Relativistic Energies Research Articles

Electromagnetic signatures of black hole clusters in the center of super-Eddington galaxies

Supermassive black holes (SMBHs) at the centers of active galaxies are fed by accretion disks that radiate from the infrared or optical to the X-ray bands. Several types of objects can orbit SMBHs, including massive stars, neutron stars, clouds from the broad- and narrow-line regions, and X-ray binaries. Isolated black holes with a stellar origin (BHs of ∼10 M⊙) should also be present in large numbers within the central parsec of the galaxies. These BHs are expected to form a cluster around the SMBH as a result of the enhanced star formation rate in the inner galactic region and the BH migration caused by gravitational dynamical friction. However, except for occasional microlensing effects on background stars or gravitational waves from binary BH mergers, the presence of a BH population is hard to verify. In this paper, we explore the possibility of detecting electromagnetic signatures of a central cluster of BHs when the accretion rate onto the central SMBH is greater than the Eddington rate. In these supercritical systems, the accretion disk launches powerful winds that interact with the objects orbiting the SMBH. Isolated BHs can capture matter from this dense wind, leading to the formation of small accretion disks around them. If jets are produced in these single microquasars, they could be sites of particle acceleration to relativistic energies. These particles in turn are expected to cool by various radiative processes. Therefore, the wind of the SMBH might illuminate the BHs through the production of both thermal and nonthermal radiation.

Study of net-baryon higher moments in PNJL model and their expectation for net-proton using the subensemble acceptance method for the search of QCD critical point

The critical point is one of the most important aspects of the QCD phase diagram of strongly interacting matter. The nonmonotonic behavior of the higher-order moments of conserved quantities like net-baryon (ΔB), net-charge (ΔQ), and net-strangeness (ΔS) are believed to be the signatures of the QCD critical point as a function of energy. We study the effect of the QCD critical point on moments of net-baryon in the Polyakov loop enhanced Nambu-Jona-Lasinio (PNJL) model of QCD with six-quark and eight-quark interactions for finite and infinite volume systems. The study is performed at energies similar to Relativistic Heavy-Ion Collider beam energy scan. Experimentally measuring conserved quantities is difficult due to systematic limitations. Therefore, net-proton, net-pion, and net-kaon are measured as the proxy of ΔB, ΔQ, and ΔS. Recent studies in the subensemble acceptance method on the hadron resonance gas (HRG) model show the dependency of the measured higher-order moment on the experimental acceptance. We applied the subensemble acceptance method to analyze the behavior of κσ2 of net-baryon distribution within the subvolume system for various acceptance fractions. These results can be directly mapped to the subvolume (particle) percentage of the total volume (conserved quantities). Our findings are compared to the solenoidal tracker at RHIC (STAR) net-proton and proton data with different energies to investigate the presence of the critical point. Additionally, these results are also compared with the ultrarelativistic quantum molecular dynamics (UrQMD), HRG model, and available lattice data. Published by the American Physical Society 2024

Molecular Structure Theory without the Born-Oppenheimer Approximation: Rotationless Vibrational States of LiH.

Low-lying rotationless states of the lithium hydride molecule are studied in the framework of the variational method without assuming the Born-Oppenheimer (BO) approximation. Highly accurate solutions to the six-particle (two nuclei and four electrons) Schrödinger equation are obtained by means of expanding the wave functions of the considered states in terms of many thousands of all-particle explicitly correlated Gausssians. The basis functions are optimized independently for each state using the analytic energy gradient with respect to the nonlinear parameters. The non-BO wave functions obtained in the calculations are used to evaluate the leading-order relativistic and quantum electrodynamics energy corrections in the framework of the perturbation theory. The geometric structure of the molecule in the ground and excited states is discussed based on the analysis of the nucleus-nucleus correlation functions. The non-BO energies and structural parameters obtained of this work are compared with the most accurate BO results currently available.

Effects of gravity rainbow on scalar bosonic and oscillator fields in Bonnor–Melvin space-time with a cosmological constant

In this paper, we explore the relativistic quantum motion of spin-zero scalar charge-free particles influenced by rainbow gravity’s (RG’s) in Bonnor–Melvin magnetic space-time, a four-dimensional solution featuring a positive cosmological constant. We solve the Klein–Gordon equation in this scenario by using two sets of rainbow function: (i) f(χ)=1(1-βχ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\chi )=\\frac{1}{(1-\\beta \\,\\chi )}$$\\end{document}, h(χ)=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h(\\chi )=1$$\\end{document} and (ii) f(χ)=1(1-βχ)=h(χ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\chi )=\\frac{1}{(1-\\beta \\,\\chi )}=h(\\chi )$$\\end{document}, where 0<χ=|E|Ep≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0 < \\chi \\left( =\\frac{|E|}{E_p}\\right) \\le 1$$\\end{document} with Ep\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_p$$\\end{document} being the Planck’s energy, E is the particle’s energy, and β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} is the rainbow parameter. Furthermore, we study the relativistic quantum oscillator through the Klein–Gordon oscillator equation in the same Bonnor–Melvin magnetic space-time under RG effects. Employing the first pair of rainbow function, we obtain an approximate eigenvalue solution of the quantum oscillator fields. Notably, we demonstrate that the relativistic energy profile of scalar and oscillator particles are influenced by the topology of the geometry and the cosmological constant which is related with the magnetic field strength lies along the symmetry axis. Additionally, we see the impact of rainbow parameter on these approximate relativistic energy profiles in both quantum systems.

High-Precision Experiments with Trapped Radioactive Ions Produced at Relativistic Energies

Research on radioactive ion beams produced with in-flight separation of relativistic beams has advanced significantly over the past decades, with contributions to nuclear physics, nuclear astrophysics, atomic physics, and other fields. Central to these advancements are improved production, separation, and identification methods.The FRS Ion Catcher at GSI/FAIRexemplifies these technological advancements. The system facilitates high-precision experiments by efficiently stopping and extracting exotic nuclei as ions and making these available at thermal energies. High-energy synchrotron beams enhance the system’s capabilities, enabling unique experimental techniques such as multi-step reactions, mean range bunching, and optimized stopping, as well as novel measurement methods for observables such as beta-delayed neutron emission probabilities. The FRS Ion Catcher has already contributed to various scientific fields, and the future with the Super-FRS at FAIR promises to extend research to even more exotic nuclei and new applications.

Tapering-enhanced high-efficiency THz waveguide oscillator

Using a waveguide in a THz FEL has been shown to maximize the coupling and enable efficient extraction of relativistic electron beam energy from a single passage through a tapered helical undulator. An oscillator configuration can further boost energy extraction above the single-pass limits and open the door toward very high average power THz sources. Embedding the undulator in an oscillator cavity is particularly useful in combination with high repetition rate electron sources, even if at reduced peak brightness, since recycling a fraction of the radiation as an intense seed can compensate for lower single-pass gain. In this paper, we investigate the efficiency scaling of a tapering-enhanced waveguide oscillator, showcasing its capability for frequency-tuning operation and high-efficiency operation at different wavelengths. Using a thermionic-driven beamline equipped with compression elements, numerical start-to-end simulation results indicate a 16% efficiency at 200 GHz and a 2.1% efficiency at 1.5 THz, resulting in kW-level average power out-coupled in radiation pulses with few hundred μJ energy and tens of MW peak power. Published by the American Physical Society 2024

Quantum geometric approach: Nature and characteristics of emerged quantum-conditioned spacetime curvatures on three-sphere

General relativity (GR) in its current classical formulation is fundamentally different from quantum mechanics (QM). We argue that the everlasting battle for exploring and understanding the Universe and then privileging a consistent perception of reality is therefore awaiting a consolidator rather than a conqueror. This should be capable of either unifying these two different benchmarks or at least bringing one closer to another! The latter conservatively describes the consolidating quantum geometric approach, which combines generalization of QM to relativistic energies and gravitational fields and continuous Riemann to discretized Finsler geometry. We found that this type of quantum geometric approach seems to unveil additional quantum-conditioned spacetime curvatures (QCC), sources of gravitation), which obviously could not be disclosed in Einstein’s GR, especially at large scales. This study introduces analytical and numerical analyses of QCC. We conclude that (i) nature and characteristics of QCC are fundamentally distinguishable from the classical GR’s spacetime curvatures, (ii) the QCC are intrinsic, real and essential, i.e. not artifacts that would be removed in a certain coordinate transformation and (iii) the magnitude of QCC are nonnegligible to be underestimated. We also conclude that the spacetime at quantum scales seems to be no longer smooth or continuous so that the proposed quantum geometric approach would be regarded as a novel mathematical framework for the emergence of quantum gravity. Last but not least, a maximal proper force is predicted as a new physical constant, which is responsible for the maximal and gravitational acceleration of a quantum particle that would live in the emerged spacetime curvatures. Thereby, the quantum geometric nature of QCC can be accessed and assessed.

Relativistic beam loading, recoil-reduction, and residual-wake acceleration with a covariant retarded-potential integrator

An algorithm is demonstrated that performs first-principles tracking of relativistic charged-particles. A covariant approach is used which relies on retarded vector potentials for trajectory integration instead of performing electromagnetic field calculations. When accounting for retardation effects, the peak vector potential and corresponding Lorentz force in the direction of travel increase asymptotically for high-β particles. This produces a very strong field distribution at small angles from the particle’s direction of travel, which can result in considerable change in momentum when approaching a conducting or charged object. We study these dynamics using protons and electrons at relativistic energies passing through apertures in conducting surfaces, where substantial energy shifts are observed for particles passing within roughly 10μm of the aperture boundary.We also simulate breaking a test particle’s line of sight with a conductor or other charged body. After this instant, the test particle continues to accelerate due to residual fields, but no longer produces an opposing force on any charged or conducting object; thus any recoil on the enclosing structure is effectively reduced. In this test, a 1% energy gain is observed for an 85MeV electron traversing its reflected wake after having conducting plate in its path screened by a dielectric object.We then incorporate a micro-scale dielectric laser acceleration (DLA) device into our simulations. Compared with a 2 mm DLA on its own, we find a factor of two increase in energy gain when adding a series of conducting-surface choppers.

On the effect of the maximal proper acceleration in the inertia

The effect of a hypothetical maximal proper acceleration on the mass of a charged particle is investigated in the context of particle accelerators. In particular, it is shown that maximal proper acceleration implies an increase in the kinetic energy of the particle being accelerated with respect to the relativistic energy. Such an increase in kinetic energy leads to a reduction of the luminosity of the bunches with respect to the expected luminosity in the relativistic models of the bunches. This relative loss in luminosity is of the order 10 −3 to 10 −5 for the Large Hadron Collider (LHC) bunches and can be of order up to 10 −3 for certain laser-plasma accelerator facilities. Although the effect is small, it increases with the square of the bunch population.

Latitudinal Mapping of Chorus Waves Growth Rates Based on Multi‐Spacecraft Wave and Plasma Measurements

AbstractWhistler mode chorus waves are one of the most intense and important electromagnetic emissions in the Earth's radiation belt, where these waves are responsible for electron acceleration to relativistic energies and for energetic electron precipitation into the Earth's atmosphere. This study reports a unique multi‐spacecraft observation event that allowed for the first time to verify theoretical models of chorus wave generation. The growth rates derived from the multi‐spacecraft observations of chorus waves Cluster WBD electric field waveforms collected during the crossing of the equatorial source region were compared to the theoretical linear and nonlinear growth rates calculated using simultaneous PEACE electron measurements. We have revealed that the growth rate estimated from wave measurements is substantially higher than the estimated linear growth rate but is quite close to the estimated nonlinear growth rate. A notable wave amplification is found up to 5 degrees of magnetic latitude and higher.

Deformation probes for light nuclei in their collisions at relativistic energies

Deformation probes for light nuclei in their collisions at relativistic energies

Energy spectra with the Dirac equation of the q-deformed generalized Pöschl-Teller potential via the Feynman approach for .

The diatomic molecules of potassium is widely used in industrial chemicals and alternative energy. Besides that, is very useful for researching molecular interactions and energy states, especially in the context of quantum chemistry and spectroscopy. In the present work, a newly proposed diatomic potential model within relativistic and non-relativistic quantum mechanics has been considered, to obtain corresponding energy eigenvalues and related normalized eigenfunctions. The Dirac equation has been solved for an arbitrary spin-orbit quantum number using the path integral technique with the -deformed generalized Pöschl-Teller potential . By including a Pekeris-type approximation to handle the centrifugal factor, it was possible to obtain the spin and pseudospin-symmetric solution of the relativistic energy eigenvalues and wave equation. To assess the correctness of this work, Maple software was used to present some numerical findings for various values of and . With the constraint , it was shown that in the situation of pseudospin symmetry, only bound states exist with negative energy. In the non-relativistic limits, the non-relativistic ro-vibrational energy expression of the diatomic molecule is derived from the relativistic energy equation under spin symmetry. Under Varshni conditions, both vibrational and ro-vibrational energies of the molecule were computed and compared with the data. The average absolute percentage deviations from the data obtained for the potassium molecule are . This demonstrates that the model is a very consistent model to study and characterize diatomic molecules.

Fully relativistic energies, transition properties, and lifetimes of lithium-like germanium

Abstract Employing two fully relativistic methods, the multi-reference configuration Dirac–Hartree–Fock (MCDHF) method and the relativistic many-body perturbation theory (RMBPT) method, we report energies and lifetime values for the lowest 35 energy levels of the (1s2)nl configurations (where the principal quantum number n = 2–6 and the angular quantum number l = 0, …, n–1) of lithium-like germanium (Ge XXX), as well as complete data on the transition wavelengths, radiative rates, absorption oscillator strengths, and line strengths between the levels. Both the allowed (E1) and forbidden (magnetic dipole M1, magnetic quadrupole M2, and electric quadrupole E2) ones are reported. The results from the two methods are consistent with each other and align well with previous accurate experimental and theoretical findings. We assess the overall accuracies of present RMBPT results to be likely the most precise ones to date. The present fully relativistic results should be helpful for soft x-ray laser research, spectral line identification, plasma modeling and diagnosing. The datasets presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00113.00135.

Non-relativistic and relativistic energy of molecules in external fields with time-dependent moving boundaries

Non-relativistic and relativistic energy of molecules in external fields with time-dependent moving boundaries

Evidence of a New Population of Weak Terrestrial Gamma‐Ray Flashes Observed From Aircraft Altitude

AbstractTerrestrial Gamma‐ray Flashes (TGFs) are ten‐to‐hundreds of microsecond bursts of gamma‐rays produced when electrons in strong electric fields in thunderclouds are accelerated to relativistic energies. Space instruments have observed TGFs with source photon brightness down to ∼1017–1016. Based on space and aircraft observations, TGFs have been considered rare phenomena produced in association with very few lightning discharges. Space observations associated with lightning ground observations in the radio band have indicated that there exists a population of dimmer TGFs. Here we show observations of TGFs from aircraft altitude that were not detected by a space instrument viewing the same area. The TGFs were found through Monte Carlo modeling to be associated with 1015–1012 photons at source, which is several orders of magnitude below what can be seen from space. Our results suggest that there exists a significant population of TGFs that are too weak to be observed from space.

Quantum geometric perspective on the origin of quantum-conditioned curvatures

Abstract The quantization of the gravitational field, which includes the metric field, has been investigated using various methods such as loop quantum gravity, quantum field theory, and string theory. Nevertheless, an alternative strategy to tackle the challenge of merging the fundamentally different theories of general relativity (GR) and quantum mechanics (QM) is through a quantum geometric approach. This particular approach entails extending QM to relativistic energies and finite gravitational fields, while also expanding the continuous Riemann to a discretized (quantized) Finsler-Hamilton geometry. By embracing this method, it may be feasible to bridge the gap between GR and QM or even achieve their unification. The resulting fundamental tensor appears to blend its original classical and quantum characteristics, effectively integrating quantum-mechanically induced revisions to the affine connections and spacetime curvatures. Our study primarily focuses on investigating the Ricci curvature tensor in the context of the Einstein-Gilbert-Straus metric. By employing both analytical and numerical methods, we have identified quantum-conditioned curvatures (QCC) that act as additional sources of gravitation. These QCC exhibit a fundamental difference from the traditional curvatures described by Einsteinian GR. While the Ricci curvatures are predominantly positive across most regions, the quantized Ricci curvatures display negativity. We conclude that the QCC a) possess an intrinsic, essential, and real character, b) should not be disregarded due to their significant magnitude, and c) are fundamentally different from the curvatures found in classical GR. Moreover, we conclude that the proposed quantum geometric approach may offer an alternative mathematical framework for understanding the emergence of quantum gravity.

Special Relativity, Mass, and Energy; E=mc2

The purpose of this paper to provide a proof of &amp;nbsp;using a derivation completely consistent with Special Relativity. We base our proof on the calculation of the relativistic kinetic energy, K, and the invariance of the momentum 4-vector in Minkowski space. This proof provides a useful pedagogical method for teaching the momentum 4-vector through an excellent example to undergraduate physics students.

Three-Dimensional Lorentz-Invariant Velocities

Lorentz invariance underlies special relativity, and the energy formula and relative velocity formula are well known to be invariant under a Lorentz transformation. Here, we determine the functional forms in terms of four arbitrary functions for those three dimensional velocity fields that are automatically invariant under the most general fully three-dimensional Lorentz transformation. For general three-dimensional motion, using rectangular Cartesian coordinates (x,y,z), we determine the first-order partial differential equations for the three velocity components u(x,y,z,t), v(x,y,z,t) and w(x,y,z,t) in the x−, y− and z−directions respectively. These partial differential equations and the associated partial differential relations connecting energy and momentum are fully compatible with the Lorentz-invariant energy–momentum relations and appear not to have been given previously in the literature. We determine the spatial and temporal dependence of the functional forms for those three-dimensional velocity fields that are automatically invariant under three-dimensional Lorentz transformations. An interesting special case gives rise to families of particle paths for which the magnitude of the velocity is the speed of light. This is indicative of the abundant possibilities existing in the “fast lane”.

Elucidate the non-relativistic and relativistic energy density functional from momentum space to coordinate space within local density approximation

Elucidate the non-relativistic and relativistic energy density functional from momentum space to coordinate space within local density approximation

Dirac fermions in a spinning conical Gödel-type spacetime

Abstract In this paper, we determine the relativistic and nonrelativistic energy levels for Dirac fermions in a spinning conical G&amp;amp;amp;ouml;del-type spacetime in (2+1)-dimensions, where we work with the Dirac equation in polar coordinates and we use the tetrads formalism. Solving a second-order differential equation for the two components of the Dirac spinor, we obtain a generalized Laguerre equation, and the relativistic energy levels, where such levels are quantized in terms of the quantum numbers n and m j, and explicitly depends on the spin parameter s, spinorial parameter u, curvature and rotation parameters α and β, and on the vorticity parameter Ω. In particular, the quantization is a direct result of the existence of Ω (i.e., Ω acts as a kind of ``external field or potential''). We see that for m j&gt;0, the energy levels do not depend on s and u; however, depend on n, m j, α, and β. In this case, α breaks the degeneracy of the energy levels and such levels can increase infinitely in the limit 4Ωβ/α→1. Already for m j&lt;0, we see that the energy levels depend on s, u and n; however, it no longer depends on m j, α and β. In this case, it is as if the fermion ``lives only in a flat Gödel-type spacetime''. Besides, we also study the low-energy or nonrelativistic limit of the system. In both cases (relativistic and nonrelativistic), we graphically analyze the behavior of energy levels as a function of Ω, α, and β for three different values of n.