arXiv subjects

Matthew Kafker

Publications and source records attributed to Matthew Kafker.

10 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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arXiv2025

Non-Equilibrium Dynamics of Hard Spheres in the Fluid, Crystalline, and Glassy Regimes

We investigate the response of a system of hard spheres to two classes of perturbations over a range of densities spanning the fluid, crystalline, and glassy regimes within a molecular dynamics framework. Firstly, we consider the relaxation of a "thermal inhomogeneity," in which a central region of particles is given a higher temperature than its surroundings and is then allowed to evolve under Newtonian dynamics. In this case, the hot central "core" of particles expands and collides with the cold surrounding material, creating a transient radially-expanding "compression wave," which is rapidly dissipated by particle-particle collisions and interaction with periodic images at the boundary, leading to a rapid relaxation to equilibrium. Secondly, we consider a rapid compression of the spheres into a disordered glassy state at high densities. Such rapidly compressed systems exhibit very slow structural relaxation times, many orders of magnitude longer than thermalization times for simple temperature inhomogeneities. We find that thermal relaxation of the velocity distribution is determined simply by the total collision rate, whereas structural relaxation requires coordinated collective motion, which is strongly suppressed at high density, although some particle rearrangement nevertheless occurs. We further find that collisions propagate significantly faster through glassy systems than through crystalline systems at the same density, which leads to very rapid relaxation of velocity perturbations, although structural relaxation remains very slow. These results extend the validity of previous observations that glassy systems exhibit a hybrid character, sharing features with both equilibrium and non-equilibrium systems. Finally, we introduce the hard sphere causal graph, a network-based characterization of the dynamical history of a hard sphere system, which encapsulates several useful...

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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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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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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

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

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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