Average pairing correlation properties and effective pairing residual interactions

TL;DR

This paper introduces a method to determine effective pairing residual interactions in nuclei, using average pair condensation energy, enabling more accurate modeling of nuclear properties across different nuclei.

Contribution

It extends the determination of pairing interaction strengths to a broader set of nuclei using a non-ambiguous, average interaction intensity approach based on pairing condensation energy.

Findings

Reproduces experimental moments of inertia with ~2 ħ²MeV⁻¹ accuracy.

Provides a reliable method to estimate pairing strengths in deformed nuclei.

Enables predictions of deformation and spectral properties beyond ground states.

Abstract

This paper describes a method to determine the intensities of effective pairing residual interactions, extending what has been done for the seniority force model [Phys. Rev. C 110, 024311 (2024)]. It has been tested in Hartree-Fock plus BCS calculations using residual pairing zero-range interactions. The average pair condensation energy is the key quantity connecting the determination of constant pairing matrix elements to the estimation of delta interaction intensities. From individually fitted delta pairing strengths of $28$ well and rigidly deformed nuclei whose proton number $Z$ ranges from $50$ to $82$ evaluated at the ground-state, we have determined average interaction intensities. They reproduce equally well the data on MoI as what is obtained within the seniority force ansatz with a r.m.s. deviation of about $2 \: \hbar^2 \mbox{MeV}^{-1}$. This approach provides a non-ambiguous way to determine reasonably well the strengths of pairing interactions at the ground-state of well deformed nuclei. It allows to perform, with some reasonable level of confidence, calculations for other nuclei in the corresponding nuclear region as well as beyond their ground states in particular to assess deformation properties as, e.g., to evaluate fission barriers or spectral properties of quasi-particle states.