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Aurel Bulgac

Publications and source records attributed to Aurel Bulgac.

At least 19 recordsLinked to original sources
arXiv2026

Large Amplitude Collective Motion and Dissipation in the Ground State and the First Isomeric Wells in the Neutron-Induced Fission of $^{235}$U

In fission induced by low energy neutrons, the mother nucleus spends a significant fraction of the time in the ground state and isomer wells, eventually passing beyond the outer barrier, where the primary fission fragments properties are defined. Despite this, the dynamics of these two early stages have not been investigated using microscopic models. This study examines the evolution of the mother nucleus in both wells separately, using time-dependent density functional theory, which has been previously used to treat the saddle-to-scission stage of fission for $^{235}$U(n,f) reactions. These two early stages of fission are essential blocks in the final theory of the formation and evolution of a compound nucleus. The present study shows that the dynamics in both wells is strongly dissipative, similar to the dynamics from saddle to scission. It also reveals that while the initial mass asymmetry of the system quickly settles to very small fluctuations in the ground state well, in the isomeric well, the mass asymmetry oscillates with a rather large amplitude, in almost harmonic motion. Furthermore, with low probability, neutrons are emitted in both wells.

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arXiv2026

Influence of the Exit Channel in $^{235}$U(n,f) and $^{239}$Pu(n,f) Reactions in Time-Dependent Density Functional Theory

This study investigates the consequences of the intrinsic deformation of the fissioning nuclear system near the outer saddle point on the shape evolution of the nucleus from saddle to scission and on the properties of the fission fragments. It is found that trajectories generally split into at least three classes, asymmetric, near-symmetric, and highly-asymmetric fission, that are roughly determined by the initial magnitude of the octupole moment, and each of which exhibits different scission dynamics and fragment properties. Near-symmetric modes result in a highly elongated neck at scission, leading to the neck rupture occurring when the proto-fragments are further apart than is the case for typical asymmetric fission, which in turn leads to a lower total kinetic energy and higher total excitation energy. The majority of this additional excitation energy goes into the heavy fission fragment, that develops a substantial quadrupole deformation. A similar trend is observed for the total kinetic energy of highly-asymmetric fission events, and the opposite trend for the excitation energy of the fission fragments as the majority of the additional excitation energy goes into the light fission fragment instead. The study also characterizes the neck rupture, including its effect on the emission of scission neutrons in near-symmetric fission.

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arXiv2026

Multi-Nucleon Transfer Reactions and the Creation and the Evolution of the Compound Nucleus

We present the first implementation of a novel extension of the Generator Coordinate Method (GCM), dubbed the enhanced GCM (eGCM), which is applied to the grazing Multi-Nucleon Transfer (MNT) reaction $^{48}$Ca+$^{208}$Pb near the Coulomb barrier. eGCM incorporates major qualitative differences with either Time-Dependent Hartree-Fock (TDHF) or GCM frameworks used until now for nuclear reactions. We demonstrate that the eGCM framework describes for the first time in a fully quantum microscopic framework the emergence and the time-evolution of Niels Bohr's 1936 conjectured Compound Nucleus (CN). The thermalization time extracted in eGCM is at least two orders of magnitude larger than the Eigenstate Thermalization Hypothesis (ETH) would predict.

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arXiv2026

W-SLDA Toolkit: A simulation platform for ultracold Fermi gases

We present the W-SLDA Toolkit, a general-purpose software package for simulating ultracold Fermi gases within the framework of density functional theory and its time-dependent extensions. The toolkit enables fully microscopic studies of interacting superfluid systems across the BCS-BEC crossover, including spin-imbalanced configurations and arbitrary external geometries. It provides both static and time-dependent solvers capable of describing a broad range of phenomena in one-, two-, and three-dimensional settings. In addition, the toolkit incorporates functionality for solving the standard Bogoliubov-de Gennes equations for fermions, extending its applicability to other physical systems such as superconductors. The code is implemented in C with GPU acceleration and is optimized for hybrid CPU/GPU execution on modern high-performance computing platforms. It ensures scalability on leadership-class supercomputers, enabling fully three-dimensional simulations with large atomic numbers, and allows for direct benchmarks of ultracold-atom experimental setups. Its modular architecture facilitates straightforward extensions, user customization, and seamless interoperability with other scientific software frameworks. Furthermore, an extensive collection of practical usage examples is provided through the integrated reproducibility packs functionality, ensuring transparency and reproducibility of computational results.

cond-mat.quant-gas↗
arXiv2025

Time-Dependent Density Functional Theory Description of $^{238}$U(n,f), $^{240,242}$Pu(n,f) and $^{237}$Np(n,f) Reactions

In nuclei with an odd nucleon number the non-vanishing spin number density is the source of a pseudo-magnetic field, which favors the splitting of the nucleon Cooper pairs. Such an pseudo-magnetic field is generated always in the dynamics of any nucleus, but its effects on Cooper pairs is significantly enhanced in the dynamic evolution of nuclei with an odd number of nucleons. We present for the first time a microscopic study of the induced fission of the odd neutron compound nuclei $^{239}$U, $^{241, 243}$Pu, and the odd proton, odd neutron compound nucleus $^{238}$Np, performed within the time-dependent density functional theory extended to superfluid fermion systems, without any simplifying assumptions and with controlled numerical approximations, and for a very large number of initial conditions. Due to the presence of the unpaired odd nucleon(s), the time-reversal symmetry of the fission compound nucleus is spontaneously broken, an aspect routinely neglected in the most advanced microscopic approaches of the past. The emerging fission fragment properties are quite similar to the properties of fission fragments of neighboring even-even nuclei. The time from saddle-to-scission is often significantly longer in odd-N-odd-Z or odd-A nuclei than for even-even nuclei since systems with unpaired nucleons are easier to excite and the potential energy surfaces of these nuclei have more structure, often resembling a very complicated obstacle course, rather than a more direct evolution of the nuclear shape from the top of the outer fission barrier to the scission configuration. The Pauli blocking approximation, often invoked in the literature, expected to inhibit the fission of nuclei with unpaired nucleons, is surprisingly strongly violated during the fission dynamics.

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arXiv2025

Impact of the Center of Mass Fluctuations on the Ground State Properties of Nuclei

Ground state properties across the entire nuclear chart are described predominantly and rather accurately within the density functional theory (DFT). DFT however breaks many symmetries, among them the most important being the translational, rotational, and gauge symmetries. The translational symmetry breaking is special, since it is broken for all nuclei, unlike the rotational and gauge symmetries. The center-of-mass (CoM) correction most commonly used in the literature [see Vautherin and Brink, Phys. Rev. C {\bf 5}, 626 (1972) and Bender {\it et al.}, Rev. Mod. Phys. {\bf 75}, 121 (2003)] leads to a gain of 15,...,19 MeV, which varies rather weakly for medium and heavy mass nuclei. A better approximation to the CoM correction was suggested by Butler {\it et al.}, Nu cl. Phys. A {\bf 422}, 157 (1984) and its magnitude varies between 10 and 5 MeV from light to heavy nuclei, a correction which is also significantly larger than the RMS energy error in the Bethe-Weizs\"acker mass formula, initially proposed by Gamow, Proc. Phys. Soc. A {\bf 126}, 157 (1930), which is at most 3.5 MeV, and which for heavy nuclei corresponds to about 0.2\% of their mass. ....

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arXiv2024

A critical assessment of the current implementations of the Generator Coordinate Method

The generator coordinate method (GCM) was introduced in nuclear physics by Wheeler and independently by Peierls and their collaborators in 1950s and it is still one of the most used approximations for treating nuclear large-amplitude collective motion. GCM was inspired by similar methods introduced in molecular and condensed-matter physics in the late 1920s, after the Schr\"odinger equation became the tool of choice to describe quantum phenomena. The interest in the 1983 extension of GCM suggested by Reinhard, Cusson, and Goeke, which includes the internal excitations (absent in the initial GCM formulation), was revived in recent years. Unfortunately, this newer version of the time-dependent GCM framework has flaws that prevent it from describing correctly many anticipated features, in particular interference and entanglement, which can play an important role in fission and many-nucleon transfer reactions. I present here an alternative formulation, the enhanced GCM (eGCM), which is free of the difficulties encountered in previous GCM implementations and which is relevant for fission and many-nucleon transfer in heavy-ion reactions, and which can be used in either static or time-dependent eGCM formulations. In the eGCM framework, the corresponding many-body wave functions have a much more complex structure, and this framework is equivalent to a configuration-interaction approach in the continuum for nuclear reactions. The eGCM is aimed at being used in the microscopic description of heavy-ion reactions and fission in particular. ....

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arXiv2023

Non-Markovian character and irreversibility of real-time quantum many-body dynamics

The presence of pairing correlations within the time-dependent density functional theory (TDDFT) extension to superfluid systems, is tantamount to the presence of a quantum collision integral in the evolution equations, which leads to an obviously non-Markovian behavior of the single-particle occupation probabilities, unexpected in a traditional quantum extension of kinetic equations. The quantum generalization of the Boltzmann equation, based on a collision integral in terms of phase-space occupation probabilities, is the most used approach to describe nuclear dynamics and which by construction has a Markovian character. By contrast, the extension of TDDFT to superfluid systems has similarities with the Baym and Kadanoff kinetic formalism, which however is formulated with much more complicated evolution equations with long-time memory terms and non-local interactions. The irreversibility of quantum dynamics is properly characterized using the canonical wave functions/natural orbitals, and the associated canonical occupation probabilities, which provide the smallest possible representation of any fermionic many-body wave function. In this basis, one can evaluate the orbital entanglement entropy, which is an excellent measure of the non-equilibrium dynamics of an isolated system. To explore the phenomena of memory effects and irreversibility, we investigate the use of canonical wave functions/natural orbitals in nuclear many-body calculations, assessing their utility for static calculations, dynamics, and symmetry restoration. As the number of single-particle states is generally quite large, it is highly desirable to work in the canonical basis whenever possible, preferably with a cutoff. We show that truncating the number of canonical wave functions can be a valid approach in the case of static calculations, but that such a truncation is not valid for time-dependent calculations...

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arXiv2023

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. I also describe several aspects of the exchange and irreducible 2-body density matrices, which depend on the character and strength of the 2-particle interaction and, which can be useful in justifying the derivation of an appropriate energy density functional.

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arXiv2023

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 {\gamma}-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. These point to a well-defined 3D FF intrinsic spin dynamics, characteristics absent in semi-phenomenological studies, due to the presence of the twisting spin modes, which artificially were suppressed in semi-phenomenological studies.

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arXiv2023

Neck Rupture and Scission Neutrons in Nuclear Fission

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.

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arXiv2022

New developments in fission studies within the time-dependent density functional theory framework

We have extended significantly the microscopic description of the fission process by examining a larger set of observables. We extract neutron and proton numbers of fission fragments, their spins and fission fragment relative orbital angular momentum and their correlations, investigate neutrons emitted at or shortly after scission, excitation energy sharing mechanism, total kinetic energy of fission fragments, and the entanglement entropy. I will present a short overview of our simulations obtained with two independent nuclear energy density functionals.

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arXiv2022

Sensitivity to the initial conditions of the Time-Dependent Density Functional Theory

Time-Dependent Density Functional Theory is mathematically formulated through non-linear coupled time-dependent 3-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 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 the study of non-equilibrium dynamics of strongly interacting many-fermion systems, the question of predictability of this theoretical framework is of paramount importance. 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 ${\cal O}(10^{10})$ and larger, suggests that its maximum Lyapunov exponents are negligible for all practical purposes.

cond-mat.stat-mech↗
arXiv2022

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 indicate that the time evolution of the entanglement entropy describes the non-equilibrium 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. 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, $n_\text{mf}(k) = {1}/\{ 1+\exp\beta[\epsilon(k)-\mu]\}$ 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.

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arXiv2022

Measures of complexity and entanglement in fermionic many-body 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 case of CI calculations reaches about 20 billion terms. 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. The canonical wave functions/natural orbitals 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 non-equilibrium 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.

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arXiv2022

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.

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arXiv2021

Time-Dependent Density Functional Theory for Fermionic Superfluids: from Cold Atomic Gases, to Nuclei and Neutron Stars Crust

In cold atoms and in the crust of neutron stars the pairing gap can reach values comparable with the Fermi energy. While in nuclei the neutron gap is smaller, it is still of the order of a few percent of the Fermi energy. The pairing mechanism in these systems is due to short range attractive interactions between fermions and the size of the Cooper pair is either comparable to the inter-particle separation or it can be as big as a nucleus, which is still relatively small in size. Such a strong pairing gap is the result of the superposition of a very large number of particle-particle configurations, which contribute to the formation of the Copper pairs. These systems have been shown to be the host of a large number of remarkable phenomena, in which the large magnitude of the pairing gap plays an essential role: quantum shock waves, quantum turbulence, Anderson-Higgs mode, vortex rings, domain walls, soliton vortices, vortex pinning in neutron star crust, unexpected dynamics of fragmented condensates and role of pairing correlations in collisions on heavy-ions, Larkin-Ovchinnikov phase as an example of a Fermi supersolid, role pairing correlations control the dynamics of fissioning nuclei, self-bound superfluid fermion droplets of extremely low densities.

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