Correlated fission fragment spin dynamics

TL;DR

This work investigates how nucleon exchange between nascent fission fragments shapes their correlated angular momenta during the saddle-to-scission evolution. By coupling Langevin-based shape dynamics with a six-dimensional Fokker-Planck transport treatment of excess fragment spins, it reveals that rotational modes fall out of equilibrium as the neck shrinks and temperature rises, leading to spin magnitudes smaller than equilibrium and weak spin-spin correlations. The study finds that the fragment-spin orientation concentrates around $ heta_F obreak\approx obreak 60^ ext{o}$ and that the qualitative results persist across reasonable variations in dissipation strength and excitation energy, with a nontrivial mass dependence of spin magnitudes. These insights provide a dynamical framework to interpret and design experiments probing nucleon-exchange effects in fission fragment spins. The methodology offers a path to distinguish dynamical evolution from purely statistical expectations in correlated fission observables.

Abstract

This study explores the role of nucleon exchange for the generation of the fission fragment angular momenta. For a number of typical fission cases, samples of 10,000 shape evolutions are generated by Langevin simulation and, subsequently, for each such evolution, the nucleon exchange transport theory previously developed for damped nuclear reactions is used to obtain the development of the fragment spin-spin distribution within the Fokker-Planck transport framework. The characteristic evolution of both parallel and perpendicular spin components is discussed. A common feature is that the rotational modes fall out of equilibrium before scission when the temperature rises rapidly while the concurrent shrinking of the neck suppresses further exchange. A number of fission observables are extracted from the event ensembles: the distribution of the magnitude of the fragment spin and its orientation relative to the fission axis, as well as the correlation between the two spins and the distribution of their opening angle. The dependence of these observables on the mass asymmetry is also examined.

Figures (14)

• Figure 1: Five snapshots of the shape of $^{236}$U($E^*$=46 MeV) calculated with $k_s=1$, as it evolves from saddle to scission for an event leading to a symmetic division.
• Figure 2: The fragment mass distributions from fission of $^{236}$U, $^{202}$Po, and $^{182}$Hg at $E^*=46\,{\rm MeV}$ as generated by Langevin simulations of $10^4$ events (solid symbols), together with the associated Gaussians (solid curves).
• Figure 3: The distributions of the saddle-to-scission times $t_{\rm ss}$ for the six cases having $E^*$=46 MeV, as obtained with the Langevin simulations of the shape evolution (symbols), and the associated gamma distributions (solid curves).
• Figure 4: The smoothed time evolution of the elongation $R$, the neck radius $c$, and the temperature $T$, for five Langevin shape evolutions of short (green), medium (blue), or long (red) duration, for fission of $^{236}$U at $E^*=46\,{\rm MeV}$ using $k_s=1$.
• Figure 5: The time dependence of the local twisting relaxation time $t_{\rm twst}(t)=1/\nu_{\rm twst}(t)$ for the evolutions shown in Fig. \ref{['f:RcT']}.