Deblurring fission fragment mass distributions

TL;DR

This work introduces a Richardson–Lucy based deblurring method to recover pre-neutron fission-fragment mass distributions from post-neutron measurements and to remove mass-resolution effects from reported pre-neutron data. Applied to spontaneous fission of $^{252}$Cf, the method yields narrower, higher $ ilde{Y}_{pre}(A)$ distributions that, when used as CGMF inputs, produce CGMF outputs that closely reproduce measured mass distributions after reblurring, while also illuminating differences in neutron and gamma observables. The approach avoids assuming specific distribution shapes and provides a principled inverse-problem framework that can be extended to more realistic transfer matrices and other fragment properties, potentially improving predictive power for fission models and guiding future experiments.

Abstract

Measurements of fission fragment mass distributions provide valuable insights into the properties of fissioning systems and the dynamics of the fission process. Pre-neutron emission distributions, essential for fission fragment evaporation codes like \cgmf{}, are extracted from distributions that are always measured after neutron emission, as the time scale of the emission of prompt fission neutrons is too short for direct measurement before the emission. However, obtaining accurate pre-neutron emission distributions requires methods that eliminate the effects of mass resolution and detector efficiency. We propose a deblurring technique based on the Richardson-Lucy (RL) algorithm, commonly used in optics for image restoration, to correct for these experimental effects. The RL algorithm uses the measured mass distributions and a transfer matrix to perform iterative deconvolution. The advantage of this method over others is that it does not assume any predefined shape such as a sum of Gaussians, as in \cgmf{}, for the distributions. In this paper, we apply the algorithm to the fission fragment mass distributions measured in the spontaneous fission of $^{252}$Cf to extract pre-neutron emission fission fragment mass distributions. The results from deblurring are then used as inputs to \cgmf{}, and we compare the \cgmf{} results obtained using deblurring inputs with the default \cgmf{} results.

Figures (16)

• Figure 1: Deblurred $Y_{pre} (A)$, dashed line obtained by deblurring pre-neutron emission FF mass distributions (red stars) extracted from Romano, et alRomano for $^{252}$Cf(sf). The solid line represents the convolved distribution obtained using Eq. \ref{['RLr']}, or Eq. \ref{['YApost']}, by convolving the deblurred distribution with the TM.
• Figure 2: Same as Fig. \ref{['ratio']} for pre-neutron emission FF mass distribution from Ref. HAMBSCH1997347.
• Figure 3: The ratio of experimental $Y_{pre}(A)$ (shown as red stars in Fig. \ref{['ratio']}) Romano to the convolved (blurred) distribution, in log scale as a function of fragment mass. Results are shown for a number of iterations, varying from 10 to 500.
• Figure 4: Fission fragment mass distributions for $^{252}$Cf(sf). Dashed line shows a FF mass distribution obtained from deblurring the experimental post-neutron emission FF mass distribution from Ref. Romano (shown by stars), using Eq. \ref{['eq:RL']}. Solid line shows distributions results from convolving the deblurred distribution (dashed line) with TM. As observed in the figure, the distribution reproduces the experimental data. The details are provided in the text.
• Figure 5: Same as Fig. \ref{['fig:YApost']} but for post neutron emission FF mass experimental data reported in Ref. MEIERBACHTOL201559.