Microscopic description of nuclear fission dynamics

Umar, A. S.; Oberacker, V. E.; Maruhn, J. A.; Reinhard, P.‐G.

doi:10.1088/0954-3899/37/6/064037

Cited by 23 publications

(15 citation statements)

References 30 publications

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“…It may be that the presented calculations lack the degrees of freedom necessary to allow a fissioning path to be found in this window at all, and that a method beyond basic TDHF, including either collisions [63] or dynamical pairing effects [36], is needed to reach the fissioned configuration. Further investigation of the link between static and dynamic configurations applying density-constrained TDHF [35,64], would certainly be of interest. This method allows the dynamic configurations to be "frozen", removing internal and collective excitations, thus bridging between static and dynamic configurations.…”

Section: B Intersection Of the One And Two-fragment Fission Pathwaysmentioning

confidence: 99%

Fission dynamics within time-dependent Hartree-Fock: Deformation-induced fission

2015

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Background: Nuclear fission is a complex large-amplitude collective decay mode in heavy nuclei. Microscopic density functional studies of fission have previously concentrated on adiabatic approaches based on constrained static calculations ignoring dynamical excitations of the fissioning nucleus and the daughter products.Purpose: We explore the ability of dynamic mean-field methods to describe fast fission processes beyond the fission barrier, using the nuclide 240 Pu as an example.Methods: Time-dependent Hartree-Fock calculations based on the Skyrme interaction are used to calculate nonadiabatic fission paths, beginning from static constrained Hartree-Fock calculations. The properties of the dynamic states are interpreted in terms of the nature of their collective motion. Fission product properties are compared to data.Results: Parent nuclei constrained to begin dynamic evolution with a deformation less than the fission barrier exhibit giant-resonance-type behaviour. Those beginning just beyond the barrier explore large amplitude motion but do not fission, whereas those beginning beyond the two-fragment pathway crossing fission to final states which differ according to the exact initial deformation.Conclusions: Time-dependent Hartree-Fock is able to give a good qualitative and quantitative description of fast fission, provided one begins from a sufficiently deformed state.

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Section: B Intersection Of the One And Two-fragment Fission Pathwaysmentioning

confidence: 99%

Fission dynamics within time-dependent Hartree-Fock: Deformation-induced fission

2015

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“…Another approach follows the evolution of the fissioning system with quantum-mechanical tools [8]. However, the inclusion of dissipative processes and phenomena of statistical mechanics within quantum-mechanical algorithms is still not sufficiently developed [9,10]. Also these calculations require very large computer resources.…”

Section: A Core Of the Gef Modelmentioning

confidence: 99%

General Description of Fission Observables: GEF Model Code

Schmidt

Jurado

Amouroux

et al. 2016

Nuclear Data Sheets

433

421

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The GEF ("GEneral description of Fission observables") model code is documented. It describes the observables for spontaneous fission, neutron-induced fission and, more generally, for fission of a compound nucleus from any other entrance channel, with given excitation energy and angular momentum. The GEF model is applicable for a wide range of isotopes from Z = 80 to Z = 112 and beyond, up to excitation energies of about 100 MeV. The results of the GEF model are compared with fission barriers, fission probabilities, fission-fragment mass-and nuclide distributions, isomeric ratios, total kinetic energies, and prompt-neutron and prompt-gamma yields and energy spectra from neutron-induced and spontaneous fission. Derived properties of delayed neutrons and decay heat are also considered.The GEF model is based on a general approach to nuclear fission that explains a great part of the complex appearance of fission observables on the basis of fundamental laws of physics and general properties of microscopic systems and mathematical objects. The topographic theorem is used to estimate the fission-barrier heights from theoretical macroscopic saddle-point and ground-state masses and experimental ground-state masses. Motivated by the theoretically predicted early localisation of nucleonic wave functions in a necked-in shape, the properties of the relevant fragment shells are extracted. These are used to determine the depths and the widths of the fission valleys corresponding to the different fission channels and to describe the fission-fragment distributions and deformations at scission by a statistical approach. A modified composite nuclear-level-density formula is proposed. It respects some features in the superfluid regime that are in accordance with new experimental findings and with theoretical expectations. These are a constant-temperature behaviour that is consistent with a considerably increased heat capacity and an increased pairing condensation energy that is consistent with the collective enhancement of the level density. The exchange of excitation energy and nucleons between the nascent fragments on the way from saddle to scission is estimated according to statistical mechanics. As a result, excitation energy and unpaired nucleons are predominantly transferred to the heavy fragment in the superfluid regime. This description reproduces some rather peculiar observed features of the prompt-neutron multiplicities and of the even-odd effect in fission-fragment Z distributions. For completeness, some conventional descriptions are used for calculating pre-equilibrium emission, fission probabilities and statistical emission of neutrons and gamma radiation from the excited fragments. Preference is given to simple models that can also be applied to exotic nuclei compared to more sophisticated models that need precise empirical input of nuclear properties, e.g. spectroscopic information.The approach reveals a high degree of regularity and provides a considerable insight into the physics of the fission process. Fission obs...

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“…Although the TDHF equation is much simpler to solve numerically and was, historically, the first version of TDDFT applied to fission studies Negele et al (1978); Umar et al (2010); Simenel and Umar (2014), it has strong limitations: unless the calculation is initialized rather close to the scission point, or with an artificial boost in energy, the time-evolution of fissile nuclei such as 240 Pu does not lead to fission Goddard et al (2015Goddard et al ( , 2016. In order to achieve actual scission, pairing correlations play an essential role ; Bulgac et al (2016).…”

Section: Time-dependent Density Functional Theorymentioning

confidence: 99%

Microscopic theory of nuclear fission: a review

2016

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This article 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 nu...

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Microscopic description of nuclear fission dynamics

Cited by 23 publications

References 30 publications

Fission dynamics within time-dependent Hartree-Fock: Deformation-induced fission

Fission dynamics within time-dependent Hartree-Fock: Deformation-induced fission

General Description of Fission Observables: GEF Model Code

Microscopic theory of nuclear fission: a review

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