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Register a new userExtension of the Hauser-Feshbach Fission Fragment Decay Model to Multi-Chance Fission
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The Hauser-Feshbach fission fragment decay model, $mathtt{HF^3D}$, which calculates the statistical decay of fission fragments, has been expanded to include multi-chance fission, up to neutron incident energies of 20 MeV. The deterministic decay takes as input pre-scission quantities - fission probabilities and the average energy causing fission - and post-scission quantities - yields in mass, charge, total kinetic energy, spin, and parity. From these fission fragment initial conditions, the full decay is followed through both prompt and delayed particle emissions, allowing for the calculation of prompt neutron and $gamma$ properties, such as multiplicity and energy distributions, both independent and cumulative fission yields, and delayed neutron observables. In this work, we describe the implementation of multi-chance fission into the $mathtt{HF^3D}$ model, and show an example of prompt and delayed quantities beyond first-chance fission, using the example of neutron-induced fission on $^{235}$U. This expansion represents significant progress in consistently modeling the emission of prompt and delayed particles from fissile systems.
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Several sources of angular anisotropy for fission fragments and prompt neutrons have been studied in neutron-induced fission reactions. These include kinematic recoils of the target from the incident neutron beam and the fragments from the emission of the prompt neutrons, preferential directions of the emission of the fission fragments with respect to the beam axis due to the population of particular transition states at the fission barrier, and forward-peaked angular distributions of pre-equilibrium neutrons which are emitted before the formation of a compound nucleus. In addition, there are several potential sources of angular anisotropies that are more difficult to disentangle: the angular distributions of prompt neutrons from fully accelerated fragments or from scission neutrons, and the emission of neutrons from fission fragments that are not fully accelerated. In this work, we study the effects of the first group of anisotropy sources, particularly exploring the correlations between the fission fragment anisotropy and the resulting neutron anisotropy. While kinematic effects were already accounted for in our Hauser-Feshbach Monte Carlo code, $mathtt{CGMF}$, anisotropic angular distributions for the fission fragments and pre-equilibrium neutrons resulting from neutron-induced fission on $^{233,234,235,238}$U, $^{239,241}$Pu, and $^{237}$Np have been introduced for the first time. The effects of these sources of anisotropy are examined over a range of incident neutron energies, from thermal to 20 MeV, and compared to experimental data from the Chi-Nu liquid scintillator array. The anisotropy of the fission fragments is reflected in the anisotropy of the prompt neutrons, especially as the outgoing energy of the prompt neutrons increases, allowing for an extraction of the fission fragment anisotropy to be made from a measurement of the neutrons.
It is shown that the unexpected character of the angular correlation between the angle of the primary fission fragment intrinsic spins, recently evaluated by performing very complex time-dependent density functional simulations, which favors fission fragment intrinsic spins pointing in opposite directions, can be understood using simple general arguments.
The CGMF code implements the Hauser-Feshbach statistical nuclear reaction model to follow the de-excitation of fission fragments by successive emissions of prompt neutrons and $gamma$ rays. The Monte Carlo technique is used to facilitate the analysis of complex distributions and correlations among the prompt fission observables. Starting from initial configurations for the fission fragments in mass, charge, kinetic energy, excitation energy, spin, and parity, $Y(A,Z,KE,U,J,pi)$, CGMF samples neutron and $gamma$-ray probability distributions at each stage of the decay process, conserving energy, spin and parity. Nuclear structure and reaction input data from the RIPL library are used to describe fission fragment properties and decay probabilities. Characteristics of prompt fission neutrons, prompt fission gamma rays, and independent fission yields can be studied consistently. Correlations in energy, angle and multiplicity among the emitted neutrons and $gamma$ rays can be easily analyzed as a function of the emitting fragments.
Experimental studies of fission induced in relativistic nuclear collisions show a systematic enhancement of the excitation energy of the primary fragments by a factor of ~ 2, before their decay by fission and other secondary fragments. Although it is widely accepted that by doubling the energies of the single-particle states may yield a better agreement with fission data, it does not prove fully successful, since it is not able to explain yields for light and intermediate mass fragments. State-of-the-art calculations are successful to describe the overall shape of the mass distribution of fragments, but fail within a factor of 2-10 for a large number of individual yields. Here, we present a novel approach that provides an account of the additional excitation of primary fragments due to final state interaction with the target. Our method is applied to the 238U + 208Pb reaction at 1 GeV/nucleon (and is applicable to other energies), an archetype case of fission studies with relativistic heavy ions, where we find that the large probability of energy absorption through final state excitation of giant resonances in the fragments can substantially modify the isotopic distribution of final fragments in a better agreement with data. Finally, we demonstrate that large angular momentum transfers to the projectile and to the primary fragments via the same mechanism imply the need of more elaborate theoretical methods than the presently existing ones.
Probabilistic machine learning techniques can learn both complex relations between input features and output quantities of interest as well as take into account stochasticity or uncertainty within a data set. In this initial work, we explore the use of one such probabilistic network, the Mixture Density Network (MDN), to reproduce fission yields and their uncertainties. We study mass yields for the spontaneous fission of $^{252}$Cf, exploring the number of training samples needed for converged predictions, how different levels of uncertainty propagate from the training set to the MDN predictions, and how well physical constraints of the yields - such as normalization and symmetry - are upheld by the algorithm. Finally, we test the ability of the MDN to interpolate between and extrapolate beyond samples in the training set using energy-dependent mass yields for the neutron-induced fission on $^{235}$U. The MDN provides a reliable way to include and predict uncertainties and is a promising path forward for supplementing sparse sets of nuclear data.
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