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Register a new userFission in a microscopic framework: from basic science to support for applications
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Recent developments, both in theoretical modeling and computational power, have allowed us to make progress on a goal not fully achieved yet in nuclear theory: a microscopic theory of nuclear fission. Even if the complete microscopic description remains a computationally demanding task, the information that can be provided by current calculations can be extremely useful to guide and constrain more phenomenological approaches, which are simpler to implement. First, a microscopic model that describes the real-time dynamics of the fissioning system can justify or rule out some of the approximations. Second, the microscopic approach can be used to obtain trends, e.g., with increasing excitation energy of the fissioning system, or even to compute observables that cannot be otherwise calculated in phenomenological approaches or that can be hindered by the limitations of the method. We briefly present in this contribution the time-dependent superfluid local density approximation (TDSLDA) approach to nuclear fission, approach that has become a very successful theoretical model in many areas of many-body research. The TDSLDA incorporates the effects of the continuum, the dynamics of the pairing field, and the numerical solution is implemented with controlled approximations and negligible numerical corrections. The main part of the current contribution will be dedicated to discussing the method, and recent results concerning the fission dynamics. In addition, we present results on the excitation energy sharing between the fragments, which are in agreement with a qualitative conclusions extracted from a limited number of experimental measurements of properties of prompt neutrons.
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We show that the total kinetic energy (TKE) of nuclei after the spontaneous fission of $^{258}$Fm can be well reproduced using simple assumptions on the quantum collective phase-space explored by the nucleus after passing the fission barrier. Assuming energy conservation and phase-space exploration according to the stochastic mean-field approach, a set of initial densities is generated. Each density is then evolved in time using the nuclear time-dependent density-functional theory. This approach goes beyond mean-field by allowing spontaneous symmetry breaking as well as a wider dynamical phase-space exploration leading to larger fluctuations in collective space. The total kinetic energy and mass distributions are calculated. New information on the fission process: fluctuations in scission time, strong correlation between TKE and collective deformation of daughter nuclei as well as pre- and post-scission particle emission, are obtained.
The role of dynamical pairing in induced fission dynamics is investigated using the time-dependent generator coordinate method in the Gaussian overlap approximation, based on the microscopic framework of nuclear energy density functionals. A calculation of fragment charge yields for induced fission of $^{228}$Th is performed in a three-dimensional space of collective coordinates that, in addition to the axial quadrupole and octupole intrinsic deformations of the nuclear density, also includes an isoscalar pairing degree of freedom. It is shown that the inclusion of dynamical pairing has a pronounced effect on the collective inertia, the collective flux through the scission hyper-surface, and the resulting fission yields, reducing the asymmetric peaks and enhancing the contribution of symmetric fission, in better agreement with the empirical trend.
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.
This article reviews how nuclear fission is described within nuclear density functional theory. In spontaneous fission, half-lives are the main observables and quantum tunnelling the essential concept, while in induced fission the focus is on fragment properties and explicitly time-dependent approaches are needed. The cornerstone of the current microscopic theory of fission is the energy density functional formalism. Its basic tenets, including tools such as the HFB theory, effective two-body effective nuclear potentials, finite-temperature extensions and beyond mean-field corrections, are presented succinctly. The EDF approach is often combined with the hypothesis that the time-scale of the large amplitude collective motion driving the system to fission is slow compared to typical time-scales of nucleons inside the nucleus. In practice, this hypothesis of adiabaticity is implemented by introducing (a few) collective variables and mapping out the many-body Schrodinger equation into a collective Schrodinger-like equation for the nuclear wave-packet. Scission configurations indicate where the split occurs. This collective Schrodinger equation depends on an inertia tensor that includes the response of the system to small changes in the collective variables and also plays a special role in the determination of spontaneous fission half-lives. A trademark of the microscopic theory of fission is the tremendous amount of computing needed for practical applications. In particular, the successful implementation of the theories presented in this article requires a very precise numerical resolution of the HFB equations for large values of the collective variables. Finally, a selection of the most recent and representative results obtained for both spontaneous and induced fission is presented with the goal of emphasizing the coherence of the microscopic approaches employed.
We describe the fission dynamics of $^{240}$Pu within an implementation of the Density Functional Theory (DFT) extended to superfluid systems and real-time dynamics. We demonstrate the critical role played by the pairing correlations, which even though are not the driving force in this complex dynamics, are providing the essential lubricant, without which the nuclear shape evolution would come to a screeching halt. The evolution is found to be much slower than previously expected in this fully non-adiabatic treatment of nuclear dynamics, where there are no symmetry restrictions and all collective degrees of freedom (CDOF) are allowed to participate in the dynamics.
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