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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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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 suggest a small set of fission observables to be used as test cases for validation of theoretical calculations. The purpose is to provide common data to facilitate the comparison of different fission theories and models. The proposed observables are chosen from fission barriers, spontaneous fission lifetimes, fission yield characteristics, and fission isomer excitation energies.
There has been much recent interest in nuclear fission, due in part to a new appreciation of its relevance to astrophysics, stability of superheavy elements, and fundamental theory of neutrino interactions. At the same time, there have been important developments on a conceptual and computational level for the theory. The promising new theoretical avenues were the subject of a workshop held at the University of York in October 2019; this report summarises its findings and recommendations.
We formulate a microscopic theory of the decay of a compound nucleus through fission which generalizes earlier microscopic approaches of fission dynamics performed in the framework of the adiabatic hypothesis. It is based on the constrained Hartree-Fock-Bogoliubov procedure and the Generator Coordinate Method, and requires an effective nucleon-nucleon interaction as the only input quantity. The basic assumption is that the slow evolution of the nuclear shape must be treated explicitely, whereas the rapidly time-dependent intrinsic excitations can be treated by statistical approximations. More precisely, we introduce a reference density which represents the slow evolution of the nuclear shape by a reduced density matrix and the state of intrinsic excitations by a canonical distribution at each given shape of the nucleus. The shape of the nuclear density distribution is described by parameters (generator coordinates), not by superabundant degrees of freedom introduced in addition to the complete set of nucleonic degrees of freedom. We first derive a rigorous equation of motion for the reference density and, subsequently, simplify this equation on the basis of the Markov approximation. The temperature which appears in the canonical distribution is determined by the requirement that, at each time t, the reference density should correctly reproduce the mean excitation energy at given values of the shape parameters. The resulting equation for the local temperature must be solved together with the equations of motion obtained for the reduced density matrix.
The fission process is a fascinating phenomenon in which the atomic nucleus, a compact self-bound mesoscopic system, undergoes a spontaneous or induced quantum transition into two or more fragments. A predictive, accurate and precise description of nuclear fission, rooted in a fundamental quantum many-body theory, is one of the biggest challenges in science. Current approaches assume adiabatic motion of the system with internal degrees of freedom at thermal equilibrium. With parameters adjusted to data, such modelling works well in describing fission lifetimes, fragment mass distributions, or their total kinetic energies. However, are the assumptions valid? For the fission occurring at higher energies and/or shorter times, the process is bound to be non-adiabatic and/or non-thermal. The vision of this project is to go beyond these approximations, and to obtain a unified description of nuclear fission at varying excitation energies. The key elements of this project are the use of nuclear density functional theory with novel, nonlocal density functionals and innovative high-performance computing techniques. Altogether, the project aims at better understanding of nuclear fission, where slow, collective, and semi-classical effects are intertwined with fast, microscopic, quantum evolution.
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