Average pairing correlation properties and effective pairing residual interactions

TL;DR

This work presents a method to determine the intensities of residual pairing interactions in nuclei by linking them to the averaged pair condensation energy derived from Strutinsky-smoothed single-particle spectra. Building on HFBCS-S and the seniority-force framework, it uses Strutinsky-averaged level densities and a uniform-gap equation to extract average pairing strengths, and then transfers this information to a residual (volume delta) pairing interaction via an iterative self-consistent procedure. Results for well-deformed nuclei show that both nucleus-by-nucleus and region-averaged delta strengths can reproduce moments of inertia as accurately as the traditional seniority approach, with averaged strengths yielding noticeable improvements in some cases (notably the delta-interaction fits). The study demonstrates convergence, explores sensitivity to initial conditions, and suggests that such a transfer enables reliable extrapolation to other nuclei and deformation regimes, including fission barrier and quasi-particle spectral properties.

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.

Figures (1)

• Figure 1: Ratio of the first $4^+$ over $2^+$ energies of the sample nuclei considered in this study.