Induced Fission of (240)Pu within a Real-Time Microscopic Framework

Fermionic quantum turbulence: Pushing the limits of high-performance computing

Ultracold atoms provide a platform for analog quantum computer capable of simulating the quantum turbulence that underlies puzzling phenomena like pulsar glitches in rapidly spinning neutron stars. Unlike other platforms like liquid helium, ultracold atoms have a viable theoretical framework for dynamics, but simulations push the edge of current classical computers. We present the largest simulations of fermionic quantum turbulence to date and explain the computing technology needed, especially improvements in the Eigenvalue soLvers for Petaflop Applications library that enable us to diagonalize matrices of record size (millions by millions). We quantify how dissipation and thermalization proceed in fermionic quantum turbulence by using the internal structure of vortices as a new probe of the local effective temperature. All simulation data and source codes are made available to facilitate rapid scientific progress in the field of ultracold Fermi gases.

Scission Deformation of the ^{120}Cd/^{132}Sn Neutronless Fragmentation in ^{252}Cf(sf)

We report on a study of the radiative decay of fission fragments populated via neutronless fission of ^{252}Cf(sf). Applying the double-energy method a perfect mass identification is achieved for these rare events. In the specific case of the ^{120}Cd/^{132}Sn cold fragmentation, we find that ^{132}Sn is produced in its ground state. We can therefore directly measure the excitation energy of the complementary fragment, ^{120}Cd. The reproduction of the γ-ray spectrum, measured in coincidence with the neutronless fission events, is sensitive to the angular momentum distribution of the studied primary fragment. The latter estimated using a time-dependent collective Hamiltonian model, allows us to constrain for the first time the deformation (β_{2}≃0.4) of the studied fission fragment at scission. The present work demonstrates the high potential of the understudied neutronless fission channel for extracting detailed information on both fission fragments and process.

Fragment Intrinsic Spins and Fragments' Relative Orbital Angular Momentum in Nuclear Fission

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.

Fission Fragment Intrinsic Spins and Their Correlations

The intrinsic spins and their correlations are the least understood characteristics of fission fragments from both theoretical and experimental points of view. In many nuclear reactions, the emerging fragments are typically excited and acquire an intrinsic excitation energy and an intrinsic spin depending on the type of the reactions and interaction mechanism. Both the intrinsic excitation energies and the fragments' intrinsic spins and parities are controlled by the interaction mechanism and conservations laws, which lead to their correlations and determines the character of their deexcitation mechanism. We outline here a framework for the theoretical extraction of the intrinsic spin distributions of the fragments and their correlations within the fully microscopic real-time density-functional theory formalism and illustrate it on the example of induced fission of ^{236}U and ^{240}Pu, using two nuclear energy density functionals. These fission fragment intrinsic spin distributions display new qualitative features previously not discussed in literature. Within this fully microscopic framework, we extract for the first time the intrinsic spin distributions of fission fragments of ^{236}U and ^{240}Pu as well as the correlations of their intrinsic spins, which have been debated in literature for more than six decades with no definite conclusions so far.

New states of matter with fine-tuned interactions: quantum droplets and dipolar supersolids

Quantum fluctuations can stabilize Bose-Einstein condensates (BEC) against the mean-field collapse. Stabilization of the condensate has been observed in quantum degenerate Bose-Bose mixtures and dipolar BECs. The fine-tuning of the interatomic interactions can lead to the emergence of two new states of matter: liquid-like self-bound quantum droplets and supersolid crystals formed from these droplets. We review the properties of these exotic states of matter and summarize the experimental progress made using dipolar quantum gases and Bose-Bose mixtures. We conclude with an outline of important open questions that could be addressed in the future.

Multiplicity of scision neutrons from density functional scission dynamics

The time evolution of the nuclear density of the fissioning system 240Pu during the scission process is obtained from the time-dependent superfluid local-density approximation (TDSLDA) to the density functional theory. A nuclear energy density functional based on the Skyrme force Skm* is used. The duration of the scission process Δt as well as the neck radius (rmin) of the ‘just-before scission’ configuration and the minimum separation (dmin) of the inner surfaces of the fragments in the ’immediately-after scission’ configuration were extracted in order to calculate the multiplicity of the scission neutrons (Vsc) using a phenomenological dynamical scission model (DSM). We find that Vsc=1.347, i.e. half of the prompt fission neutrons measured in the reaction 239Pu(nth; f) are released at scission. After scission, the fragments are left excited and with some extra deformation energy (mainly the heavy one). In this way we can account for the evaporation of the other half and for the emission of γ rays.

Fission in a microscopic framework: From basic science to support for applications

Recent developments, both in theoretical modeling and computational power, have allowed us to make progress on a goal not fully achieved yet in nuclear theory: a microscopic theory of nuclear fission. Even if the complete microscopic description remains a computationally demanding task, the information that can be provided by current calculations can be extremely useful to guide and constrain more phenomenological approaches, which are simpler to implement. First, a microscopic model that describes the real-time dynamics of the fissioning system can justify or rule out some of the approximations. Second, the microscopic approach can be used to obtain trends, e.g., with increasing excitation energy of the fissioning system, or even to compute observables that cannot be otherwise calculated in phenomenological approaches or that can be hindered by the limitations of the method. We briefly present in this contribution the time-dependent superfluid local density approximation (TDSLDA) approach to nuclear fission, approach that has become a very successful theoretical model in many areas of many-body research. The TDSLDA incorporates the effects of the continuum, the dynamics of the pairing field, and the numerical solution is implemented with controlled approximations and negligible numerical errors. The main part of the current contribution will be dedicated to discussing the method, and recent results concerning the fission dynamics. In addition, we present results on the excitation energy sharing between the fragments, which are in agreement with a qualitative conclusions extracted from a limited number of experimental measurements of properties of prompt neutrons.

Fission of ^{240}Pu with Symmetry-Restored Density Functional Theory

Nuclear fission plays an important role in fundamental and applied science, from astrophysics to nuclear engineering, yet it remains a major challenge to nuclear theory. Theoretical methods used so far to compute fission observables rely on symmetry-breaking schemes where basic information on the number of particles, angular momentum, and parity of the fissioning nucleus is lost. In this Letter, we analyze the impact of restoring broken symmetries in the benchmark case of ^{240}Pu.

Fission of Relativistic Nuclei with Fragment Excitation and Reorientation

Experimental studies of fission induced in relativistic nuclear collisions show a systematic enhancement of the excitation energy of the primary fragments by a factor of ∼2, before their decay by fission and other secondary fragments. Although it is widely accepted that by doubling the energies of the single-particle states may yield a better agreement with fission data, it does not prove fully successful, since it is not able to explain yields for light and intermediate mass fragments. State-of-the-art calculations are successful to describe the overall shape of the mass distribution of fragments, but fail within a factor of 2-10 for a large number of individual yields. Here, we present a novel approach that provides an account of the additional excitation of primary fragments due to final state interaction with the target. Our method is applied to the ^{238}U+^{208}Pb reaction at 1  GeV/nucleon (and is applicable to other energies), an archetype case of fission studies with relativistic heavy ions, where we find that the large probability of energy absorption through final state excitation of giant resonances in the fragments can substantially modify the isotopic distribution of final fragments in a better agreement with data. Finally, we demonstrate that large angular momentum transfers to the projectile and to the primary fragments via the same mechanism imply the need of more elaborate theoretical methods than the presently existing ones.

Microscopic Calculation of Fission Fragment Distributions in Actinides

The simulation of independent and cumulative yields requires precise knowledge of the initial conditions of the fission fragments immediately after scission. In this paper, we use a quantum-mechanical description of fission dynamics to extract the initial mass distribution of fission fragments for the neutron-induced fission of the two major actinides239Pu and235U, both for thermal fission and as a function of the incident neutron energy.

Bayesian Evaluation of Incomplete Fission Yields

Fission product yields are key infrastructure data for nuclear applications in many aspects. It is a challenge both experimentally and theoretically to obtain accurate and complete energy-dependent fission yields. We apply the Bayesian neural network (BNN) approach to learn existing fission yields and predict unknowns with uncertainty quantification. We demonstrated that the BNN is particularly useful for evaluations of fission yields when incomplete experimental data are available. The BNN evaluation results are quite satisfactory on distribution positions and energy dependencies of fission yields.

First Direct Measurement of Isotopic Fission-Fragment Yields of ^{239}U

A direct and complete measurement of isotopic fission-fragment yields of ^{239}U has been performed for the first time. The ^{239}U fissioning system was produced with an average excitation energy of 8.3 MeV in one-neutron transfer reactions between a ^{238}U beam and a ^{9}Be target at Coulomb barrier energies. The fission fragments were detected and isotopically identified using the VAMOS++ spectrometer at the GANIL facility. The measurement allows us to directly evaluate the fission models at excitation energies of fast neutrons, which are relevant for next-generation nuclear reactors. The present data, in agreement with model calculations, do not support the recently reported anomaly in the fission-fragment yields of ^{239}U, and they confirm the persistence of spherical shell effects in the Sn region at excitation energies exceeding the fission barrier by a few mega-electron volts.

Collisions of Self-Bound Quantum Droplets

We report on the study of binary collisions between quantum droplets formed by an attractive mixture of ultracold atoms. We distinguish two main outcomes of the collision, i.e., merging and separation, depending on the velocity of the colliding pair. The critical velocity v_{c} that discriminates between the two cases displays a different dependence on the atom number N for small and large droplets. By comparing our experimental results with numerical simulations, we show that the nonmonotonic behavior of v_{c}(N) is due to the crossover from a compressible to an incompressible regime, where the collisional dynamics is governed by different energy scales, i.e., the droplet binding energy and the surface tension. These results also provide the first evidence of the liquidlike nature of quantum droplets in the large N limit, where their behavior closely resembles that of classical liquid droplets.

Impact of pear-shaped fission fragments on mass-asymmetric fission in actinides

Nuclear fission of heavy (actinide) nuclei results predominantly in asymmetric mass splits¹. Without quantum shell effects, which can give extra binding energy to their mass-asymmetric shapes, these nuclei would fission symmetrically. The strongest shell effects appear in spherical nuclei, such as the spherical 'doubly magic' (that is, both its atomic and neutron numbers are 'magic' numbers) nucleus ¹³²Sn, which contains 50 protons and 82 neutrons. However, a systematic study of fission² has shown that heavy fission fragments have atomic numbers distributed around Z = 52 to Z = 56, indicating that the strong shell effects in ¹³²Sn are not the only factor affecting actinide fission. Reconciling the strong spherical shell effects at Z = 50 with the different Z values of fission fragments observed in nature has been a longstanding puzzle³. Here we show that the final mass asymmetry of the fragments is also determined by the extra stability provided by octupole (pear-shaped) deformations, which have been recently confirmed experimentally around ¹⁴⁴Ba (Z = 56)^4,5, one of very few nuclei with shell-stabilized octupole deformation⁶. Using a quantum many-body model of superfluid fission dynamics⁷, we find that heavy fission fragments are produced predominantly with 52 to 56 protons, which is associated with substantial octupole deformation acquired on the way to fission. These octupole shapes, which favour asymmetric fission, are induced by deformed shells at Z = 52 and Z = 56. By contrast, spherical magic nuclei are very resistant to octupole deformation, which hinders their production as fission fragments. These findings may explain surprising observations of asymmetric fission in nuclei lighter than lead⁸.

Review on the progress in nuclear fission-experimental methods and theoretical descriptions

An overview is given on some of the main advances in the experimental methods, experimental results, theoretical models and ideas of the last few years in the field of nuclear fission. New approaches have considerably extended the availability of fissioning systems for the experimental study of nuclear fission, and have provided a full identification of all fission products in A and Z for the first time. In particular, the transition from symmetric to asymmetric fission around ²²⁶Th, some unexpected structures in the mass distributions in the fission of systems around Z  =  80-84, and an extended systematics of the odd-even effect in the fission fragment Z distributions have all been measured (Andreyev et al 2018 Rep. Prog. Phys. 81 016301). Three classes of model descriptions of fission presently appear to be the most promising or the most successful. Self-consistent quantum-mechanical models fully consider the quantum-mechanical features of the fission process. Intense efforts are presently being made to develop suitable theoretical tools (Schunck and Robledo 2016 Rep. Prog. Phys. 79 116301) for modeling the non-equilibrium, large-amplitude collective motion leading to fission. Stochastic models provide a fully developed technical framework. The main features of the fission-fragment mass distribution have been well reproduced from mercury to fermium and beyond (Möller and Randrup 2015 Phys. Rev. C 91 044316). However, limited computer resources still impose restrictions, for example, on the number of collective coordinates and on an elaborate description of the fission dynamics. In an alternative semi-empirical approach (Schmidt et al 2016 Nucl. Data Sheets 131 107), considerable progress in describing the fission observables has been achieved by combining several theoretical ideas, which are essentially well known. This approach exploits (i) the topological properties of a continuous function in multidimensional space, (ii) the separability of the influence of fragment shells and the macroscopic properties of the compound nucleus, (iii) the properties of a quantum oscillator coupled to a heat bath of other nuclear degrees of freedom, (iv) an early freeze-out of collective motion, and (v) the application of statistical mechanics for describing the thermalization of intrinsic excitations in the nascent fragments. This new approach reveals a high degree of regularity and allows the calculation of high-quality data that is relevant to nuclear technology without specifically adjusting the empirical data of individual systems.

Suppressed Solitonic Cascade in Spin-Imbalanced Superfluid Fermi Gas

Cold atoms experiments offer invaluable information on superfluid dynamics, including decay cascades of topological defects. While the cascade properties are well established for Bose systems, our understanding of their behavior in Fermi counterparts is very limited, in particular in spin-imbalanced systems, where superfluid (paired) and normal (unpaired) particles naturally coexist giving rise to complex spatial structure of the atomic cloud. Here we show, based on a newly developed microscopic approach, that the decay cascades of topological defects are dramatically modified by the spin polarization. We demonstrate that decay cascades end up at different stages: "dark soliton," "vortex ring," or "vortex line," depending on the polarization. We reveal that it is caused by sucking of unpaired particles into the soliton's internal structure. As a consequence vortex reconnections are hindered and we anticipate that quantum turbulence phenomenon can be significantly affected, indicating new physics induced by polarization effects.

Implementing and testing theoretical fission fragment yields in a Hauser-Feshbach statistical decay framework

We implement fission fragment yields, calculated using Brownian shape-motion on a macroscopic-microscopic potential energy surface in six dimensions, into the Hauser-Feshbach statistical decay code CGMF. This combination allows us to test the impact of utilizing theoretically-calculated fission fragment yields on the subsequent prompt neutron and γ-ray emission. We draw connections between the fragment yields and the total kinetic energy TKE of the fission fragments and demonstrate that the use of calculated yields can introduce a difference in the 〈TKE〉 and, thus, the prompt neutron multiplicity v, as compared with experimental fragment yields. We deduce the uncertainty on the 〈TKE〉 and v from this procedure and identify possible applications.

Nuclear fission: a review of experimental advances and phenomenology

In the last two decades, through technological, experimental and theoretical advances, the situation in experimental fission studies has changed dramatically. With the use of advanced production and detection techniques both much more detailed and precise information can now be obtained for the traditional regions of fission research and, crucially, new regions of nuclei have become routinely accessible for fission studies. This work first of all reviews the recent developments in experimental fission techniques, in particular the resurgence of transfer-induced fission reactions with light and heavy ions, the emerging use of inverse-kinematic approaches, both at Coulomb and relativistic energies, and of fission studies with radioactive beams. The emphasis on the fission-fragment mass and charge distributions will be made in this work, though some of the other fission observables, such as prompt neutron and γ-ray emission will also be reviewed. A particular attention will be given to the low-energy fission in the so far scarcely explored nuclei in the very neutron-deficient lead region. They recently became the focus for several complementary experimental studies, such as β-delayed fission with radioactive beams at ISOLDE(CERN), Coulex-induced fission of relativistic secondary beams at FRS(GSI), and several prompt fusion-fission studies. The synergy of these approaches allows a unique insight in the new region of asymmetric fission around [Formula: see text]Hg, recently discovered at ISOLDE. Recent extensive theoretical efforts in this region will also be outlined. The unprecedented high-quality data for fission fragments, completely identified in Z and A, by means of reactions in inverse kinematics at FRS(GSI) and VAMOS(GANIL) will be also reviewed. These experiments explored an extended range of mercury-to-californium elements, spanning from the neutron-deficient to neutron-rich nuclides, and covering both asymmetric, symmetric and transitional fission regions. Some aspects of heavy-ion induced fusion-fission and quasifission reactions will be also discussed, which reveal their dynamical features, such as the fission time scale. The crucial role of the multi-chance fission, probed by means of multinucleon-transfer induced fission reactions, will be highlighted. The review will conclude with the discussion of the new experimental fission facilities which are presently being brought into operation, along with promising 'next-generation' fission approaches, which might become available within the next decade.

Dynamics of Fragmented Condensates and Macroscopic Entanglement

The relative phase of the order parameters in the collision of two condensates can influence the outcome of their collision in the case of weak coupling. With increasing interaction strength, however, the initially independent phases of the two order parameters in the colliding partners quickly become phase locked, as the strong coupling favors an overall phase rigidity of the entire condensate, and upon their separation the emerging superfluid fragments become entangled.

Novel Role of Superfluidity in Low-Energy Nuclear Reactions

We demonstrate, within symmetry unrestricted time-dependent density functional theory, the existence of new effects in low-energy nuclear reactions which originate from superfluidity. The dynamics of the pairing field induces solitonic excitations in the colliding nuclear systems, leading to qualitative changes in the reaction dynamics. The solitonic excitation prevents collective energy dissipation and effectively suppresses the fusion cross section. We demonstrate how the variations of the total kinetic energy of the fragments can be traced back to the energy stored in the superfluid junction of colliding nuclei. Both contact time and scattering angle in noncentral collisions are significantly affected. The modification of the fusion cross section and possibilities for its experimental detection are discussed.

Microscopic Phase-Space Exploration Modeling of ^{258}Fm Spontaneous Fission

We show that the total kinetic energy (TKE) of nuclei after the spontaneous fission of ^{258}Fm can be well reproduced using simple assumptions on the quantum collective phase space explored by the nucleus after passing the fission barrier. Assuming energy conservation and phase-space exploration according to the stochastic mean-field approach, a set of initial densities is generated. Each density is then evolved in time using the nuclear time-dependent density-functional theory with pairing. This approach goes beyond the mean-field theory by allowing spontaneous symmetry breaking as well as a wider dynamical phase-space exploration leading to larger fluctuations in collective space. The total kinetic energy and mass distributions are calculated. New information on the fission process: fluctuations in scission time, strong correlation between TKE and collective deformation, as well as prescission particle emission, are obtained. We conclude that fluctuations of the TKE and mass are triggered by quantum fluctuations.

Vortex Pinning and Dynamics in the Neutron Star Crust

The nature of the interaction between superfluid vortices and the neutron star crust, conjectured by Anderson and Itoh in 1975 to be at the heart vortex creep and the cause of glitches, has been a long-standing question in astrophysics. Using a qualitatively new approach, we follow the dynamics as superfluid vortices move in response to the presence of "nuclei" (nuclear defects in the crust). The resulting motion is perpendicular to the force, similar to the motion of a spinning top when pushed. We show that nuclei repel vortices in the neutron star crust, and characterize the force per unit length of the vortex line as a function of the vortex element to the nucleus separation.

Microscopic theory of nuclear fission: a review

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 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. 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.