Microscopic Theory of Nuclear Fission: A Review

Schunck, N.; Robledo, L. M.

doi:10.1088/0034-4885/79/11/116301

Title: Microscopic Theory of Nuclear Fission: A Review

Journal Article · Tue Oct 11 00:00:00 EDT 2016 · Reports on Progress in Physics

DOI:https://doi.org/10.1088/0034-4885/79/11/116301· OSTI ID:1341968

Schunck, N. ^[1]; Robledo, L. M. ^[2]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Nuclear and Chemical Science Division
Autonomous Univ. of Madrid (Spain). Dept. de Fisica Teorica

This paper reviews how nuclear fission is described within nuclear density functional theory. A distinction should be made between spontaneous fission, where half-lives are the main observables and quantum tunnelling the essential concept, and induced fission, where the focus is on fragment properties and explicitly time-dependent 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 well-known tools such as the Hartree–Fock–Bogoliubov (HFB) theory, effective two-body nuclear potentials such as the Skyrme and Gogny force, finite-temperature extensions and beyond mean-field corrections, are presented succinctly. The energy density functional 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 Schrödinger equation into a collective Schrödinger-like equation for the nuclear wave-packet. 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 Schrödinger-like 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 time-dependent 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 half-lives from multi-dimensional 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 time-dependent methods that have been used in fission studies. Concerning the latter, both the semi-classical approaches to time-dependent nuclear dynamics and more microscopic theories involving explicit quantum-many-body 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.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1341968

Alternate ID(s):: OSTI ID: 1328599

Report Number(s):: LLNL-JRNL-680281; TRN: US1701535

Journal Information:: Reports on Progress in Physics, Vol. 79, Issue 11; ISSN 0034-4885

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 164 works

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Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (II) HFBTHO v2.00d: a new version of the program Stoitsov, M. V.; Schunck, N.; Kortelainen, M. arXiv https://doi.org/10.48550/arxiv.1210.1825	text	January 2012
Spontaneous fission lifetimes from the minimization of self-consistent collective action Sadhukhan, Jhilam; Mazurek, K.; Baran, A. arXiv https://doi.org/10.48550/arxiv.1310.2003	text	January 2013
Microscopic description of fission in Uranium isotopes with the Gogny energy density functional Rodriguez-Guzman, R.; Robledo, L. M. arXiv https://doi.org/10.48550/arxiv.1312.7229	text	January 2013
Solution of the Skyrme HF+BCS equation on a 3D mesh. II. A new version of the Ev8 code Ryssens, W.; Hellemans, V.; Bender, M. arXiv https://doi.org/10.48550/arxiv.1405.1897	text	January 2014
The Skyrme Interaction in finite nuclei and nuclear matter Stone, J. R.; Reinhard, P. -G. arXiv https://doi.org/10.48550/arxiv.nucl-th/0607002	text	January 2006
Gauge-Invariant Formulation of Adiabatic Self-Consistent Collective Coordinate Method Hinohara, Nobuo; Nakatsukasa, Takashi; Matsuo, Masayuki arXiv https://doi.org/10.48550/arxiv.nucl-th/0701004	text	January 2007
Superdeformed rotational bands in the Mercury region; A Cranked Skyrme-Hartree-Fock-Bogoliubov study Gall, B.; Bonche, P.; Dobaczewski, J. arXiv https://doi.org/10.48550/arxiv.nucl-th/9312011	text	January 1993
Relativistic Hartree-Bogoliubov theory with finite range pairing forces in coordinate space: Neutron halo in light nuclei Poeschl, W.; Vretenar, D.; Lalazissis, G. A. arXiv https://doi.org/10.48550/arxiv.nucl-th/9709027	text	January 1997
Potential energy surfaces of superheavy nuclei Bender, M.; Rutz, K.; Reinhard, P. -G. arXiv https://doi.org/10.48550/arxiv.nucl-th/9902058	text	January 1999

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Using excitation-energy dependent fission yields to identify key fissioning nuclei in r -process nucleosynthesis Vassh, N.; Vogt, R.; Surman, R. Journal of Physics G: Nuclear and Particle Physics, Vol. 46, Issue 6 https://doi.org/10.1088/1361-6471/ab0bea	journal	April 2019
Yields distribution of induced fission with improved scission point model Ruan, XinHui; Hu, JiangTao; Rong, Tao Journal of Physics G: Nuclear and Particle Physics, Vol. 46, Issue 12 https://doi.org/10.1088/1361-6471/ab4820	journal	November 2019
Diabatic paths through the scission point in nuclear fission Bertsch, G. F.; Younes, W.; Robledo, L. M. Physical Review C, Vol. 100, Issue 2 https://doi.org/10.1103/physrevc.100.024607	journal	August 2019
Benchmark of the GEF code for fission-fragment yields over an enlarged range in fissioning nucleus mass, excitation energy, and angular momentum Schmitt, C.; Schmidt, K. -H.; Jurado, B. Physical Review C, Vol. 98, Issue 4 https://doi.org/10.1103/physrevc.98.044605	journal	October 2018
Nuclear Fission: from more phenomenology and adjusted parameters to more fundamental theory and increased predictive power Bulgac, Aurel; Jin, Shi; Magierski, Piotr EPJ Web of Conferences, Vol. 163 https://doi.org/10.1051/epjconf/201716300007	journal	January 2017
Superfluidity in nuclear systems and neutron stars Sedrakian, Armen; Clark, John W. The European Physical Journal A, Vol. 55, Issue 9 https://doi.org/10.1140/epja/i2019-12863-6	journal	September 2019
Review on the progress in nuclear fission—experimental methods and theoretical descriptions Schmidt, Karl-Heinz; Jurado, Beatriz Reports on Progress in Physics, Vol. 81, Issue 10 https://doi.org/10.1088/1361-6633/aacfa7	journal	September 2018
Scission dynamics with $K$ partitions Bertsch, G. F.; Younes, W.; Robledo, L. M. Physical Review C, Vol. 97, Issue 6 https://doi.org/10.1103/physrevc.97.064619	journal	June 2018
Daniel Gogny’s vision for a microscopic theory of fission Younes, W. The European Physical Journal A, Vol. 53, Issue 5 https://doi.org/10.1140/epja/i2017-12314-6	journal	May 2017
Nuclear fission: a review of experimental advances and phenomenology Andreyev, A. N.; Nishio, K.; Schmidt, K-H Reports on Progress in Physics, Vol. 81, Issue 1 https://doi.org/10.1088/1361-6633/aa82eb	journal	November 2017
First Direct Measurement of Isotopic Fission-Fragment Yields of ${}^{239}U$ Ramos, D.; Caamaño, M.; Lemasson, A. Physical Review Letters, Vol. 123, Issue 9 https://doi.org/10.1103/physrevlett.123.092503	journal	August 2019
Fission properties of superheavy nuclei for r-process calculations Giuliani, Samuel A.; Martinez-Pinedo, Gabriel; Robledo, Luis M. arXiv https://doi.org/10.48550/arxiv.1704.00554	text	January 2017

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