Relative motion correction to fission barriers

TL;DR

This paper introduces a correction scheme for fission barrier calculations in mean-field models, accounting for spurious relative motion energy, which impacts predicted fission half-lives and stability of hyperdeformed states.

Contribution

A new energy correction method for Hartree-Fock calculations that reduces spurious relative motion effects in fission barrier estimations.

Findings

Correction reduces fission barrier in $^{198}$Hg from ~8 MeV to 4 MeV.

Corrected barriers suggest shorter fission half-lives for $^{238}$U.

Lowered barriers for multipartition and less stable hyperdeformed minima.

Abstract

We discuss the effect of kinetic energy of the relative motion becoming spurious for separate fragments on the selfconsistent mean-field fission barriers. The treatment of the relative motion in the cluster model is contrasted with the necessity of a simpler and approximate approach in the mean-field theory. A scheme of the energy correction to the Hartree-Fock is proposed. The results obtained with the effective Skyrme interaction SLy6 show that the correction, previously estimated as $\sim$ 8 MeV in $A=70-100$ nuclei, amounts to 4 MeV in the medium heavy nucleus $^{198}$Hg and to null in $^{238}$U. However, the corrected barrier implies a shorter fission half-life of the latter nucleus. The same effect is expected to lower barriers for multipartition (i.e. ternary fission, etc) and make hyperdeformed minima less stable.