Emission processes in a self-consistent field

TL;DR

This paper develops a microscopic, self-consistent field model for cluster emission processes in nuclei, incorporating a Woods-Saxon mean field, pairing, and a density-dependent residual interaction to accurately describe ground states and decay widths.

Contribution

It introduces a novel self-consistent approach combining Woods-Saxon mean field, pairing, and a density-dependent residual interaction for nuclear cluster emission modeling.

Findings

Accurately reproduces spherical nucleus ground states.

Enhances radial tails of single particle orbitals.

Provides adequate alpha-decay width predictions.

Abstract

We present a microscopic description of cluster emission processes within the Cluster--Hartree--Fock (CHF) self--consistent field (SCF) theory. The starting point is a Woods--Saxon (WS) mean field (MF) with spin--orbit and Coulomb terms. Pairing is treated through standard Bardeen--Cooper--Schrieffer (BCS) quasiparticles. The residual two--body interaction is given by a density--dependent Wigner force having a Gaussian shape with a center of mass (com) correction located in a region of low nuclear density slightly beyond the geometrical contact radius of a system comprised from a nucleus and a surface cluster. We show that such a description adequately reproduces the ground state (gs) shape of a spherical nucleus while the surface correction enhances the radial tail of single particle orbitals, thus allowing for an adequate description of the $\alpha$-decay width for unstable systems.