Microscopic theory of angular momentum distributions across the full range of fission fragments

TL;DR

This work delivers the first microscopic angular-momentum distributions for the full spectrum of primary fission fragments by marrying joint angular-momentum and particle-number projection with time-dependent generator-coordinate dynamics. The framework uses constrained HFB to define scission configurations, restores good quantum numbers via projection, and employs TDGCM+GOA to weight configurations and propagate them to scission, yielding pre-neutron yields and AM distributions. Key findings include a pronounced sawtooth pattern in the average fragment AM, strong correlations between fragment deformation and AM, and substantial isobaric dependence of AM distributions, with only a weak AM-magnitude correlation between partner fragments. The results offer a route to feed microscopic AM inputs into decay models and highlight the need for refined scission descriptions and intrinsic-excitation effects to improve predictive power for fission observables.

Abstract

Modern nuclear theory provides qualitative insights into the fundamental mechanisms of nuclear fission and is increasingly capable of making reliable quantitative predictions. Most quantities of interest pertain to the primary fission fragments, whose subsequent decay is typically modeled using statistical reaction models. Consequently, a key objective of fission theory is to inform these models by predicting the initial conditions of the primary fragments. In this work, we employ a framework that combines joint angular momentum and particle number projection with time-dependent configuration mixing to calculate the angular momentum distributions of primary fragments. Focusing on the benchmark cases of neutron-induced fission of $^{235}$U and $^{239}$Pu, we predict - for the first time - microscopic angular momentum distributions for all fragments observed in experiments. Our results reveal a pronounced sawtooth pattern in the average angular momentum as a function of fragment mass, consistent with recent measurements. Additionally, we observe substantial variations in angular momentum distributions along isobaric chains, indicating that commonly used empirical formulas lack sufficient accuracy. We also quantify a strong correlation between the angular momentum and the deformation of the fragments at scission, and a weak correlation in the magnitude of the angular momentum between fragment partners. The generated data will enable estimation of the impact of microscopic distributions on fission spectra, paving the way toward fission modeling based on microscopic inputs.

Figures (11)

• Figure 1: Properties of $N_{\rm{conf}} = 384$ scission configurations in $^{236}$U (left column) and $N_{\rm{conf}}=404$ scission configurations in $^{240}$Pu (right column). Panels (a) and (b) show each configuration as a black point in the $(q_{20}, q_{30})$ PES. Note that there are typically several neck values $q_N$ per each $(q_{20}, q_{30})$ value. Panels (c) and (d) show the distributions in left FF average mass $\braket{A_l}$, Eq. \ref{['eq:average_mass']}, with a bin width of $2$. Panels (e) and (f) show the distributions in left FF average charge $\braket{Z_l}$, Eq. \ref{['eq:average_charge']}, with a bin width of $1$. The relevant ranges of $(q_{20}, q_{30})$, $\braket{A_l}$, and $\braket{Z_l}$ in both nuclei are properly covered by the chosen sets.
• Figure 2: Quantum number distributions in two scission configurations of $^{236}$U (left column) and $^{240}$Pu (right column) near the most likely fragmentation; see text for more details. Panels (a) and (b) show the angular momentum distributions in both FFs, obtained by marginalizing the full distribution over nucleon numbers [Eq. \ref{['eq:scission_AM']}]. Panels (c) and (d) show the neutron and proton number distributions in heavy FFs, obtained by marginalizing the full distribution over angular momentum [Eq. \ref{['eq:scission_NZ']}]. Panels (e) and (f) show the same for light FFs. Note the logarithmic scale on panels (c)-(f).
• Figure 3: Average angular momentum magnitude [Eq. \ref{['eq:average_angular_momentum']}] of left FFs (blue squares) and right FFs (red circles) in all scission configurations for $^{236}$U (panel (a)) and $^{240}$Pu (panel (b)), as a function of the average FF mass [Eq. \ref{['eq:average_mass']}]. A sawtooth pattern is apparent in both nuclei.
• Figure 4: Primary FF mass distribution (normalized to 200) in $^{236}$U, for three different cases. The distribution obtained from the full set of scission configurations with $q_N \in [1, 3]$, as described in Sec. \ref{['subsubsec:average_properties']}, is shown in green squares. The distribution obtained using only the $q_N = 3$ configurations is shown in grey triangles. The distribution obtained from the full set of scission configurations with $q_N \in [1, 3]$ by additionally applying a Gaussian folding with $\sigma=3$ is shown with blue circles.
• Figure 5: Primary FF mass distribution (normalized to $200$) in $^{236}$U (left) and $^{240}$Pu (right). The predictions of the model, calculated at $E_n = 1$ MeV, are compared to experimental data mueller1984geltenbort1986simon1990zeynalov2006romano2010wagemans1984schillebeeckx1992nishio1995tsuchiya2000.