Efficient method for estimation of fission fragment yields of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>r</mml:mi></mml:math>-process nuclei

Abstract

Background: More than half of all the elements heavier than iron are made by the rapid neutron capture process (or $r$ process). For very-neutron-rich astrophysical conditions, such at those found in the tidal ejecta of neutron stars, nuclear fission determines the $r$-process endpoint, and the fission-fragment yields shape the final abundances of $110\ensuremath{\le}A\ensuremath{\le}170$ nuclei. The knowledge of fission-fragment yields of hundreds of nuclei inhabiting very-neutron-rich regions of the nuclear landscape is thus crucial for the modeling of heavy-element nucleosynthesis.Purpose: In this study, we propose a model for the fast calculation of fission-fragment yields based on the concept of shell-stabilized prefragments defined with help of the nucleonic localization functions.Methods: To generate realistic potential-energy surfaces and nucleonic localizations, we apply Skyrme density-functional theory. The distribution of the neck nucleons among the two prefragments is obtained by means of a statistical model.Results: We benchmark the method by studying the fission yields of $^{178}\mathrm{Pt},^{240}\mathrm{Pu},^{254}\mathrm{Cf}$, and $^{254,256,258}\mathrm{Fm}$ and show that it satisfactorily explains the experimental data. We then make predictions for $^{254}\mathrm{Pu}$ and $^{290}\mathrm{Fm}$ as two representative cases of fissioning nuclei that are expected to significantly contribute during the $r$-process nucleosynthesis occurring in neutron-star mergers.Conclusions: The proposed framework provides an efficient alternative to microscopic approaches based on the evolution of the system in a space of collective coordinates all the way to scission. It can be used to carry out global calculations of fission-fragment distributions across the $r$-process region.