Finite-range pairing in nuclear density functional theory

TL;DR

This paper introduces finite-range pairing functionals in nuclear density functional theory by folding pair densities with Gaussians, improving numerical stability and reducing divergences in large model spaces.

Contribution

The study proposes a finite-range pairing functional using Gaussian folding to address deficiencies of zero-range functionals in nuclear DFT.

Findings

Folding radius of about 1 fm optimizes quality and stability.

Finite-range functionals reduce divergence issues in large model spaces.

Improves numerical behavior for pairing correlations in nuclear calculations.

Abstract

Pairing correlations are ubiquitous in low-energy states of atomic nuclei. To incorporate them within nuclear density functional theory, often used for global computations of nuclear properties, pairing functionals that generate nucleonic pair densities and pairing fields are introduced. Many pairing functionals currently used can be traced back to zero-range nucleon-nucleon interactions. Unfortunately, such functionals are plagued by deficiencies that become apparent in large model spaces that contain unbound single-particle (continuum) states. In particular, the underlying computational schemes diverge as the single-particle space increases, and the results depend on how marginally occupied states are incorporated. These problems become more pronounced for pairing functionals that contain gradient-density dependence, such as in the Fayans functional. To remedy this, finite-range pairing functionals are introduced. In this study, this is done by folding the pair density with Gaussians. We show that a folding radius of about 1\,fm offers the best compromise between quality and stability, and substantially reduces the pathological behavior in different numerical applications.