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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 quantum entanglement is indispensable in the appearance of sawtooth distributions of average excitation energies of fragments and thus neutron multiplicities, but not in average neuron excess of fragments. Both sawtooth slopes from particle-number projections are found to be steep -- a feature which can be alleviated by random fluctuations. These findings may impact the understanding of quantum entanglement more broadly in mesoscopic systems., Comment: 11 pages, 3 figures

In the coming decades, the United States aims to undergo an energy transition away from fossil fuels and toward a fully decarbonized power grid. There are many pathways that the US could pursue toward this objective, each of which relies on different types of generating technologies to provide clean and reliable electricity. One potential contributor to these pathways is advanced nuclear fission, which encompasses various innovative nuclear reactor designs. 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 \$5.1-\$6.6/W to gain an initial market share (assuming 30 year asset life and 3.5-6.5% real WACC), while those that include thermal storage in their designs can cost up to \$5.5-\$7.0/W (not including cost of storage). Since the marginal value of advanced fission reactors declines as market penetration increases, break-even costs fall around 19% at 100 GW of cumulative capacity and around 40% at 300 GW. Additionally, policies that provide investment tax credits for nuclear energy create the most favorable environment for advanced nuclear fission. Stakeholders and investors should consider these findings when deciding which technologies to consider for decarbonizing the US power grid., Comment: 29 pages, 12 figures, plus appendices. Submitted to Applied Energy

For both reactions we use an approach similar to that of compound-nucleus reaction theory. For neutron-induced fission, we describe the compound system generated by absorption of the neutron and the nuclear system near the scission point as two statistically independent systems governed by random-matrix theory. The systems are connected either by a barrier penetration factor or by a set of transition states above the barrier. Each system is coupled to a different set of channels. An analogous model is used for heavy-ion fusion. Assuming that (seen from the entrance channel) the system on the other side of the barrier is in the regime of strongly overlapping resonances, we obtain for fixed spin and parity closed-form analytical expressions for the total probability for fission and for fusion. Parts of these expressions can be calculated reliably within existing compound-nucleus reaction theory. The remaining parts are the probabilities for passage through or over the barrier. These may be determined theoretically from the liquid-drop model or experimentally from total fission or fusion cross sections.

Quantum fluctuations are ubiquitous and play crucial roles across various scales and systems, such as the Big Bang, black hole dynamics, quantum phase transitions in microscopic many-body systems, and so on. Nuclear fission manifests as a complex nuclear shape stretching until it splits into fragments with substantial angular momenta, also exhibiting complex quantum fluctuations and specifically shape fluctuations. For over 40 years, researchers have puzzled how the fission fragment angular momenta are generated dynamically from (almost) zero spin, as well as the particular role played by quantum fluctuations. Here, for the first time, we report the quantum shape fluctuations that drive fragment angular momenta during nuclear fission, based on a global, microscopic, and dynamical simulation. The calculated probability distributions of fragment angular momenta are in good agreement with the experimental measurements, and the sawtooth-like mass dependence of average angular momenta is reproduced very well. It is noteworthy to find that the shape fluctuations -- multiple rotations, vibrations, and their couplings -- drive the generation and chaotic evolution of fragment angular momenta during fission fragment formation and induce strong correlations between angular momentum orientations of partner fragments at small, medium, and large opening angles ($\phi_{LH}\approx 30^\circ, 90^\circ, 160^\circ$). Our work not only deepens the fundamental understanding of the nuclear fission mechanism but also has implications for the $\gamma$-ray heating problem in nuclear reactors and the synthesis of superheavy elements.

Nowdays, modern microscopic approaches for fission are generally based on the framework of nuclear density functional theory (DFT), which has enabled a self-consistent treatment of both static and dynamic aspects of fission. The key issue is a DFT solver with high precision and efficiency especially for the large elongated configurations. Purpose: To develope a DFT solver with high precision and efficiency based on the point coupling covariant density functional theory (CDFT), which has achieved great success in describing properties of nuclei for the whole nuclear chart. Method: We have extended the point-coupling CDFT to be based on the two-center harmonic oscillator (TCHO) basis, which matches well with the large elongated configurations during the fission process. Multi-dimensional constraint and time-dependent generator coordinate method (TDGCM) have been used to analyze the fission potential energy surface and fission dynamics, respectively. To simulate the splitting process of the nascent fragments beyond scission, we also introduce a density constraint into the new CDFT framework. Results: Illustrative calculations have been done for the PESs and induced fission dynamics of two typical examples: $^{226}$Th and $^{240}$Pu. A more reasonable PES is obtained in the new framework compared to that based on the once-center harmonic oscillator (OCHO) with the same basis space. An optimization of about $0.2\sim0.3$ MeV has been achieved for the outer fission barriers and large elongated configurations. The dynamical simulations based on TCHO basis presents a trend to improve the description for fission yields. Conclusions: The new developed CDFT solver optimizes the elongated configurations, improves the calculation efficiency, and provides a basis for large-scale multi-dimensional constraint calculations and dynamical simulations.

Just before a nucleus fissions a neck is formed between the emerging fission fragments. It is widely accepted that this neck undergoes a rather violent rupture, despite no direct experimental evidence, and only a few contentious theoretical treatments of this fission stage were ever performed in the more than eight decades since nuclear fission was experimentally observed by Hahn and Strassmann and described by Meitner and Frisch in 1939. In the same year, Bohr and Wheeler conjectured that the fission of the nuclear liquid drop would likely be accompanied by the rapid formation of tiny droplets, later identified with either scission neutrons or other ternary fission fragments, a process which has not yet been discussed in a fully quantum many-body framework. The main difficulty in addressing both of these stages of nuclear fission is both are highly non-equilibrium processes. Here we will present the first fully microscopic characterization of the scission mechanism, along with the spectrum and the spatial distribution of scission neutrons, and some upper limit estimates for the emission of charged particles., Comment: 5 pages, 4 figures

Electron-positron pairs can be produced via the Schwinger mechanism in the presence of strong electric fields. In particular, the fields involved in $\alpha$ decay and nuclear fission are strong enough to produce them. The energy of the $e^+e^-$ pair is related to the relative distance and velocity of the daughter nuclei. Thus, the energy distribution of the produced pairs can give information about the dynamics of the fission and $\alpha$ decay processes. A neck model of nuclear fission is used to illustrate how the pairs can be used as a probe of the dynamics., Comment: 4 pages, 4 figures

In this paper, using a quasi-classical statistical approach based on the Langevin equation, we simulate the fission dynamics of selected even-even $\rm U$, $\rm Pu$, $\rm Cm$, $\rm Cf$ and $\rm Fm$ actinide nuclei. As a preparatory part of the work, before solving the Langevin equations, the determination of transport parameters such as inertia and friction tensors within the hydrodynamic model is performed. Potential energy surfaces are calculated within a macroscopic-microscopic approach in a three-dimensional space of deformation parameters defined within the Fourier decomposition of the surface radius function in cylindrical coordinates. Using the Lublin-Strasbourg drop model, Strutinsky shell correction and BCS-like pairing energy model with the projection onto good particle number, we calculate the nuclear total potential energy surfaces (PES). The restoration of the particle number in the superfluid approach is realized within the Generator Coordinate Method (GCM) with the so called Gaussian Overlap Approximation (GOA). The final study is concerned with the effect of the starting point of the stochastic Langevin trajectory on its time evolution and, more importantly, the conditions for judging whether such a trajectory for a given time moment describes an already passed fission nucleus or not. Collecting a large number of such stochastic trajectories allows us to assess the resulting fragment mass distributions, which appear to be in good agreement with their experimental counterparts for light and intermediate actinides. More serious discrepancies are observed for single isotopes of californium and fermium.

We propose a new, rapidly convergent, the so-called Fourier over Spheroid (FoS), shape parametrization to model fission of heavy nuclei. Four collective coordinates are used to characterize the shape of the fissioning system, being its elongation, left-right asymmetry, neck size, and non-axiality. The potential energy landscape is computed within the macroscopic-microscopic approach, on the top of which the multi-dimensional Langevin equation is solved to describe the dynamics. Charge equilibration at scission and de-excitation of the primary fragments after scission are further considered. The model gives access to a wide variety of observables, including fission fragments mass, charge, and kinetic energy yields, fragment mean N/Z and post-scission neutron multiplicities, and importantly, their correlations. The latter are crucial to unravel the complexity of the fission process. The parameters of the model were tuned to reproduce experimental observation from thermal neutron-induced fission of 235U, and next used to discuss the transition from the asymmetric to symmetric fission along the Fm isotopic chain., Comment: 15th pages, 18 figures

Type-Ia supernovae (SN Ia) are powerful stellar explosions that provide important distance indicators in cosmology. Recently, we proposed a new SN Ia mechanism that involves a nuclear fission chain reaction in an isolated white dwarf (WD) [PRL 126, 1311010]. The first solids that form as a WD starts to freeze are actinide rich and potentially support a fission chain reaction. In this letter we explore thermonuclear ignition from fission heating. We perform thermal diffusion simulations and find at high densities, above about 7x10^8 g/cm^3, that the fission heating can ignite carbon burning. This could produce a SN Ia or another kind of astrophysical transient., Comment: 6 pages, 3 figures, Accepted ApJ Letters

This dissertation deals with theoretical descriptions of nuclear fission and synthesis of superheavy elements via fusion. The associated shape evolutions are treated using a random-walk approach where both the potential energy and the nuclear level density influence the dynamics. The work in this thesis extends the random-walk model by, in addition to the previous description of fragment mass yields, also simulating how much kinetic energy the fission-fragments obtain and the number of neutrons they emit, as well as how these two quantities are correlated. The thesis also presents studies of how different ways of fissioning, called fission modes, are present in different nuclei and how the presence of these modes depends on the energy of the system. The model is furthermore applied to the description of the shape evolution in fusion for production of superheavy elements., Comment: PhD thesis, 130 pages, Defended 17 June 2021. Full academic version can be found at https://portal.research.lu.se/en/publications/nuclear-fission-and-fusion-in-a-random-walk-model

Atomic nuclei are quantum many-body systems of protons and neutrons held together by strong nuclear forces. Under the proper conditions, nuclei can break into two (sometimes three) fragments which will subsequently decay by emitting particles. This phenomenon is called nuclear fission. Since different fission events may produce different fragmentations, the end-products of all fissions that occurred in a small chemical sample of matter comprise hundreds of different isotopes, including $\alpha$ particles, together with a large number of emitted neutrons, photons, electrons and antineutrinos. The extraordinary complexity of this process, which happens at length scales of the order of a femtometer, mostly takes less than a femtosecond but is not completely over until all the lingering $\beta$ decays have completed - which can take years - is a fascinating window into the physics of atomic nuclei. While fission may be more naturally known in the context of its technological applications, it also plays a pivotal role in the synthesis of heavy elements in astrophysical environments. In both cases, experimental measurements are not sufficient to provide complete data. Simulations are needed, yet at levels of accuracy and precision that pose formidable challenges to nuclear theory. The goal of this article is to provide a comprehensive overview of the theoretical methods employed in the description of nuclear fission., Comment: 106 pages, 28 figures, 1 table, 513 references; submitted for publication in Progress in Nuclear and Particle Physics

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 theory to describe the fission process and of some recent successes achieved by this class of methods., Comment: 37 pages, 8 figures; chapter for the upcoming Handbook in Nuclear Physics edited by I. Tanihata, H. Toki and T. Kajino

The nuclear fission process is a dramatic example of the large-amplitude collective motion in which the nucleus undergoes a series of shape changes before splitting into distinct fragments. This motion can be represented by a pathway in the many-dimensional space of collective coordinates. The collective action along the fission pathway determines the spontaneous fission half-lives as well as mass and charge distributions of fission fragments. We study the performance and precision of various methods to determine the minimum action and minimum-energy fission trajectories in the collective space. We apply the nudged elastic band method (NEB), grid-based methods, and Euler Lagrange approach to the collective action minimization in two and three dimensional collective spaces. The performance of various approaches to the fission pathway problem is assessed by studying the collective motion along both analytic energy surfaces and realistic potential energy surfaces obtained with the Hartree-Fock-Bogoliubov theory. The uniqueness and stability of the solutions is studied. The NEB method is capable of efficient determination of the exit points on the outer turning surface that characterize the most probable fission pathway and constitute the key input for fission studies. This method can also be used to accurately compute the critical points (i.e., local minima and saddle points) on the potential energy surface of the fissioning nucleus that determine the static fission path. The NEB method is the tool of choice for finding the least-action and minimum energy fission trajectories. It will be particularly useful in large-scale fission calculation of superheavy nuclei and neutron-rich fissioning nuclei contributing to the astrophysical r-process recycling., Comment: 12 Pages, 9 Figures

In the exothermic process of fission decay, an atomic nucleus splits into two or more independent fragments. Several aspects of nuclear fission are not properly understood, in particular the formation of the neck between the nascent fragments, and the subsequent mechanism of scission into two or more independent fragments. Using an implementation of time-dependent density functional theory, based on a relativistic energy density functional and including pairing correlations, we analyze the final phase of the process of induced fission of $^{240}$Pu, and show that the time-scale of neck formation coincides with the assembly of two $\alpha$-like clusters (less than 1 zs = 10$^{-21}$ s). Because of its much larger binding energy, the dynamical synthesis of 4He in the neck predominates over other light clusters, e.g., $^3$H and $^6$He. At the instant of scission the neck ruptures exactly between the two $\alpha$-like clusters, which separate because of the Coulomb repulsion and are eventually absorbed by the two emerging fragments. The newly proposed mechanism of light charged clusters formation at scission provides a natural explanation of ternary fission., Comment: 5 pages, 4 figures, Final version for publication

Type-Ia supernovae (SN Ia) are powerful stellar explosions that provide important distance indicators in cosmology. Recently, we proposed a new SN Ia mechanism that involves a nuclear fission chain-reaction in an isolated white dwarf [PRL 126, 1311010]. Here we perform novel reaction network simulations of the actinide-rich first solids in a cooling white dwarf. The network includes neutron-capture and fission reactions on a range of U and Th isotopes with various possible values for U-235 enrichment. We find, for modest U-235 enrichments, neutron-capture on U-238 and Th-232 can breed additional fissile nuclei so that a significant fraction of all U and Th nuclei may fission during the chain-reaction. The resulting large energy release could ignite thermonuclear carbon burning and possibly trigger a SN Ia., Comment: 8 pages, 5 figures, revised introduction, accepted Phys. Rev. C

Since its beginnings, fission theory has asumed that low-energy induced fission takes place through transition-state channels at the barrier tops. Neverthess, up to now there is no microscopic theory applicable to those conditions. We suggest that modern reaction theory is suitable for this purpose, and propose a methodology based on a configuration-interaction framework using the Generator Coordinate Method (GCM). Simple reaction-theoretic models are constructed with the Gaussian Overlap Approximation (GOA) to parameterize both the dynamics within the channels and their incoherent couplings to states outside the barrier. The physical characteristics of the channels examined here are their effective bandwidths and the quality of the coupling to compound-nucleus states as measured by the transmission factor $T$. We also investigate the spacing of GCM states with respect to their degree of overlap. We find that a rather coarse mesh provides an acceptable accuracy for estimating the bandwidths and transmission factors. The common numerical stability problem in using the GCM is avoided due to the choice of meshes and the finite bandwidths of the channels. The bandwidths of the channels are largely controlled by the zero-point energy with respect to the collective coordinate in the GCM configurations., Comment: This version is the revised version submitted to Physical Review C on 2//22/2022

The first solids that form as a white dwarf (WD) starts to crystallize are expected to be greatly enriched in actinides. Previously [PRL 126, 1311010] we found that these solids might support a nuclear fission chain reaction that could ignite carbon burning and provide a new Type Ia supernova (SN Ia) mechanism involving an {\it isolated} WD. Here we explore this fission mechanism in more detail and calculate the final temperature and density after the chain reaction and discuss a number of open physics questions., Comment: 8 pages, 4 figures

The dynamics of low-energy induced fission is explored using a consistent microscopic framework that combines the time-dependent generator coordinate method (TDGCM) and time-dependent nuclear density functional theory (TDDFT). While the former presents a fully quantum mechanical approach that describes the entire fission process as an adiabatic evolution of collective degrees of freedom, the latter models the dissipative dynamics of the final stage of fission by propagating the nucleons independently toward scission and beyond. By combining the two methods, based on the same nuclear energy density functional and pairing interaction, we perform an illustrative calculation of the charge distribution of yields and total kinetic energy for induced fission of $^{240}$Pu. For the saddle-to-scission phase a set of initial points for the TDDFT evolution is selected along an iso-energy curve beyond the outer fission barrier on the deformation energy surface, and the TDGCM is used to calculate the probability that the collective wave function reaches these points at different times. Fission observables are computed with both methods and compared with available data. The relative merits of including quantum fluctuations (TDGCM) and the one-body dissipation mechanism (TDDFT) are discussed., Comment: 7 pages,6 figures

Within a density matrix approach for nuclear many--body system, it is derived non--Markovian Langevin equations of motion for nuclear collective parameters, where memory effects are defined by memory time. The developed stochastic approach is applied to study both the nuclear descent from fission barrier to a scission point and thermal diffusive overcoming of the barrier. The present paper is partly a review of our results obtained earlier and contains new results on the non--Markovian generalization of Kramers' theory of escape rate and on time features of the collective dynamics in the presence of periodic external modulation.

Dinuclear systems that occur in the post-saddle to scission stage in nuclear fission process are special transient formations. The diabatic evolution at this stage is studied using the methods of non-equilibrium thermodynamics. A novel explanation for the emergence of intrinsic rotational modes that occur in such a dinucleus is developed by identifying these modes together as an open subsystem that exchanges matter and energy with its environment. The environment consists of all remaining degrees of freedom of the dinucleus, and a weak coupling of the subsystem to this environment facilitates a diabatic energy exchange. Under appropriate non-equilibrium conditions, the available energy is coupled to the work needed for the emergence of self organizing rotational modes. This comes at the expense of increasing microscopic disorder in the form of intrinsic excitations in the prefragments. A simple formalism is presented such that the magnitudes of relevant energy flow through the subsystem are obtained in terms of entropy production rate, entropy expulsion rate and net rate of change of entropy in sub-units of $MeV zs^{-1} K^{-1}$., Comment: 8 pages, 3 figures

We present the first fully unrestricted microscopic calculations of the primary fission fragment intrinsic spins and of the fission fragments' relative orbital angular momentum for $^{236}$U$^*$, $^{240}$Pu$^*$, and $^{252}$Cf using the time-dependent density functional theory framework. Within this microscopic approach, free of restrictions and unchecked assumptions and which incorporates the relevant physical observables for describing fission, we evaluate the triple distribution of the fission fragment intrinsic spins and of their fission fragments' relative orbital angular momentum and show that their dynamics is dominated by their bending collective modes, in contradistinction to the predictions of the existing phenomenological models and some interpretations of experimental data., Comment: 6 pages, 4 figures, accepted version

We propose a configuration-interaction (CI) representation to calculate induced nuclear fission with explicit inclusion of nucleon-nucleon interactions in the Hamiltonian. The framework is designed for easy modeling of schematic interactions but still permits a straightforward extension to realistic ones. As a first application, the model is applied to branching ratios between fission and capture in the decay modes of excited fissile nuclei. The ratios are compared with the Bohr-Wheeler transition-state theory to explore its domain of validity. The Bohr-Wheeler theory assumes that the rates are insensitive to the final-state scission dynamics; the insensitivity is rather easily achieved in the CI parameterizations. The CI modeling is also capable of reproducing the branching ratios of the transition-state hypothesis which is one of the key ingredients in the present-day theory of induced fission., Comment: 5 pages, 5 figures (4 pages, 2 figures for the Supplemental Material)

In recent years, investigations of angular distributions of fragments in neutron-induced nuclear fission have been extended to intermediate energies, up to 200 MeV, as well as to a wide range of target isotopes. Using as an example the latest data obtained by our group for the reaction 237-Np(n,f), we discuss the specific features of fission fragment angular distribution and present a method for their simulation based on the code TALYS. It is shown that a simplified model reasonably describes energy dependence of the angular distribution in the whole range 1-200 MeV. The ways to improve the model are discussed along with the possibilities to use it for obtaining new information on fission and pre-equilibrium processes in neutron-nucleus interaction. We consider also the relevant problems of describing fission fragment angular distributions., Comment: 11 pages, 3 figures, Research was presented at the THEORY-5 Scientific Workshop on "Nuclear Fission Dynamics and the Emission of Prompt Neutrons and Gamma Rays", Castelvecchio Pascoli, Barga, Italy, September 24-26, 2019