Engineering topics

Bulgac, Aurel

Publications and source records attributed to Bulgac, Aurel.

14 records

DOE OSTI2024

Neck Rupture and Scission Neutrons in Nuclear Fission

Just before a nucleus undergoes fission, a neck is formed between the emerging fission fragments. It is widely accepted that this neck undergoes a rather violent rupture, despite the absence of unambiguous experimental evidence. The main difficulty in addressing the neck rupture and saddle-to-scission stages of fission is that both are highly nonequilibrium processes. Here, we present the first fully microscopic characterization of the scission mechanism, along with the spectrum and the spatial distribution of scission neutrons (SNs), and some upper limit estimates for the emission of charged particles. The spectrum of SNs has a distinct angular distribution, with neutrons emitted in roughly equal numbers in the equatorial plane and along the fission axis. They carry an average energy around 3±0.5 MeV for the fission of 236 U, 240 Pu, and 252 Cf, and a maximum of 16–18 MeV. We estimate a conservative lower bound of 9%–14% of the total emitted neutrons are produced at scission.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Microscopic evidence for scission neutrons

We discuss the neck rupture stage of fission and the emission of particles afterwards, two extremely rapid and highly non-equilibrium processes. Currently, the neck rupture cannot be directly probed by experiment, highlighting the importance of reliable theoretical predictions for this stage of fission. Time-dependent density functional theory (TDDFT) is used to simulate the spontaneous fission of 252 Cf. In conjunction with statistical models, inputs from microscopic calculations can be used to make predictions for prompt neutron and gamma emission spectra, quantities which can be experimentally measured. Here we characterize the scission mechanism within TDDFT and estimate the number of scission neutrons and their kinetic energies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Microscopic Evidence for Scission Neutrons

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Spatial orientation of the fission fragment intrinsic spins and their correlations

New experimental and theoretical results obtained in 2021 made it acutely clear that more than 80 years after the discovery of nuclear fission we do not understand the generation and dynamics of fission fragment (FF) intrinsic spins well, in particular their magnitudes, their spatial orientation, and their correlations. The magnitude and orientation of the primary FFs have a crucial role in defining the angular distribution and correlation between the emitted prompt neutrons, and subsequent emission of statistical (predominantly $E1$) and stretched $E2$ $γ$ rays, and their correlations with the final fission fragments. Here, we present detailed microscopic evaluations of the FF intrinsic spins, for both even- and odd-mass FFs, and of their spatial correlations. In conclusion, these point to a well-defined three-dimensional FF intrinsic spin dynamics, characteristics absent in semiphenomenological studies, due to the presence of the twisting spin modes, which artificially were suppressed in semiphenomenological studies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Examining the justification for the introduction of a fermion localization function

Becke and Edgecombe suggested in 1990 a theoretical tool to describe electron localization in atoms and molecules, an idea which was borrowed by a large number of nuclear theorists since 2011 to describe nucleon localization in nuclear systems. I argue here that these arguments are highly questionable and cannot be used in interacting systems where effects beyond the naive mean field or the simple Hartree-Fock framework are important and the inclusion of correlations induced by particle interactions is necessary in order to introduce such a localization function. Furthermore, I also describe several aspects of the exchange and irreducible two-body density matrices, which depend on the character and strength of the two-particle interaction and which can be useful in justifying the derivation of an appropriate energy density functional.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Entanglement entropy, single-particle occupation probabilities, and short-range correlations

For quantum many-body systems with short-range correlations (SRCs), the intimate relationship between their magnitude, the behavior of the single-particle occupation probabilities at momenta larger than the Fermi momentum, and the entanglement entropy is a new qualitative aspect not studied and exploited yet. A large body of recent condensed matter studies indicates that the time evolution of the entanglement entropy describes the nonequilibrium dynamics of isolated and strongly interacting many-body systems, in a manner similar to the Boltzmann entropy, which is strictly defined for dilute and weakly interacting many-body systems. Both theoretical and experimental studies in nuclei and cold atomic gases have shown that the fermion momentum distribution has a generic behavior n(k)=C/k 4 at momenta larger than the Fermi momentum, due to the presence of SRCs, with approximately 20% of the particles having momenta larger than the Fermi momentum. Further, the presence of the long momentum tails in the presence of SRCs changes the textbook relation between the single-particle kinetic energy and occupation probabilities, n mf ⁡(k) = 1/{1+ exp ⁡β[ϵ⁡(k)-μ]} for momenta very different form the Fermi momentum, particularly for dynamics processes. SRCs induced high-momentum tails of the single-particle occupation probabilities increase the entanglement entropy of fermionic systems, which in its turn affects the dynamics of many nuclear reactions, such as heavy-ion collisions and nuclear fission.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Measures of complexity and entanglement in many-fermion systems

There is no unique and widely accepted definition of the complexity measure (CM) of a many-fermion wave function in the presence of interactions. The simplest many-fermion wave function is a Slater determinant. In shell-model or configuration interaction (CI) and other related methods, the state is represented as a superposition of a large number of Slater determinants, which in the case of CI calculations reaches about 20 billion terms [Johnson, arXiv:1809.07869]. Although in practice this number has been used as a CM for decades, it is ill defined: it is not unique, and it depends on the particular type and the number of single-particle wave functions used to construct the Slater determinants. Further, the canonical wave functions and/or natural orbitals [Löwdin, Adv. Phys. 5, 1 (1956); Löwdin and Shull, Phys. Rev. 101, 1730 (1956); Bardeen et al., Phys. Rev. 108, 1175 (1957); N. N. Bogoljubov, Il Nuovo Cimento 7, 794 (1958); Valatin, Il Nuovo Cimento 7, 843 (1958); de Gennes, Superconductivity of Metals and Alloys (CRC Press, Boca Raton, FL, 1999); Ring and Schuck, The Nuclear Many-Body Problem, 1st ed. (Springer-Verlag, Berlin, 2004)] and their corresponding occupation probabilities are intrinsic properties of any many-body wave function, irrespective of the representation, and they provide a unique solution to characterize the CM. The non-negative orbital entanglement entropy, which vanishes for a Slater determinant, provides the simplest CM, while a more complete measure of complexity is the entanglement spectrum. We illustrate these aspects in the case of a complex nonequilibrium time-dependent process, induced nuclear fission described within a real-time density functional theory framework extended to superfluid systems, which can describe simultaneously the long-range and the short-range correlations between fermions. The orbital entanglement entropy of the fissioning nucleus illustrates the localization mechanism of the many-body wave function in Fock and/or Hilbert space. The (minimal) number of Slater determinants required to represent such a complex many-body wave function with a well-defined number of particles in the case presented here is about 10 500 . The realistic case of the highly nonequilibrium nuclear fission process illustrated here is equivalent to a system of 23.328×10 9 interacting quantum spin-1/2 particles, a very large system for the study of quantum entanglement.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Angular correlation between the fission fragment intrinsic spins

The generation of fission fragment (FF) spins and of their relative orbital angular momentum has been debated for more than six decades, and no consensus has been achieved so far. The interpretation of recent experimental results of Wilson et al., has been challenged by several recent theoretical studies, which are not in agreement with one another. According to the interpretation by Wilson et al., the FF spins emerge very long after scission occurrs. Randrup and Vogt, while agreeing that the FF spins are uncorrelated, conclude on the basis of a phenomenological model that these spins are uncorrelated already before scission. Bulgac et al., in a fully microscopic study demonstrate that the primordial FF spin final values are defined before the emission of prompt neutrons and statistical gammas and are strongly correlated with a relative angle between spins close to 2π/3, a result in full agreement with the present independent analysis. The prompt neutrons and statistical gammas carry a significant amount of angular momentum according to the study of Stetcu et al. which can lead to a decorrelation of the FF bandhead spins of the yrast lines measured by Wilson et al., and which also provides arguments why these measured spins are so different from the primordial FF spins evaluated by Bulgac et al.. Here, I show that the unexpected character of the angular correlation between the primordial FF intrinsic spins, recently evaluated by Bulgac et al., which favors FF intrinsic spins pointing predominantly in opposite directions, can be understood by using simple general phase space arguments. The observation by Wilson et al., that the FF spins are uncorrelated follows from both the results of the microscopic calculation of Bulgac et al., and the present analysis of the full correlated probability distribution of the FF spins together with the relative orbital angular momentum of the primordial FFs. These arguments may apply also to heavy-ion collisions and, since there is no use of specifics of the particle interactions, the present results might apply to atomic and molecular systems as well.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Sensitivity of time-dependent density functional theory to initial conditions

Time-dependent density-functional theory is mathematically formulated through nonlinear coupled time-dependent three-dimensional partial differential equations, and it is natural to expect a strong sensitivity of its solutions to variations of the initial conditions, akin to the butterfly effect ubiquitous in classical dynamics. Since the Schrödinger equation for an interacting many-body system is, however, linear and mathematically the exact equations of the density-functional theory reproduce the corresponding one-body properties, it would follow that the Lyapunov exponents are also vanishing within a density-functional theory framework. Whether for realistic implementations of the time-dependent density-functional theory the question of the absence of the butterfly effect and whether the dynamics provided is indeed a predictable theory was never discussed. At the same time, since the time-dependent density-functional theory is a unique tool allowing us to study the nonequilibrium dynamics of strongly interacting many-fermion systems, the question of predictability of this theoretical framework is of paramount importance. Here our analysis, for a number of quantum superfluid many-body systems (unitary Fermi gas, nuclear fission, and heavy-ion collisions) with a classical equivalent number of degrees of freedom O(10 10 ) and larger, suggests that its maximum Lyapunov exponents are negligible for all practical purposes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Pure quantum extension of the semiclassical Boltzmann-Uehling-Uhlenbeck equation

The Boltzmann equation is the traditional framework in which one extends the time-dependent mean field classical description of a many-body system to include the effect of particle-particle collisions in an approximate manner. A semiclassical extension of this approach to quantum many-body systems was suggested by Uehling and Uhlenbeck in 1933 for both Fermi and Bose statistics, and many further developments of this approach are known as the Boltzmann-Uehling-Uhlenbeck (BUU) equations. In this paper I introduce a pure quantum version of the BUU type of equations, which is mathematically equivalent to a generalized time-dependent density functional theory extended to superfluid systems. As expected, during nonequilibrium processes the quantum Boltzmann one-body entropy increases during evolution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

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

In this work, 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.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

The LISE package: solvers for static and time-dependent superfluid local density approximation equations in three dimensions

Nuclear implementation of the density functional theory (DFT) is at present the only microscopic framework applicable to the whole nuclear landscape. The extension of DFT to superfluid systems in the spirit of the Kohn-Sham approach, the superfluid local density approximation (SLDA) and its extension to time-dependent situations, time-dependent superfluid local density ap- proximation (TDSLDA), have been extensively used to describe various static and dynamical problems in nuclear physics, neutron star crust, and cold atom systems. In this paper, we present the codes that solve the static and time-dependent SLDA equations in three-dimensional coordinate space without any symmetry restriction. These codes are fully parallelized with the message passing interface (MPI) library and take advantage of graphic processing units (GPU) for accelerating execution. The dynamic codes have checkpoint/restart capabilities and for initial conditions one can use any generalized Slater determinant type of wave function. The code can describe a large number of physical problems: nuclear fission, collisions of heavy ions, the interaction of quantized vor- tices with nuclei in the nuclear star crust, excitation of superfluid fermion systems by time dependent external fields, quantum shock waves, domain wall generation and propagation, the dynamics of the Anderson-Bogoliubov-Higgs mode, dynamics of fragmented condensates, vortex rings dynamics, generation and dynamics of quantized vortices, their crossing and recombinations and the incipient phases of quantum turbulence.

Jin, Shi↗

DOE OSTI2021

Angular Momentum Removal by Neutron and γ-Ray Emissions during Fission Fragment Decays

In this work, we investigate the angular momentum removal from fission fragments (FFs) through neutron and γ-ray emission, finding that about half the neutrons are emitted with angular momenta ≥ 1.5 ℏ and that the change in angular momentum after the emission of neutrons and statistical γ rays is significant, contradicting usual assumptions. Per fission event, in our simulations, the neutron and statistical γ-ray emissions change the spin of the fragment by 3.5 – 5 ℏ , with a large standard deviation comparable to the average value. Such wide angular momentum removal distributions can hide any underlying correlations in the fission fragment initial spin values. Within our model, we reproduce data on spin measurements from discrete transitions after neutron emissions, especially in the case of light FFs. The agreement further improves for the heavy fragments if one removes from the analysis the events that would produce isomeric states. Finally, we show that while in our model the initial FF spins do not follow a sawtoothlike behavior observed in recent measurements, the average FF spin computed after neutron and statistical γ emissions exhibits a shape that resembles a sawtooth. This suggests that the average FF spin measured after statistical emissions is not necessarily connected with the scission mechanism as previously implied.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Restoring broken symmetries for nuclei and reaction fragments

In typical microscopic approaches, particularly when pairing correlations are present, nuclei and nuclear fragments do not have well defined quantum numbers and symmetries should be restored. In this work, I present a formalism for the simultaneous projection of total particle numbers of a nucleus, particle number of reaction fragments, and of the reaction fragment intrinsic spins and of their correlation, and also for their symmetry restored densities and total energies. These formulas for the symmetry restored quantities, are free of any singularities, unlike those in the previously introduced prescriptions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗