Nucleon localization and fragment formation in nuclear fission

Abstract

Background: An electron localization measure was originally introduced to characterize chemical bond structures in molecules. Recently, a nucleon localization based on Hartree-Fock densities has been introduced to investigate $\ensuremath{\alpha}$-cluster structures in light nuclei. Compared to the local nucleonic densities, the nucleon localization function has been shown to be an excellent indicator of shell effects and cluster correlations.Purpose: Using the spatial nucleon localization measure, we investigate the emergence of fragments in fissioning heavy nuclei.Methods: To illustrate basic concepts of nucleon localization, we employ the self-consistent energy density functional method with a quantified energy density functional optimized for fission studies.Results: We study the particle densities and spatial nucleon localization distributions along the fission pathways of $^{264}\mathrm{Fm}$, $^{232}\mathrm{Th}$, and $^{240}\mathrm{Pu}$. We demonstrate that the fission fragments are formed fairly early in the evolution, well before scission. We illustrate the usefulness of the localization measure by showing how the hyperdeformed state of $^{232}\mathrm{Th}$ can be understood in terms of a quasimolecular state made of $^{132}\mathrm{Sn}$ and $^{100}\mathrm{Zr}$ fragments.Conclusions: Compared to nucleonic distributions, the nucleon localization function more effectively quantifies nucleonic clustering: its characteristic oscillating pattern, traced back to shell effects, is a clear fingerprint of cluster/fragment configurations. This is of particular interest for studies of fragment formation and fragment identification in fissioning nuclei.