Fluctuation of fission observables investigated with a Monte Carlo method

TL;DR

This work addresses the challenge of characterizing fluctuations in fission observables by developing a Monte Carlo sampling framework that draws configurations from a Bogoliubov vacuum projected onto good particle numbers. By representing nucleons in coordinate and intrinsic-spin space and using diagonal kernels for one- and two-body observables, the method reconstructs full pdfs and higher moments, enabling analysis of complex two-body and torque-related quantities near scission. The main findings show that most fluctuations in several observables, including the total kinetic energy and fragment torques, originate from inter-fragment nuclear interactions near scission and are strongly influenced by a few nucleons in the neck region; multipole fluctuations of the entire system are relatively small due to the large particle number. These insights advance the microscopic understanding of fission dynamics and provide a practical tool for visualizing and quantifying fluctuations within EDF-based approaches, with potential extensions to non-diagonal observables and more sophisticated Monte Carlo techniques.

Abstract

Nuclear fission dynamics described within nuclear energy density functional frameworks (EDF) have seen substantial advances in the last decade. Part of this success stems from projection techniques, which allow the computation f probability distribution functions (pdf) for selected observables such as particle number and angular momentum of the fragments. Predicting the pdf of other observables, such as the total kinetic energy of the fragments, remains undone. This work proposes a method to determine the complete pdf of a new category of observables from a Bogoliubov vacuum projected onto good particle number. It relies on sampling nucleonic configurations in coordinate and intrinsic-spin representation. We assess the feasibility and convergence properties of the method and apply it to states representative of the scission of an actinide. Fluctuations in fragment shapes, inter-fragment Coulomb and nuclear interaction as well as the corresponding torques are analyzed. We find that a significant fraction of the fluctuation of several measured fission observables is already present within the mean-field picture.

Figures (9)

• Figure 1: Local nucleon one-body density for the $^{20}$Ne (top) and the $^{252}$Cf (bottom) Bogoliubov vacua considered in Sec. \ref{['sec:numerics']}.
• Figure 2: (a) Gelman-Rubin ratio minus one obtained for $\beta_{20}$ in the $^{20}$Ne ground state. (b) Square roots of the estimators of the variance of $\beta_{20}$ among the Markov chains ($V$) and of the intra-chain variance ($W$).
• Figure 3: Burn-in periods as a function of the Markov chain parameters values $\sigma_{space}$ and $P_{flip}$. The blue continuous line stands for the quadrupole moment and the yellow dashed line for the Coulomb interaction. The spatial width is varied while the spin flip probability is set to $P_{flip}=0.1$. The spin flip probability is varied while $\sigma_{space}=2$ fm.
• Figure 4: (a) Autocorrelation between successively recorded configurations from one Markov chain. We focus on the quadrupole moment and the Coulomb interaction in a $^{20}$Ne ground state. (b) Idem for a pre-scission configuration of $^{252}$Cf.
• Figure 5: (a) Energy landscape of $^{252}$Cf obtained with constraints on the quadrupole and octupole moments. It corresponds to the HFB energy with a vibrational zero-point-energy correction. The energy is relative to the ground state. Calculations were limited to configurations with a number of particle in the neck $Q_{neck}>5$. (b) Local one-body density of a Bogoliubov vacuum representative of the SII fission mode. (c) Local one-body density of a Bogoliubov vacuum representative of the SL fission mode.