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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Microscopic Theory of Nuclear Fission

Nuclear fission represents the ultimate test for microscopic theories of nuclear structure and reactions. Fission is a large-amplitude, time-dependent phenomenon taking place in a self-bound, strongly interacting many-body system. It should, at least in principle, emerge from the complex interactions of nucleons within the nucleus. The goal of microscopic theories is to build a consistent and predictive theory of nuclear fission by using as only ingredients protons and neutrons, nuclear forces, and quantum many-body methods. Thanks to a constant increase in computing power, such a goal has never seemed more within reach. This chapter gives an overview both of the set of techniques used in microscopic theories to describe the fission process and of some recent successes achieved by this class of methods.

Nuclear physics and radiation physics↗
DOE OSTI2013

The Future of Energy from Nuclear Fission

Nuclear energy is an important part of our current global energy system, and contributes to supplying the significant demand for electricity for many nations around the world. There are 433 commercial nuclear power reactors operating in 30 countries with an installed capacity of 367 GWe as of October 2011 (IAEA PRIS, 2011). Nuclear electricity generation totaled 2630 TWh in 2010 representing 14% the world’s electricity generation. The top five countries of total installed nuclear capacity are the US, France, Japan, Russia and South Korea at 102, 63, 45, 24, and 21 GWe, respectively (WNA, 2012a). The nuclear capacity of these five countries represents more than half, 68%, of the total global nuclear capacity. The role of nuclear power in the global energy system today has been motivated by several factors including the growing demand for electric power, the regional availability of fossil resources and energy security concerns, and the relative competitiveness of nuclear power as a source of base-load electricity. There is additional motivation for the use of nuclear power because it does not produce greenhouse gas (GHG) emissions or local air pollutants during its operation and contributes to low levels of emissions throughout the lifecycle of the nuclear energy system (Beerten, J. et. al., 2009). Energy from nuclear fission primarily in the form of electric power and potentially as a source of industrial heat could play a greater role for meeting the long-term growing demand for energy worldwide while addressing the concern for climate change from rising GHG emissions. However, the nature of nuclear fission as a tremendously compact and dense form of energy production with associated high concentrations of radioactive materials has particular and unique challenges as well as benefits. These challenges include not only the safety and cost of nuclear reactors, but proliferation concerns, safeguard and storage of nuclear materials associated with nuclear fuel cycles. In March of 2011, an unprecedented earthquake of 9 magnitude and ensuing tsunami off the east coast of Japan caused a severe nuclear accident in Fukushima, Japan (Prime Minister of Japan and His Cabinet, 2011). The severity of the nuclear accident in Japan has brought about a reinvestigation of nuclear energy policy and deployment activities for many nations around the world, most notably in Japan and Germany (BBC, 2011; Reuter, 2011). The response to the accident has been mixed and its full impact may not be realized for many years to come. The nuclear accident in Fukushima, Japan has not directly affected the significant on-going nuclear deployment activities in many countries. China, Russia, India, and South Korea, as well as others, are continuing with their deployment plans. As of October 2011, China had the most reactors under construction at 27, while Russia, India, and South Korea had 11, 6, and 5 reactors under construction, respectively (IAEA PRIS, 2011). Ten other nations have one or two reactors currently under construction. Many more reactors are planned for future deployment in China, Russia, and India, as well as in the US. Based on the World Nuclear Association’s data, the realization of China’s deployment plan implies that China will surpass the US in total nuclear capacity some time in the future.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Quantum entanglement in nuclear fission

Nuclear fission presents a unique example of quantum entanglement in strongly interacting many-body systems. A heavy nucleus can split into hundreds of combinations of two complementary fragments in the fission process. The entanglement of fragment wave functions is persistent even after separation and impacts the partition of particles and energies between fragments. Based on microscopic dynamical calculations of the fission of 240 Pu, this work finds that dynamical quantum entanglement is indispensable in the appearance of sawtooth distributions of average excitation energies of fragments and thus neutron multiplicities, but not in average neutron excess of fragments. Both sawtooth slopes from particle-number projections are found to be steep – a feature which can be alleviated by random fluctuations. The persistent entanglement is mainly due to non-adiabatic dynamics since the final splitting is so fast that the non-localization of wave functions is kept during the separation. These findings may impact the understanding of quantum entanglement more broadly in mesoscopic systems

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Nuclear Fission: from more phenomenology and adjusted parameters to more fundamental theory and increased predictive power

Two major recent developments in theory and computational resources created the favorable conditions for achieving a microscopic description of fission dynamics in classically allowed regions of the collective potential energy surface, almost eighty years after its discovery in 1939 by Hahn and Strassmann [1]. The first major development was in theory, the extension of the Time-Dependent Density Functional Theory (TDDFT) [2–5] to superfluid fermion systems [6]. The second development was in computing, the emergence of powerful enough supercomputers capable of solving the complex systems of equations describing the time evolution in three dimensions without any restrictions of hundreds of strongly interacting nucleons. Thus the conditions have been created to renounce phenomenological models and incomplete microscopic treatments with uncontrollable approximations and/or assumptions in the description of the complex dynamics of fission. Even though the available nuclear energy density functionals (NEDFs) are phenomenological still, their accuracy is improving steadily and the prospects of being able to perform calculations of the nuclear fission dynamics and to predict many properties of the fission fragments, otherwise not possible to extract from experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

Density Functional Theory Approach to Nuclear Fission

The Skyrme nuclear energy density functional theory (DFT) is used to model neutron-induced fission in actinides. This paper focuses on the numerical implementation of the theory. In particular, it reports recent advances in DFT code development on leadership class computers, and presents a detailed analysis of the numerical accuracy of DFT solvers for near-scission calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Boson Fermion Nucleus And The Phenomenon Of Nuclear Fission (Monograph #14)

Nuclear fission can be induced by a neutron with insufficient energy to physically impact and disrupt the nucleus. A boson fermion nucleus (BFN) capturing an incident neutron at the same quantum state as a neutron in the BFN structure, or an assimilated incident neutron altering the quantum state of a neutron or proton in the structure to match another, is sufficient by the Pauli exclusion principle to disrupt the organized nuclear structure. This creates a scission point and force imbalance where the inverse radius squared (1/r 2 ) electrostatic repulsive force among protons dominates over the inverse radius exponential (1/e µr ) strong, short-range attractive Yukawa force among nucleons. The result is nuclear fission.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Cement As a Waste Form for Nuclear Fission Products: The Case of 90 Sr and Its Daughters [Cement As a Container for Nuclear Fission Products: The Case of 90 Sr and Its Daughters]

One of the main challenges faced by the nuclear industry is the long-term confinement of nuclear waste. Because it is inexpensive and easy to manufacture, cement is the material of choice to store large volumes of radioactive materials, in particular the low-level medium-lived fission products. It is therefore of utmost importance to assess the chemical and structural stability of cement containing radioactive species. Here, we use ab initio calculations based on density functional theory (DFT) to study the effects of 90 Sr insertion and decay in C–S–H (calcium-silicate-hydrate) in order to test the ability of cement to trap and hold this radioactive fission product and to investigate the consequences of its β-decay on the cement paste structure. We show that 90 Sr is stable when it substitutes the Ca 2+ ions in C–S–H, and so is its daughter nucleus 90 Y after β-decay. Interestingly, 90 Zr, daughter of 90 Y and final product in the decay sequence, is found to be unstable compared to the bulk phase of the element at zero K but stable when compared to the solvated ion in water. Furthermore, cement appears as a suitable waste form for 90 Sr storage.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS2019

The Kilopower Space Nuclear Fission Power Reactor

Nuclear fission power offers an attractive alternative to solar electric or radioisotope power systems for certain applications on the Moon, Mars, and deep space science missions. The advantages of independence from solar irradiance, high energy density, and abundance of fuel allow fission power systems to enable novel, high power mission architectures. While NASA has had numerous fission power programs throughout its history, few have gone far beyond the design phase. The recent test campaign called the Kilopower Reactor Using Stirling Technology project (KRUSTY) focused on a low power, kilowatt-scale design for simplicity and reduced cost, with the driving motivation to perform a full nuclear hardware prototype test. Following the successful completion of the KRUSTY nuclear hardware test in March of 2018, NASA has begun the formulation process for a Technology Demonstration Mission (TDM) using the Kilopower reactor technology. In support of NASA's lunar surface initiatives, the Kilopower TDM will target a 1-3 kW fission electric power system that can survive the lunar night and operate for one year. The system will be heavily influenced by the KRUSTY reactor design, using a solid Uranium metal core with high temperature heat pipes and Stirling engine power conversion. During this formulation phase, continued engineering efforts are ongoing to improve heat transfer efficiency in the system, examine fission radiation damage effects, and begin to address the thermal and structural requirements of a Kilopower flight system.

Chaiken, Max↗
DOE OSTI2016

Sequential character of low-energy ternary and quaternary nuclear fission

An analysis of low-energy true ternary (quaternary) nuclear fission leads to the conclusion that these fission modes have a sequential two-step (three-step) character such that the emission of a third particle (third and fourth particles) and the separation of fission fragments occur at distinctly different instants, in contrast to the simultaneous emergence of all fission products in the case of onestep ternary (quaternary) fission. This conclusion relies on the following arguments. First, the emission of a third particle (third and fourth particles) from a fissile nucleus is due to a nonevaporative mechanism associated with a nonadiabatic character of the collective deformation motion of this nucleus at the stages preceding its scission. Second, the axial symmetry of the deformed fissile compound nucleus and the direction of its symmetry axis both remain unchanged at all stages of ternary (quaternary) fission. This circumstancemakes it possible to explain themechanism of the appearance of observed anisotropies and T — odd asymmeries in the angular distributions of products of ternary (quaternary) nuclear fission. Third, the T —odd asymmetry discovered experimentally in ternary nuclear fission induced by cold polarized neutrons obeys the T —invariance condition only in the case of a sequential two-step (three-step) character of true ternary (quaternary) nuclear fission. At the same time, this asymmetry is not a T —invariant quantity in the case of the simultaneous emission of products of true ternary (quaternary) nuclear fission from the fissile compound nucleus.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2011

Heavy-ion versus {sup 3}He/{sup 4}He fusion-fission reactions: Angular momentum dependence of dissipation in nuclear fission

The stochastic Langevin model is employed to study dissipation properties in fission in the {sup 16}O + {sup 181}Ta {yields}{sup 197}Tl system by analyzing prescission neutron yields measured in this reaction. It has been found that the {sup 197}Tl nuclei undergo fission that is not in accordance with the standard Bohr-Wheeler statistical theory. A detailed comparison with previously published work in which fission excitation functions measured in {sup 3,4}He + {sup 197}Au {yields}{sup 200,201}Tl are shown to be in excellent agreement with the fission width formula predicted by the traditional models of nuclear fission suggests that nuclear dissipation strength may have an angular momentum dependence in addition to the known deformation and temperature dependence. Implications for the basic understanding of the observed abnormal rise in prescission particles at high energy and the need for further experimental confirmations are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Muon-induced fission as a probe of the underlying dynamics in nuclear fission

Muon-induced fission could be utilized as a probe to study the underlying dynamics of nuclear fission. Here, the probability of muon attachment to the light asymmetric fission fragment is sensitive to fission dynamics, such as the timescale and friction of the fission event, charge asymmetry, and possibly the shape of the fission fragments. We focus on muonic atoms that are formed with actinide nuclei. A relativistic approach is employed, solving the Dirac equation for the muonic wave function in the presence of a time-dependent electromagnetic field generated by the fissioning nucleus. Computations are carried out on a three-dimensional Cartesian lattice with no symmetry assumptions. The results show a strong dependence of the attachment probability on the fission charge asymmetry and a more modest dependence on friction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Evaluating advanced nuclear fission technologies for future decarbonized power grids

Advanced nuclear fission, which encompasses various innovative nuclear reactor designs, could contribute to the decarbonization of the United States electricity sector. However, little is known about how cost-competitive these reactors would be compared to other technologies, or about which aspects of their designs offer the most value to a decarbonized power grid. We employ an electricity system optimization model and a case study of a decarbonized U.S. Eastern Interconnection circa 2050 to generate initial indicators of future economic value for advanced reactors and the sensitivity of future value to various design parameters, the availability of competing technologies, and the underlying policy environment. These results can inform long-term cost targets and guide near-term innovation priorities, investments, and reactor design decisions. We find that advanced reactors should cost $\$5.7$–$\$7.3$/W to gain an initial market share (assuming 30 year asset life and 3.5 %–6.5 % real weighted average cost of capital), while those that include thermal storage in their designs can cost up to $\$6.0$/W–$\$7.7$/W (not including cost of storage). Since the marginal value of advanced fission reactors declines as market penetration increases, break-even costs fall ~32 % at 100 GW of cumulative capacity and ~51 % at 300 GW. Additionally, policies that provide investment tax credits for nuclear energy create the most favorable environment for advanced nuclear fission. In conclusion, these findings can inform near-term resource allocation decisions by stakeholders, innovators and investors working in the energy technology sector.

Capacity expansion↗
DOE OSTI2020

Future of nuclear fission theory

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.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

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 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.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗