Physical Sciences

Abstract: We consider quasi-one-dimensional (Q1D) continuous waves (CWs) in the two-dimensional (2D) optical system with the cubic-quintic nonlinearity and a Q1D potential trough. In the case of a smooth trough profile, we confirm the known modulational instability (MI) of Q1D CWs with the transverse structure corresponding to the 1D ground state (GS) in the potential trough, and demonstrate the MI of CWs with the dipole-mode (DM) transverse structure, corresponding to the lowest 1D excited state in the potential trough. The CWs of both GS and DM types remain nearly stable close to edges of their existence regions. Stable stationary states in the form of periodic chains of 2D solitons, trapped in the potential trough, are produced in a numerical form. The dynamics of the soliton chains excited by a localized kick is studied too. For the potential trough with the singular delta-functional profile, we find two species of exact analytical solutions for CWs, one of which is completely stable.

Abstract: The new approach is develop to determine the hyperfine structure of the rotationally excited 1s_µnℓ_e-states in the three-body helium-muonic ³He µ e and ⁴He µ e atoms. The formulas derived in this study allow one to determine the hyperfine structure splittings for an arbitrary rotationally excited 1s_µnℓ_e-state in the three-body helium-muonic atoms. We also created the new approximate method which can be used for fast numerical evaluations of the hyperfine structure splittings in the both 1s_µnp_e and 1s_µnd_e-states of the 3He µ e and 4He µ e atoms. Similar formulas were never produced in earlier studies.

Abstract: We reformulate matrix mechanics by incrementally heating a single hydrogen atom in order to derive the complete, diagonalized Hamiltonian matrix. The spectral lines and transition probabilities cannot be generated by reversing time thereby demonstrating asymmetry. Experimental evidence in support of the theoretical model is obtained from experiments performed with the simplest quantum system, an electron cyclotron. Wave mechanics is also reformulated by altering the original Schrödinger equation describing a time symmetric, conservative system to a system of two independent equations describing a time asymmetric, non-conservative system.

Abstract: Critical binding of quantum states in Screened Coulomb Potentials such as Yukawa/Debye, Hulthén, and ECSC (Exponential Cosine Screened Coulomb) potentials is of perennial interest and relevance in many fields of science, ranging from nuclear and particle physics; plasma physics, astrophysics, cosmology, and nuclear fusion; physical chemistry, condensed matter, and materials physics; to synthetic nanostructures and nanophotonics. The purpose of this paper is to heuristically explore two related mysteries, one new, the other more than 50 years old. The solutions to these mysteries have implications for a much broader class of potentials, those addressed by Klaus and Simon. In our recent paper [1], we presented numerical calculations using the Phase Method (PM), accurate to 60 digits and to screening lengths D ≤ 10³ au, l = 0–20, of the critical binding parameters for these potentials; an for Yukawa and ECSC, l = 0–12, to D ≤ 10⁵ au, at 30 digits. In doing so, we discovered anomalous period-40 sawtooth structure in the critical parameters of the ECSC potential that is not observed for the Yukawa potential. In this second paper, we quantitatively explain the origin and periodicity of this newly discovered structure. To do so, we use two complementary approaches: a “neoclassical” (NC) variant of conventional semiclassical phase space quantization; and the PM for very precise fullyquantum calculations. The observed period-40 sawtooth structure is quantitatively explained in terms of a novel “tick-tock” mechanism. The periodicity is calculated in terms of the ratio of phase-space integrals for the primary and secondary potential wells. A quartic double-well potential is used as a simple model to further illustrate the tick-tock mechanism. Using NC, an approximate expression is derived to predict the locations of tick-tock glitches from higher order wells; it is confirmed by a PM calculation up to D ≤ 10⁶ au. The second mystery is a strangely linear dependence of the total number of bound states vs screening length for both the Yukawa and ECSC potentials. Using the PM we confirm and extend these empirical relations. We show using the PM that an approximate trivariate linear relation between the square root of the critical screening length √D_c, state number n, and angular momentum l applies to these potentials. This, plus a geometrical state accumulation argument solve the second mystery. We show these properties derive from the scaling relation between screening length and coupling constant, and as such are predicted to be applicable to the whole class of potentials. These results are expected to be of both theoretical interest and experimental relevance when interpreting spectra or calculating thermal properties. The significance of these results, and the applicability of these methods and conclusions to a vast array of related potentials is briefly discussed. Tables of critical screening parameters for Yukawa, Hulthén and ECSC D ≤ 10⁵ and l = 0 − 12 are posted as supplementary data.

Abstract: We present new and improved calculations of Stark-broadened profiles for ionized helium, a key ingredient in the spectroscopic analysis of helium-atmosphere DO white dwarfs. Our approach builds upon the computer simulation framework previously developed for neutral helium, which fully accounts for the dynamical interactions of both ions and electrons with the emitting helium atom. We extend this theoretical formalism by relaxing the assumption of straight-line trajectories for the perturbing particles (electrons and ionized helium) and adopting the hyperbolic trajectories appropriate for their interaction with a charged emitter, thereby accounting for their dynamical influence on the line-broadening process. In this exploratory study, we focus on the He II λ4686 line, the strongest absorption feature observed in the spectra of DO white dwarfs. We present the resulting Stark profiles and perform a detailed comparison with those available in the literature.

Abstract: Electron configurations are known to provide (valuable) insights into the electronic structure and behavior of atoms. They specify which and how the electronic (sub-) shells are occupied, and is thus an essential ingredient for most atomic observables. When combined with the shell model and the successive filling of shells, these configurations help explain the Periodic Table and much of chemical binding. They also establish a qualitative framework for analyzing excitation, ionization and relaxation processes and may facilitate–a wide range of–astrophysical and plasma simulations. — Here, we review the role of electron configurations for understanding atomic behavior in interactions with particles and radiation. In particular, we identify several central requirements for an efficient treatment of configuration lists and define a domain-specific language in order to generate, manipulate and analyze such lists as well as to extract physically relevant information. We also demonstrate the implementation of this language in Jac, the Jena Atomic Calculator. An efficient handling of configurations will refine the coupling of structure codes with the spectral synthesis of plasma radiation, the setup of ionic cascades or even non-LTE plasma simulations. This common framework for dealing with electron configurations therefore improves consistency, reproducibility and scalability of atomic modeling.

Abstract: We present a theoretical study focused on the photoelectron spectrum of near-infrared (NIR) laser-driven ionization of hydrogen atoms by attosecond pulse trains composed of several high-order harmonics of the former. We analyze the effects of increasing the intensity of the NIR probe laser to account for the interference of multiple quantum pathways arising from mainbands formed in ionization by the attosecond pulse train within the strong-field approximation (SFA) beyond the commonly used first-order perturbative (in the NIR laser intensity) reconstruction of attosecond beating by interference of two-photon transitions (RABBIT). The structure of the energy bands formed in the photoelectron spectrum is governed by quantum interferences of the photoelectron wave packet released within one optical cycle of the NIR probe laser field –intracycle interference– and by the number of active high harmonic components, leading to higher-order Fourier contributions as a function of the NIR–XUV relative phase delay. Our results demonstrate a significant departure from the standard two-path quantum-interference RABBIT picture, showing that both the phase-dependent oscillations of mainbands and sidebands and the extracted phase delays depend strongly on the probing laser intensity. The predictions of the SFA reveal that the above-threshold ionization bands exhibit systematic splitting and oscillation patterns as a function of the NIR intensity. SFA predictions are compared with results obtained within ab initio solutions of the time-dependent Schrödinger equation (TDSE), showing an excellent agreement, which evidences that the negligible effect of the Coulomb potential of the remaining ion on the escaping photoelectron for high energy above-threshold ionization. These findings provide new insights into attosecond chronoscopy in the strong-field regime.

Abstract: Classical subatomic particles simulations were applied to protons, neutrons and electrons to simulate a complete atom using pseudo potentials to simulate nucleus and electrons distributed around nucleus. Molecular dynamics algorithms were applied to subatomic particles to simulate a complete atom for Hydrogen, Carbon and Uranium atoms that were reported in previous studies. Further analysis of energies of Carbon atom reveals that atom has quantized discrete energy values rather than continuous energies as expected in classical simulations. Changes in atom's total energy were observed to be in step changes going to higher/lower energy states and energy values are observed to be in quantized rather than continuous. Electrons energy profiles was observed during the atom's quantum energy shifts and only one electron got affected that has step change in its energies, for short duration, leaving other electrons unaffected. To observe similar phenomenon in other atoms, Fluorine, Magnesium and Chlorine atom were considered in this study and found to have similar quantized discrete energy values properties. This study implements subatomic particles simulations using classical mechanics that explains why atom's energies are quantized in nature as observed in discrete lines in atomic emission/absorption spectrum for atoms.

Abstract: A phenomenological geometrical model is presented for the hyperfine structure of hydrogenic systems. The approach extends a previously published fine-structure analysis to hyperfine splittings by introducing a compact set of empirically constrained geometric corrections. Unlike conventional quantum electrodynamic treatments which reference the Lamb shift to the hyperfine centroid, the present framework targets the hyperfine mid-point, corresponding to a substantially larger reference interval. Despite this difference in reference scale, agreement with experimental hyperfine and Lamb-shift-related data at the 0.01 MHz level is obtained across multiple hydrogen states. The model is further extended to deuterium, tritium, 3He⁺, and 7Li²⁺, revealing systematic cross-nuclear behaviour and a universal scaling relation involving nuclear mass number and charge. The calculations employ a simplified geometric scheme that does not rely on perturbative quantum electrodynamics but is intended as a complementary phenomenological description. Possible physical interpretations in terms of structured internal dynamics are discussed, together with limitations and directions for further development.

Abstract: String theory has long pursued a mechanism to compactify its extra dimensions into the observable physical constants of our universe, yet the vast landscape of ~10⁵⁰⁰ possible vacua remains unresolved. Our 4G Model Solution: The 4G Model introduces four interaction-dependent scalar gravitational constants (GN, Ge, Gn, Gw) as the practical bridge, deriving a fundamental 33 pm interaction length—the geometric mean of nuclear and electromagnetic gravity. This scale constrains atomic structure and nuclear radii via the empirical A¹/³ scaling law. Validation: The 4G Model’s fundamental scaling law (A¹/³ × 33 pm) predicts Carbon’s covalent radius at 75.6 pm-matching the experimental 75 pm value to under 1% error without the proposed common correction term. This precise agreement without corrections suggests that the geometric mean of nuclear and electromagnetic gravity [√(Gn*Ge)] may play a key role in atomic structure. Broader Deviations Contextualized: Secondary deviations in other groups stem from Z-dependent quantum screening of Ge and Gn, not flaws in the underlying scale- paralleling Bohr model successes for hydrogen before Sommerfeld’s fine-structure refinements addressed relativistic effects. Theoretical Confirmation: This selective precision affirms 4G’s unification: atomic radii emerge directly from string-like compactification geometry, with screening as tunable perturbations. Carbon’s validation anchors the model as a working hypothesis, indicating that gravitational constants could play a significant role in constraining chemistry at the 33 pm scale. Extension: Finally, by applying the proton’s charge‑mass “dual discreteness formalism,” we propose that atoms can be interpreted as quantum gravitational compact objects within this framework. These are structured into a hierarchy of 7 fundamental shells, dictated by the stability condition , n=1,2,3.., Z/Root(A) . Light magic numbers emerge from the integer values of Z/Root(A_stable) , while heavy magic numbers correspond to the half-integer form, [Z/Root(A_stable)+0.5].

Abstract: Electron collision broadening parameters calculations were performed for 33 singly ionized yttrium spectral lines, 27 with special relevance in astrophysical applications (can be found in the Atmospheres of FGK Stars). Calculations were made in the semi-empirical Griem approach using the Gaunt factors proposed by Van Regemorter and those proposed by Douglas H. Sampson. Furthermore, to test our calculations, the electron collision broadening of 4 well isolated spectral lines of Y II was experimentally measured in laser- induced breakdown experiments using a Q-switched Nd:YAG laser focused on Pb-Y alloy samples.

Abstract: The Theory of Inventive Problem Solving (TRIZ) has long been a cornerstone for systematic innovation in engineering domains, including chemical and materials science. This paper proposes a novel framework that integrates TRIZ principles with large language models (LLMs) to emulate researcher-like reasoning in atomistic materials science. By structuring LLM prompts around TRIZ tools—such as patterns of evolution, contradiction matrices, and inventive principles—we enable models to identify problems, frame contradictions, and generate inventive solutions for challenges like data scarcity, poor interpretability, and unphysical predictions in quantum-chemical simulations and machine learning (ML) models. Drawing on recent artificial intelligence-TRIZ hybrids, like AutoTRIZ and TRIZ-GPT (generative pre-trained transformer), we demonstrate applications in molecular design, such as resolving contradictions in shape-memory polymers. This approach not only amplifies current trends in physics-informed ML and generative design but also democratizes advanced problem-solving, accelerating discoveries toward ideality.

Abstract: Resonant transfer and excitation (RTE) is a correlated two-electron process mediated by the two-center electron-electron interaction: A projectile electron is excited while a target electron is captured, forming doubly excited states. These decay via X-ray (RTEX) or Auger (RTEA) emission. For fast enough collisions with light targets, RTE becomes analogous to dielectronic capture (DC)—a key plasma process—and is described by the impulse approximation (IA). Early (1983–1992) RTEX and the more stringent, state-selective RTEA measurements at accelerator facilities provided indirectly, essential DC cross section information before direct electron-ion DC measurements became available. The 1992 review [1], focusing on zero-degree Auger projectile spectroscopy (ZAPS) of state-selective KLL D states, validated the IA for low-Z_p ions (Z_p ≤ 9). However, a puzzling systematic discrepancy was revealed: IA cross sections were consistently larger than experiment, with the disagreement increasing as projectile atomic number Z_p decreased. This review updates RTEA progress since 1992: Refinements to IA calculations include the use of more accurate Auger rates, considerations of Auger anisotropic emission, novel target binding corrections and even an exact IA formulation. Experimental ZAPS improvements feature a hemispherical spectrograph and a proven in situ more accurate standardized absolute cross section calibration using binary encounter electrons. A methodical analysis demonstrates impressive agreement across all measurements spanning both pre- and post-1992 eras including measurements presented here for the first time, eliminating systematic discrepancies. IA validity is confirmed down to boron ions, with He⁺ ions as the sole clear exception together with some borderline Li-like ion cases. Recently, a rigorous ion-atom collision treatment has also emerged: Nonperturbative close-coupling calculations of transfer excitation of He-like ions in collisions with He confirms RTE dominance via two-center electron-electron interactions at large impact parameters, while providing unexpected insights into many-body collision dynamics at the lowest collision energies.

Abstract: N-dimensional simplices, apart of their highly symmetric properties, exhibit interesting properties, both in the structure of the coordinates of their vertices and in the uniform distances between pairs of them. Relationships of simplices with the vertices of dimensional hypercubes are also of interest. Discussing these facts in depth as an introduction, the present study examines the implications of the coordinate structure of simplices for the Theoretical and Quantum Mechanical formalism, applied to swarms of particles located at the vertices of a simplex. Also, the properties of the topological matrices that represent such a distance-conformation will be studied. Some interesting results arise from this analysis. Among others, a paradox about the existence of swarms of particles with dimensional simplex-vertex distance structure and the possibility of overcoming it, allowing the description of an dimensional description of the particles’ location. A brief discussion on the time-dependence of simplex coordinates is also provided.

Abstract: For nearly a century screened Coulomb potentials have been of recognized importance in diverse areas of physics and chemistry. A key feature of interest in these potentials is the phenomenon of critical screening. This paper has three main purposes: To present an extensive, open-access, high accuracy (60 digit) benchmark reference data set of critical screening parameters, with validation; to confirm excellent past work in the field (to 30 digits), and to correct an historical oversight in its literature; and to present the essentials of our new approach, the “Phase Method” (PM), for computing them. Using the PM we calculate critical screening parameters, accurate to 60 decimal digits, for the Yukawa/Debye, Hulthén, Pseudo-Hulthén, and Exponential Cosine Screened Coulomb (ECSC)) potentials. The practical feasibility of such calculations on inexpensive hardware opens up new possibilities in research and education. We highlight an apparently overlooked 1989 paper of Demiralp on critical screening parameters of the Yukawa potential, which accurately calculated them to 30 decimal digits. Our main results are computations of the critical screening parameters µ_c= 1/D_c for screening lengths D ≤ 1000 au and angular momenta l = 0 . . . 20. The claimed accuracy of our results is supported by several independent lines of evidence: comparison with the most accurate (30 digit) values available in the print literature for the Yukawa, Hulthén, and ECSC potentials; comparison to 60 decimal digits accuracy with exactly known eigenvalues and critical binding parameters of the Pseudo-Hulthén potential; consistency tests between computed critical parameters, for various l-values for the Pseudo-Hulthén Potential, and known exact relations between eigenvalues; and application of a novel consistency test between results with different potential parameters, that exploits an exact scaling symmetry of this entire class of potentials. Similar calculations were done for ECSC and Yukawa potentials for screening lengths up to D ≤ 10⁵ and l ≤ 12, to 30 digit accuracy, which show interesting (and to our knowledge not previously reported) periodic structure in D_c(n, l) for the ECSC potential that is not observed for the Yukawa potential. The asymptotic scaling behavior for the Yukawa and Hulthén potentials is explained quantitatively by simple semiclassical calculations.

Abstract: We propose a novel theoretical framework for describing photon--electron interactions and electron collision processes in a unified manner within quantum electrodynamics. Specifically, we develop a method to construct the Dirac operator in curved spacetime using only matrix representations rooted in the basis structure of four-dimensional gamma matrix algebra, without introducing vierbeins (tetrads) or independent spin connections. We realize 16 gamma matrices with two indices as $256\times256$ matrices and embed the spacetime metric directly into the matrix elements. This reduces geometric operations such as covariantization, connection-like operations, and basis transformations to matrix products and trace calculations, yielding a unified and transparent computational scheme. The spacetime dimension remains four, and the number ``16'' represents the number of basis elements of four-dimensional gamma matrix algebra ($2^{4}=16$). Based on the extended QED Lagrangian, vertex rules, propagators, spin sums, and traces can be handled uniformly, making it suitable for automation. As validation of this method, we analyzed four fundamental scattering processes in atomic and particle physics: (i) Compton scattering (photon--electron scattering), (ii) muon pair production ($e^+e^-\to\mu^+\mu^-$), (iii) M{\o}ller scattering (electron--electron collision), and (iv) Bhabha scattering (electron--positron collision). In the flat spacetime limit, we confirmed exact reproduction of standard quantum electrodynamics (QED) results including the Klein--Nishina formula. Furthermore, trial calculations using a metric with off-diagonal components show systematic deviations from flat results near scattering angle $\theta\approx90^{\circ}$, suggesting that metric-induced angular dependence could in principle serve as an observable signature. The matrix representation developed in this work enables unified pipeline execution of theoretical calculations for photon interactions and charged particle collision processes, with expected applications to precision calculations in atomic and particle physics.

Abstract: Reliable estimation of kinetic parameters in molecular dynamics (MD) requires distinguishing physical phenomena from numerical artifacts. Standard MD workflows often mask integration errors through empirical damping, potentially obscuring rare configurational transitions. We introduce a calibration framework employing intentionally conservative numerical parameters—including reduced timesteps (0.10 fs) and attenuated intermolecular forces—to establish a numerical fidelity baseline. This approach isolates integration artifacts from force-field complexities, providing a reference against which production MD methods can be benchmarked. By demonstrating stable integration under maximally challenging conditions, we provide a methodology for validating the numerical foundations of kinetic inference in drug discovery applications.

Abstract: This paper aims to provide a thorough critical analysis of two foundational concepts in modern physics — the Landé g-factor and the electron spin quantum number 1/2. Through meticulous historical examination and logical analysis, this paper argues that these concepts are essentially mathematical fitting parameters introduced to bridge the gap between the old quantum theory and experimental data, lacking a solid foundation in physical mechanism. The core contradiction lies in the subsequent development of wave mechanics, which concluded that "the orbital angular momentum of the hydrogen atom ground state is zero," a conclusion that fundamentally conflicts with observational facts such as the Stern-Gerlach experiment, forcing the spin concept to assume a "remedial" role it never needed to bear. As a solution, this paper presents a new framework based on the "Great Tao Model" and the "Unified Theory of Atomic and Molecular Structure." This framework firmly returns to the realism of classical physics, affirms the orbital motion of electrons around the nucleus and their intrinsic angular momentum, and interprets spin as a real mechanical motion. Crucially, this theory naturally derives the universal magnetic moment-angular momentum relation μ = (e/m) L from the "Existence Field" principle, eliminating the need for any artificial correction factors. Based on this, the paper successfully provides a unified and self-consistent explanation for key phenomena such as the Stern-Gerlach experiment and the normal and anomalous Zeeman effects, thereby achieving a simpler and more fundamental description of physics at the atomic scale.

Abstract: A program package for calculating regularized classical trajectories for Coulomb n−body problem is developed. The Coulomb singularities from the equations of motion are removed by transformations of variables including the time. This effectively conserves the energy of the time-independent systems to a high accuracy for long time propagation. Sample calculations are shown for the cases of 2,3,4, and 5 particle systems giving comparisons with the un-regularized trajectories. The program can be used for general purposes including the classical-trajectory Monte-Carlo simulations for charged-particle collisions in free or laser environments.

Abstract: Revealing the structure of atoms and molecules has always been one of the important research goals in the field of quantum mechanics. The currently well-known atomic and molecular structure theories include Rutherford's planetary model, Bohr Sommerfeld atomic structure model, as well as atomic orbital theory, hybrid orbital theory, and molecular orbital theory. However, although these theories can explain atomic or molecular structures to some extent, they all have their own shortcomings, and there is currently no unified theory of atomic and molecular structures established. Here, we propose the Dynamic Entity Model of Electron Orbits, the Electron Spin Theory, and the Spatial Configuration Theory of Electron Orbits. Based on these new concepts and theories, we rearranged the extranuclear electrons of all elements in the periodic table, and explained the structure of atoms, the physical mechanisms of molecular formation, and the spatial structure of molecules. The theories of atomic and molecular structures based on quantum mechanics are often complex, difficult to understand, and inconsistent, while our new concepts and theories are based on classical physics and have the characteristics of being simple, intuitive, and easy to understand, and can logically and consistently explain the structure of atoms and molecules. Therefore, we have established a unified atomic and molecular structure theory based on the framework of classical physics, which has important scientific significance and application value.