arXiv subjects

Ibrahim Abdurrahman

Publications and source records attributed to Ibrahim Abdurrahman.

12 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

Pair Transfer and Reaction Dynamics in $^{40,48}$Ca + $^{96}$Zr Collisions Below the Coulomb Barrier

Sub-barrier fusion reactions are ideal for probing the effects of pairing correlations on simultaneous neutron transfer. Previous calculations using the BCS approximation showed an enhancement of pair transfer, relative to treatments with no pairing, but failed to reproduce the observed enhancement factor between one- and two-neutron transfer probabilities. This work aims to microscopically investigate the dynamics of $^{40,48}$Ca + $^{96}$Zr head-on collisions below the Coulomb barrier, focusing on the role of pairing correlations in neutron transfer. We employ time-dependent energy density functional theory extended to superfluid systems, TDSLDA. Transfer probabilities, including contributions to specific $K$-angular momentum projections, are extracted using projection operators and compared to results from calculations without pairing. Our calculations show that pairing is correlated to the dynamic deformability of the nucleus, which influences mean neutron transfer in sub-barrier reactions. We also show that TDSLDA reproduces the experimentally observed enhancement factor by significantly increasing the probability of transferring a neutron pair in the $K = 0$ spin channel. These results confirm the strong influence of pairing and structure on sub-barrier multi-nucleon transfer, and demonstrate that TDSLDA provides a reliable microscopic framework for describing the interplay between nuclear superfluidity and reaction dynamics.

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arXiv2026

Angular and Kinetic Properties of Scission Neutrons within Time-dependent Density Functional Theory

Scission-neutron emission is investigated in $^{235}\mathrm{U}(\mathrm{n}_{\mathrm{th}},\mathrm{f})$, $^{239}\mathrm{Pu}(\mathrm{n}_{\mathrm{th}},\mathrm{f})$ and $^{252}\mathrm{Cf}(\mathrm{sf})$ within time-dependent density functional theory. Using a substantially larger simulation domain than in previous studies, the angular and energy distributions of emitted scission neutrons are extracted over a specific range of emission angles. At these angles, scission neutrons are absent below a threshold energy of roughly $1.5$--$2\,\mathrm{MeV}$, and instead contribute predominantly to the higher energy part of the prompt fission neutron spectrum. Combining the calculated scission-neutron spectrum with a Maxwellian model for the evaporated component, constrained by low-energy experimental data, reproduces the measured high-energy prompt-fission-neutron yield in both $^{239}\mathrm{Pu}(\mathrm{n}_{\mathrm{th}},\mathrm{f})$ and $^{252}\mathrm{Cf}(\mathrm{sf})$, whereas the evaporation-only model systematically underestimates it. This identifies a signature of scission neutrons already present in existing high-energy prompt fission neutron spectra and constitutes direct evidence for a non-negligible scission-neutron component in prompt fission neutron emission.

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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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arXiv2024

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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arXiv2024

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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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 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. 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

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

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.

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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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arXiv2020

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 approximation (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 vortices 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.

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