Search Results (38)

We present a comprehensive general relativistic analysis of the Lemaître–Tolman–Bondi (LTB) metric, incorporating a cosmological constant $\mathrm{\Lambda }$ and a central pointlike mass $M_{\mathrm{d}}$ at the geometric origin. Within this framework, $M_{\mathrm{d}}$ is identified as the material source of dark matter in cosmology, yielding a scale-dependent total matter–density parameter ${\mathrm{\Omega }}_{\mathrm{m}}\left(L\right)$ characterized by an $L^{-3}$ decay of its dark component ${\mathrm{\Omega }}_{\mathrm{d}}\left(L\right)$. We demonstrate that the Hubble and $S_8$ tensions are not independent anomalies but interconnected consequences of spacetime inhomogeneity. These discrepancies arise from a combination of physical and methodological factors: the probing of radial gradients at different characteristic scales and the subsequent interpretation of these data through a global FLRW template. This approach, compounded by the practice of isotropic sky averaging, masks the underlying LTB geometry and converts the physical variation of the manifold into the observed cosmological tensions. Our framework provides a self-consistent geometric explanation for current anomalies while preserving the Copernican principle, identifying the crisis in cosmology as arising from the application of homogeneous models to a manifold characterized by radial gradients and scale-dependent dynamics, where the observer and probes reside within the same inhomogeneous regime. Full article

The Atomic Clock Ensemble in Space (ACES) mission, currently operating aboard the International Space Station (ISS), is designed to provide high-precision time and frequency measurements and to test fundamental aspects of relativistic physics. Gravitational redshift (GRS), a fundamental prediction of General Relativity (GR), implies that clocks positioned at different gravitational potentials experience relative time dilation. Previous GRS experiments have focused primarily on microwave technologies, with negligible experimental coverage in the optical domain, particularly for ground-to-space links. Motivated by the European Laser Timing (ELT) experiment and the high-precision laser-cooled cesium clock aboard ACES, we introduce and evaluate an optical time-transfer method designed to achieve high-accuracy measurements of GRS. In the absence of actual ELT/ACES optical data, a high-fidelity numerical simulation framework was developed to assess the performance of this method. The framework incorporates representative ELT/ACES mission parameters, including the space-based cesium clock and the H-MASER clock located at the reference ground station, both providing frequency stability at the level of ${10}^{-15}$ for 1000 s averaging time. Applying a $\pm 1\sigma$ filtering criterion, we obtain a simulated dataset comprising 33 ELT/ACES passes, representing a total observation time of 4.38 h over a single week. Analysis of this high-fidelity dataset reveals a GRS deviation from GR of $(-7.19\pm 0.63)\times {10}^{-5}$, achieving a 3.4 orders of magnitude improvement over the best previous laser-ranging experiment conducted at the University of Maryland (UMD), USA, 51 years ago. These simulation results demonstrate that the optical time-transfer link constitutes a powerful tool for testing fundamental physics and, when combined with next-generation optical atomic clocks, enables unprecedented capabilities in space-based timekeeping and geoscience applications. Full article

Auger decay of all levels of the double core-hole states $4d^{-2}$ of Xe²⁺, including collective Auger decay (CAD) pathways, is investigated using the relativistic distorted-wave approximation. Large-scale configuration interaction calculations were performed to obtain level-to-level Auger decay rates. In addition to the typical Auger decay final levels associated with the configurations of $4d^{-1}5s^{2}5p^4$, $4d^{-1}5s^{1}5p^5$, and $4d^{-1}5s^{0}5p^6$, evident contributions are identified from excited channels, leading to configurations such as $4d^{9}4f^{1}5s^{2}5p^3$, $4d^{9}5s^{2}5p^{3}5d^1$, $4d^{9}5s^{2}5p^{3}6s^1$, and $4d^{9}5s^{2}5p^{3}6p^1$. These contributions arise from strong electron correlation between the valence electronic orbitals and the $4d$ inner-shell orbital. The CAD rates and branching ratios (BRs) are determined for each double core-hole level with a minimum CAD BR of 1.28% and a maximum of 4.08% among all CAD channels. The configuration-averaged CAD BR is predicted to be 1.93%, which helps explain recent unexplained experimental findings. The inclusion of CAD processes enriches Auger electron spectroscopy, thereby extending potential applications of this important experimental tool in both fundamental and applied research. Full article

The often used analytical representation of the Maxwell–Boltzmann classical speed distribution function (F) for elastic, indivisible particles assumes an infinite limit for the speed. Consequently, volume and the number of particles (n) extend to infinity: Both infinities contradict assumptions underlying this non-relativistic formulation. Finite average kinetic energy and temperature (T) result from normalization of F removing n: However, total energy (i.e., heat of the collection) remains infinite because n is infinite. This problem persists in recent adaptations. To better address real (finite) systems, wherein T depends on heat, we generalize this one-parameter distribution (F, cast in energy) by proposing a two-parameter gamma distribution function (F*) in energy which reduces to F at large n. Its expectation value of kT (k = Boltzmann’s constant) replicates F, whereas the shape factor depends on n and affects the averages, as expected for finite systems. We validate F* via a first-principle, molecular dynamics numerical model of energy and momentum conserving collisions for 26, 182, and 728 particles in three-dimensional physical space. Dimensionless calculations provide generally applicable results; a total of 10⁷ collisions suffice to represent an equilibrated collection. Our numerical results show that individual momentum conserving collisions in three-dimensions provide symmetrical speed distributions in all Cartesian directions. Thus, momentum and energy conserving collisions are the physical cause for equipartitioning of energy: Validity of this theorem for other systems depends on their specific motions. Our numerical results set upper limits on kinetic energy of individual particles; restrict the n particles to some finite volume; and lead to a formula in terms of n for conserving total energy when utilizing F* for convenience. Implications of our findings on matter under extreme conditions are briefly discussed. Full article

This study investigates the masses and quadrupole deformations of even-Z nuclei within the range $8⩽Z⩽104$ using the triaxial relativistic Hartree–Bogoliubov model (TRHB) with the PC-PK1 density functional. For odd-mass nuclei, the global minima were determined using the automatic blocking method and their dynamical correlation energies (DCEs) were approximated using the average values of neighboring even–even nuclei calculated from a microscopic, five-dimensional, collective Hamiltonian (5DCH). The mean-field results underestimate the binding energies of most open-shell nuclei, with an initial root–mean–square (rms) deviation of 2.56 MeV for 1223 even-Z nuclei. Incorporating DCEs significantly reduces this deviation to 1.36 MeV. Additionally, the descriptions of two-neutron and one-neutron separation energies are improved, with rms deviations decreasing to 0.75 MeV and 0.65 MeV, respectively. Further refinement through accounting for odd–even differences in DCEs reduces the rms deviations for binding energies and one-neutron separation energies to 1.30 MeV and 0.63 MeV, respectively. Regarding the quadrupole deformations, TRHB calculations reveal spherical shapes near shell and subshell closures, well-deformed shapes at the mid-shell, and rapid shape transitions in medium- and heavy-mass regions. Oblate shapes dominate in regions $(Z,N)\sim (14,14),(34,36)$, and $(40,60)$, and the neutron-deficient Pb region, with notable odd–even shape staggering attributed to the blocking effect of the odd nucleon. Triaxial shapes are favored in the mass regions $(Z,N)\sim (60,76)$ and $(76,116)$. Full article

We present an economical approach to treat spin–orbit coupling (SOC) in the state-averaged driven similarity renormalization group second-order perturbation theory (SA-DSRG-PT2). The electron correlation is first introduced by forming the SA-DSRG-PT2 dressed spin-free Hamiltonian. This Hamiltonian is then augmented with the Breit–Pauli Hamiltonian and diagonalized using spin-pure reference states to obtain the SOC-corrected energy spectrum. The spin–orbit mean-field approximation is also assumed to reduce the cost associated with the two-electron spin–orbit integrals. The resulting method is termed BP1-SA-DSRG-PT2c, and it possesses the same computational scaling as the non-relativistic counterpart, where only the one- and two-body density cumulants are required to obtain the vertical transition energy. The accuracy of BP1-SA-DSRG-PT2c is assessed on a few atoms and small molecules, including main-group diatomic molecules, transition-metal atoms, and actinide dioxide cations. Numerical results suggest that BP1-SA-DSRG-PT2c performs comparably to other internally contracted multireference perturbation theories with SOC treated using the state interaction scheme. Full article

The problem posed in this study is to determine the density distribution within an ideal spherically symmetric neutron star based on only two constraints: the volumetrically averaged density and a moment of inertia factor, f. In order to deal with the above, it is recognized that space within these objects is heavily curved, and thus lengths, densities, and the moment of inertia have to be adjusted for relativistic effects. For the first time, the minimum relative entropy methodology (MRE) is used to find the expected value of a series of effective densities within a neutron star. In numerical experiments, we use the data from the star PSR J0737-3039A, which has a mass of $2.6\times {10}^{30}$ kg and a radius of 13.75 km. Here, the factor f is based on a range of values of moments of inertia (MOI): 1.30–1.63 $\times {10}^{45}$ g cm². For $f=0.324$, at no time do densities cross over $1\times {10}^{15}$ gm/cc. For the most part, densities > $6\times {10}^{14}$ gm/cc are shown at radial dimensions of less than about 4 km. When $f=0.258$, densities closer to the core are pushed higher, as one might expect, and peak at slightly over $4\times {10}^{15}$ gm/cc. If recent values of MOI are more appropriate at $1.15\times {10}^{45}$ g cm², this then suggests core densities greater than $4\times {10}^{15}$ gm/cc. These various density models lead to quantitative statements about qualitative interpretations, and as time goes on, any internal density models should satisfy the two constraints posed. Also, since the model presented here is probabilistic, it can be established that density at a certain depth is constrained within a certain confidence limit. The expected values of densities for PSR J0737-3039A are in reasonable agreement with current conceptual neutron star models but are highly sensitive to assumed MOI values. It is emphasized that the probabilities and the mean values of density obtained are conditional on the imposed moments, namely, $\mathcal{M}$ and f, and also the radius $\mathcal{R}$. Full article

This review article provides the basics and discusses some important applications of thermal field theory, namely, the combination of statistical mechanics and relativistic quantum field theory. In the first part, the fundamentals are covered: the density matrix, the corresponding averages, and the treatment of fields of various spin in a medium. The second part is dedicated to the computation of thermal Green’s function for scalars, vectors, and fermions with path-integral methods. These functions play a crucial role in thermal field theory as explained here. A more applicative part of the review is dedicated to the production of particles in a medium and to phase transitions in field theory, including the process of vacuum decay in a general theory featuring a first-order phase transition. To understand this review, the reader should have good knowledge of non-statistical quantum field theory. Full article

The semi-inclusive cross-section of two-nucleon emission induced by neutrinos and antineutrinos is computed by employing the relativistic mean field model of nuclear matter and the dynamics of meson-exchange currents. Within this model, we explore a factorization approximation based on the product of an integrated two-hole spectral function and a two-nucleon cross-section averaged over hole pairs. We demonstrate that the integrated spectral function of the uncorrelated Fermi gas can be analytically computed, and we derive a simple, fully relativistic formula for this function, showcasing its dependency solely on both missing momentum and missing energy. A prescription for the average momenta of the two holes in the factorized two-nucleon cross-section is provided, assuming that these momenta are perpendicular to the missing momentum in the center-of-mass system. The validity of the factorized approach is assessed by comparing it with the unfactorized calculation. Our investigation includes the study of the semi-inclusive cross-section integrated over the energy of one of the emitted nucleons and the cross-section integrated over the emission angles of the two nucleons and the outgoing muon kinematics. A comparison is made with the pure phase-space model and other models from the literature. The results of this analysis offer valuable insights into the influence of the semi-inclusive hadronic tensor on the cross-section, providing a deeper understanding of the underlying nuclear processes. Full article

Finding affine parameters for null geodesics is often of considerable physical importance, especially when studying null geodesics or dealing with conservation laws and/or averaged energy conditions. But explicitly finding null affine parameters is also often quite tedious and can sometimes even be somewhat tricky. Herein we shall demonstrate that the existence of a conformally related spacetime containing a conformal Killing vector, timelike in the domain of outer communication, is quite sufficient to define a preferred set of spatial three-slices—on which a well-defined “affine” three-metric can be introduced to capture the notion of affine null parameter—before explicitly finding the null geodesics. The construction depends on the properties of conformal transformations and on the conserved quantity associated with the conformal Killing vector. Having the affine null parameter in hand before attempting to find the actual null geodesics often quite radically simplifies other parts of the analysis. We emphasize that the successful identification of affine null parameters is a general-purpose tool of wide applicability in both general relativistic and astrophysical settings. Full article

We introduce a method for consistently incorporating meson-exchange currents (MEC) within the superscaling analysis with relativistic effective mass, featuring a new scaling variable, ${\psi }^{*}$, and single-nucleon cross-sections derived from the relativistic mean field (RMF) model of nuclear matter. The single-nucleon prefactor is obtained from the 1p1h matrix element of the one-body current, combined with the two-body current, averaged over a momentum distribution of Fermi kind. The approach is applied to selected quasielastic cross-sectional data on ${}^{12}$C. The results reveal a departure from scaling behavior, yet, intriguingly, the data collapse into a discernible band that is parametrized using a simple function of ${\psi }^{*}$. This calculation, as developed, is not intended to provide pinpoint precision in extracting nuclear responses. Instead, it offers a global description of the quasielastic data with a considerable level of uncertainty. However, this approach effectively captures the overall trends of the quasielastic data beyond the Fermi gas model with a minimal number of parameters. The model incorporates partially transverse enhancement of the response, as embedded within the relativistic mean field framework. However, it does not account for enhancements attributed to the combined effects of tensor correlations and MEC, given that the initial RMF model lacks these correlations. A potential avenue for improvement involves starting with a correlated Fermi gas model to incorporate additional enhancements into single-nucleon responses. This study serves as a practical demonstration of implementing such corrections. Full article

The analysis and measurement of Wigner time delays can provide detailed information about the electronic environment within and around atomic and molecular systems, with one the key differences being the lack of a long-range potential after a halogen ion undergoes photoionization. In this work, we use relativistic random-phase approximation to calculate the average Wigner delay from the highest occupied subshells of the atomic pairings (2p, 2s in Fluorine, Neon), (3p, 3s in Chlorine, Argon), (4p, 4s, 3d, in Bromine, Krypton), and (5p, 5s, 4d in Iodine, Xenon). The qualitative behaviors of the Wigner delays between the isoelectronic pairings were found to be similar in nature, with the only large differences occurring at photoelectron energies less than $20 \mathrm{e}\mathrm{V}$ and around Cooper minima. Interestingly, the relative shift in Wigner time delays between negatively charged halogens and noble gases decreases as atomic mass increases. All atomic pairings show large differences at low energies, with noble gas atoms showing large positive Wigner delays, while negatively charged halogen ions show negative delays. The implications for photoionization studies in halide-containing molecules is also discussed. Full article

3D shape generation is widely applied in various industries to create, visualize, and analyse complex data, designs, and simulations. Typically, 3D shape generation uses a large dataset of 3D shapes as the input. This paper proposes a variational autoencoder with a signed distance function relativistic average generative adversarial network, referred to as 3D-VAE-SDFRaGAN, for 3D shape generation from 2D input images. Both the generative adversarial network (GAN) and variational autoencoder (VAE) algorithms are typical algorithms used to generate realistic 3D shapes. However, it is very challenging to train a stable 3D shape generation model using VAE-GAN. This paper proposes an efficient approach to stabilize the training process of VAE-GAN to generate high-quality 3D shapes. A 3D mesh-based shape is first generated using a 3D signed distance function representation by feeding a single 2D image into a 3D-VAE-SDFRaGAN network. The signed distance function is used to maintain inside–outside information in the implicit surface representation. In addition, a relativistic average discriminator loss function is employed as the training loss function. The polygon mesh surfaces are then produced via the marching cubes algorithm. The proposed 3D-VAE-SDFRaGAN is evaluated with the ShapeNet dataset. The experimental results indicate a notable enhancement in the qualitative performance, as evidenced by the visual comparison of the generated samples, as well as the quantitative performance evaluation using the chamfer distance metric. The proposed approach achieves an average chamfer distance score of 0.578, demonstrating superior performance compared to existing state-of-the-art models. Full article

The electron impact excitation and ionization processes are crucial for modeling the spectra of different astrophysical objects, from atmospheres of late-type stars to remnants of supernovae and up to the light emission from neutron star mergers, to name just a few. Despite their significance, however, little is known quantitatively about these processes for low- and medium-impact energies of, say, $E_{\mathrm{kin}}\lesssim 5000$ eV of the free incident electron. To further explore the role of impact excitation, we here expanded Jac, the Jena Atomic Calculator, to the computation of distorted wave collision strengths for fine-structure-resolved, as well as configuration-averaged transitions. While we excluded the formation of dielectronic resonances, these tools can be readily applied for ions with a complex shell structure and by including the major relativistic contributions to these strengths. Detailed computations of the collision strengths are shown and explained for the impact excitation of lithium- and chlorine-like ions. When compared with other, well-correlated methods, good agreement was found, and hence, these tools will support studies of effective collision strengths for a wide range of electron impact energies, levels, and ionic charge states. Full article

Behind succeeding measurements of anomalies in semileptonic decays at LHCb and several collider experiments hinting at the possible violation of lepton flavor universality, we undertake a concise review of theoretical foundations of the tree- and loop-level b-hadron decays, $b\to cl{\nu }_l$ and $b\to s{l}^{+}{l}^{-}$ along with experimental environments. We revisit the world averages for $R_{D\left(D^{*}\right)}$, $R_{K\left(K^{*}\right)}$, $R_{J/\psi }$, and $R_{{\eta }_c}$, for the semileptonic transitions and provide results within the framework of the relativistic independent quark model in addition to the results from model-independent studies. If the ongoing evaluation of the data of LHC Run 2 confirms the measurements of Run 1, then the statistical significance of the effect in each decay channel is likely to reach 5 $\sigma$. A confirmation of these measurements would soon turn out to be the first remarkable observation of physics beyond the Standard Model, providing a wider outlook on the understanding of new physics. Full article