Microscopic Theory of Nuclear Fission: A Review
This paper reviews how nuclear fission is described within nuclear density functional theory. A distinction should be made between spontaneous fission, where halflives are the main observables and quantum tunnelling the essential concept, and induced fission, where the focus is on fragment properties and explicitly timedependent approaches are often invoked. Overall, the cornerstone of the density functional theory approach to fission is the energy density functional formalism. The basic tenets of this method, including some wellknown tools such as the Hartree–Fock–Bogoliubov (HFB) theory, effective twobody nuclear potentials such as the Skyrme and Gogny force, finitetemperature extensions and beyond meanfield corrections, are presented succinctly. The energy density functional approach is often combined with the hypothesis that the timescale of the large amplitude collective motion driving the system to fission is slow compared to typical timescales of nucleons inside the nucleus. In practice, this hypothesis of adiabaticity is implemented by introducing (a few) collective variables and mapping out the manybody Schrödinger equation into a collective Schrödingerlike equation for the nuclear wavepacket. The region of the collective space where the system transitions from one nucleus to two (or more) fragments defines what are called the scission configurations. The inertia tensor that enters themore »
 Authors:

^{[1]};
^{[2]}
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Nuclear and Chemical Science Division
 Autonomous Univ. of Madrid (Spain). Dept. de Fisica Teorica
 Publication Date:
 Report Number(s):
 LLNLJRNL680281
Journal ID: ISSN 00344885; TRN: US1701535
 Grant/Contract Number:
 AC5207NA27344
 Type:
 Accepted Manuscript
 Journal Name:
 Reports on Progress in Physics
 Additional Journal Information:
 Journal Volume: 79; Journal Issue: 11; Journal ID: ISSN 00344885
 Publisher:
 IOP Publishing
 Research Org:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
 OSTI Identifier:
 1341968
 Alternate Identifier(s):
 OSTI ID: 1328599
Schunck, N., and Robledo, L. M.. Microscopic Theory of Nuclear Fission: A Review. United States: N. p.,
Web. doi:10.1088/00344885/79/11/116301.
Schunck, N., & Robledo, L. M.. Microscopic Theory of Nuclear Fission: A Review. United States. doi:10.1088/00344885/79/11/116301.
Schunck, N., and Robledo, L. M.. 2016.
"Microscopic Theory of Nuclear Fission: A Review". United States.
doi:10.1088/00344885/79/11/116301. https://www.osti.gov/servlets/purl/1341968.
@article{osti_1341968,
title = {Microscopic Theory of Nuclear Fission: A Review},
author = {Schunck, N. and Robledo, L. M.},
abstractNote = {This paper reviews how nuclear fission is described within nuclear density functional theory. A distinction should be made between spontaneous fission, where halflives are the main observables and quantum tunnelling the essential concept, and induced fission, where the focus is on fragment properties and explicitly timedependent approaches are often invoked. Overall, the cornerstone of the density functional theory approach to fission is the energy density functional formalism. The basic tenets of this method, including some wellknown tools such as the Hartree–Fock–Bogoliubov (HFB) theory, effective twobody nuclear potentials such as the Skyrme and Gogny force, finitetemperature extensions and beyond meanfield corrections, are presented succinctly. The energy density functional approach is often combined with the hypothesis that the timescale of the large amplitude collective motion driving the system to fission is slow compared to typical timescales of nucleons inside the nucleus. In practice, this hypothesis of adiabaticity is implemented by introducing (a few) collective variables and mapping out the manybody Schrödinger equation into a collective Schrödingerlike equation for the nuclear wavepacket. The region of the collective space where the system transitions from one nucleus to two (or more) fragments defines what are called the scission configurations. The inertia tensor that enters the kinetic energy term of the collective Schrödingerlike equation is one of the most essential ingredients of the theory, since it includes the response of the system to small changes in the collective variables. For this reason, the two main approximations used to compute this inertia tensor, the adiabatic timedependent HFB and the generator coordinate method, are presented in detail, both in their general formulation and in their most common approximations. The collective inertia tensor enters also the Wentzel–Kramers–Brillouin (WKB) formula used to extract spontaneous fission halflives from multidimensional quantum tunnelling probabilities (For the sake of completeness, other approaches to tunnelling based on functional integrals are also briefly discussed, although there are very few applications.) It is also an important component of some of the timedependent methods that have been used in fission studies. Concerning the latter, both the semiclassical approaches to timedependent nuclear dynamics and more microscopic theories involving explicit quantummanybody methods are presented. One of the hallmarks 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. This aspect is often overlooked, and several sections are devoted to discussing the resolution of the HFB equations, especially in the context of very deformed nuclear shapes. In particular, the numerical precision and iterative methods employed to obtain the HFB solution are documented in detail. 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. In conclusion, although impressive progress has been achieved over the last two decades to understand fission microscopically, much work remains to be done. Several possible lines of research are outlined in the conclusion.},
doi = {10.1088/00344885/79/11/116301},
journal = {Reports on Progress in Physics},
number = 11,
volume = 79,
place = {United States},
year = {2016},
month = {10}
}