouless-Valatin corrections). The sample includes 24 even-even and 31 odd-mass nuclei selected according to two criteria: they should have good rotor properties and should not correspond to low pairing-correlation regimes in their ground states. Calculations are performed in the self-consistent Hartree-Fock plus BCS framework (implementing a self-consistent blocking in the case of odd-mass nuclei). The Skyrme SIII parametrization is used in the particle-hole channel and the fitted quantities are the strengths of |Tz|=1 proton and neutron seniority residual interactions. As a result, the two fits yield sets of strengths in excellent agreement: about 0.1% for the neutron parameters and 0.2% for protons. In contrast when one performs such a fit on odd-even staggering from quantities deduced from BCS gaps or minimal quasiparticle energies in even-even nuclei, as is traditional, one obtains results significantly different from those obtained in the same nuclei by a fit of moments of inertia. As a conclusion, beyond providing a phenomenological tool for microscopic calculations in this region, we have illustrated the proposition made in the seminal paper of Bohr, Mottelson and Pines that moments of inertia and odd-even staggering in selected nuclei were excellent measuring sticks of nuclear pairing correlations.