Multielectron Atoms Research Articles

Alchemical insights into approximately quadratic energies of iso-electronic atoms.

Accurate quantum mechanics based predictions of property trends are so important for material design and discovery that even inexpensive approximate methods are valuable. We use the alchemical integral transform to study multi-electron atoms and to gain a better understanding of the approximately quadratic behavior of energy differences between iso-electronic atoms in their nuclear charges. Based on this, we arrive at the following simple analytical estimate of energy differences between any two iso-electronic atoms, ΔE≈-(1+2γNe-1)ΔZZ̄. Here, γ ≈ 0.3766 ± 0.0020 Ha corresponds to an empirical constant, and Ne, ΔZ, and Z̄, respectively, to electron number, nuclear charge difference, and average. We compare the formula's predictive accuracy using experimental numbers and non-relativistic, numerical results obtained via density functional theory (pbe0) for the entire periodic table up to Radon. A detailed discussion of the atomic helium-series is included.

Atomic binding corrections for high-energy fixed target experiments

High-energy beams incident on a fixed target may scatter against atomic electrons. To a first approximation, one can treat these electrons as free and at rest. For precision experiments, however, it is important to be able to estimate the size of, and when necessary calculate, subleading corrections. We discuss atomic binding corrections to relativistic lepton-electron scattering. We analyze hydrogen in detail, before generalizing our analysis to multi-electron atoms. Using the virial theorem, and many-body sum rules, we find that the corrections can be reduced to measured binding energies, and the expectation value of a single one-body operator. We comment on the phenomenological impact for neutrino flux normalization and an extraction of hadronic vacuum polarization from elastic muon electron scattering at MUonE. Published by the American Physical Society 2024

Four-Dimensional Scaling of Dipole Polarizability: From Single-Particle Models to Atoms and Molecules.

Scaling laws enable the determination of physicochemical properties of molecules and materials as a function of their size, density, number of electrons or other easily accessible descriptors. Such relations can be counterintuitive and nonlinear, and ultimately yield much needed insight into quantum mechanics of many-particle systems. In this work, we show on the basis of single-particle models, multielectron atoms and molecules that the dipole polarizability of quantum systems is generally proportional to the fourth power of a characteristic length, computed from the ground-state wave function. This four-dimensional (4D) scaling is independent of the ratio of bound-to-bound and bound-to-continuum electronic transitions and applies to many-electron atoms when a correlated length metric is used. Finally, this scaling law is applied to predict the polarizability of molecules by electrostatically coupled atoms-in-molecules approach, obtaining approximately 8% absolute and relative accuracy with respect to hybrid density functional theory (DFT) on the QM7-X data set of organic molecules, providing an efficient and scalable model for the anisotropic polarizability tensors of extended (bio)molecules.

Wigner molecular crystals from multielectron moiré artificial atoms.

Semiconductor moiré superlattices provide a versatile platform to engineer quantum solids composed of artificial atoms on moiré sites. Previous studies have mostly focused on the simplest correlated quantum solid-the Fermi-Hubbard model-in which intra-atom interactions are simplified to a single onsite repulsion energy U. Here we report the experimental observation of Wigner molecular crystals emerging from multielectron artificial atoms in twisted bilayer tungsten disulfide moiré superlattices. Using scanning tunneling microscopy, we demonstrate that Wigner molecules appear in multielectron artificial atoms when Coulomb interactions dominate. The array of Wigner molecules observed in a moiré superlattice comprises a crystalline phase of electrons: the Wigner molecular crystal, which is shown to be highly tunable through mechanical strain, moiré period, and carrier charge type.

L- and M-subshell ionization cross-sections of heavy atoms by electron and proton impact

Inner-shell ionization has many applications related to material analysis. However, full theoretical calculations in heavy multielectronic atoms are scarce. In this contribution, we assess proton and electron impact Li and Mi-subshell ionization cross-sections of heavy targets (72≤Z≤83) using two theoretical models. These calculations are based on the Distorted Plane Wave Born Approximation for electron impact and the shellwise local plasma approximation for the proton impact, combined with relativistic calculations of these deep subshells wave functions and binding energies. We analyze the L-shell ionization of W, Au, and Bi and the M-shell of Hf, Ta, W, Re, Os, Pt, Au, Pb, and Bi. Present values are compared with available experimental data from the literature, with disparate agreement. The convergence of proton and electron impact cross-sections at high-impact velocities is also discussed.

Inner-shell ionization cross sections of atoms by positron impact

The relativistic binary-encounter-Bethe model with Wannier-type threshold law is employed to obtain the inner-shell ionization cross sections of multi-electron atoms (Ni, Cu, Y, Ag, Au, Yb, Ta, and Pb) for positron impact energies from the thresholds up to 105 keV. There is good agreement between the present calculations and the experimental data. The constant in the acceleration term derived from the Wannier law is determined to be 0.2 and 0.5 for the K- and L-shells, respectively.

Undergraduate students’ models of single- and multi-electron atoms

ABSTRACT Quantum physics forms the basis for exciting new technologies, including quantum computers, quantum encryption, and quantum entanglement. The advancement of science and technology highlights the importance of mastering quantum physics and its applications, not only at the college level but also as early as high school. In this multiple case study, we investigated first- and second-year undergraduate college students’ models of single and multi-electron atoms after completing a modern mechanics course, which addressed basic QM topics. The students’ models were categorised into four primary categories: the discrete entity (particle) model, hybrid model, quantum-like model, and quantum model, and subcategories for atom structure and electron attribution and motion. Despite being introduced to quantum concepts in high school and first-year undergraduate calculus-based physics classes, many students constructed incomplete, inaccurate, or incoherent models. Seven of eight students’ atomic structure models and six of eight students’ electron attribution and motion models were classified as discrete entity and hybrid models. The findings of this study reveal students’ conceptual challenges in explaining the structure of single and multiple-electron atoms and shed light on the factors contributing to the persistent difficulties in their understanding of atomic structure in the realm of quantum mechanics.

Dynamic effective charge in the continuum of the CDW-EIS model for ionization in ion–atom collisions: angular and energy dependence

In this work, a dynamic charge is employed in the continuum distorted wave–eikonal initial state theoretical model to describe the non-Coulomb potential of the residual target for single ionization in bare ion–multielectron atom collisions. A comparison between the well-known Belkić prescription and the effective charge depending on emission angle and energy in the final residual-target continuum state is shown. The obtained results show that this effective charge improves the description of double-differential cross sections for backward emission angles over the whole emission energy range allowing the calculation of simple differential and total cross sections.

Gauge Invariance of Quantum Electrodynamics of Multi-Electron Atoms

The proof of the gauge invariance of the quantum electrodynamics of photons and electrons does not apply directly to the quantum electrodynamics of photons, electrons, and nuclei, since the multi-electron atoms belong to the space of asymptotic states of the extended theory. We indicate two possible ways to circumvent this problem and prove, using a fairly general model for the description of nucleon–nucleon interaction in nuclei, the gauge invariance of the masses and electromagnetic form factors of multi-electron atoms in all orders of perturbation theory.

Convergent close-coupling calculations of positron scattering from atomic carbon

We report on the extension of the single-center convergent close-coupling method to positron scattering on multielectron atoms, along with the development of a technique for separating the direct ionization and positronium-formation channels in single-center calculations. We have performed calculations of positron scattering on carbon and present total elastic, momentum transfer, excitation, direct ionization, total ionization, total inelastic, positronium-formation, stopping power, and total cross sections from threshold to 5000 eV. We also present oscillator strengths, the scattering length, the hidden Ramsauer-Townsend minimum, the energy of the positron-carbon virtual state, and the mean excitation energy. Agreement with electron-scattering experiment and positron-scattering theory for several cross sections has been demonstrated for high energies. However, discrepancies exist between different theoretical methods at lower energies and for the ionization and positronium-formation processes.

Rigorous Negative Ion Binding Energies in Low-Energy Electron Elastic Collisions with Heavy Multi-Electron Atoms and Fullerene Molecules: Validation of Electron Affinities

Dramatically sharp resonances manifesting stable negative ion formation characterize Regge pole-calculated low-energy electron elastic total cross sections (TCSs) of heavy multi-electron systems. The novelty of the Regge pole analysis is in the extraction of rigorous and unambiguous negative ion binding energies (BEs), corresponding to the measured electron affinities (EAs) of the investigated multi-electron systems. The measured EAs have engendered the crucial question: is the EA of multi-electron atoms and fullerene molecules identified with the BE of the attached electron in the ground, metastable or excited state of the formed negative ion during a collision? Inconsistencies in the meaning of the measured EAs are elucidated and new EA values for Bk, Cf, Fm, and Lr are presented.

Многоуровневая модель многофотонных процессов в атоме гелия в сильном лазерном поле: учет ионизации

A multilevel model that makes it possible to describe multiphoton processes taking into account ionization in a multielectron atom irradiated by an intense laser field is proposed. Using the He atom as an example, it is shown that this model reproduces the main regularities of multiphoton ionization of an atom by an intense high-frequency laser field.

Modeling Hartree-Fock approximations of the Schrödinger Equation for multielectron atoms from Helium to Xenon using STO-nG basis sets

The energy of an atom is extremely useful in nuclear physics and reaction mechanism pathway determination but is challenging to compute. Thus, we aimed to synthesize regression models for Pople Gaussian expansions of Slater-type Orbitals (STO-nG) atomic energy vs. atomic number scatter plots to allow for easy approximation of atomic energies without using computational chemistry methods. Using the Hartree-Fock method, we calculated atomic energies for elements helium to xenon (He to Xe) using STO-nG electron orbital basis set models. After calculating atomic energies for each basis set, we plotted them as tables of atomic energy (in Hartrees) versus the atomic number. We hypothesized that there would be a non-linear correlation in the scatter plot. We first formed the regressions using data from helium to krypton (He to Kr), and then we added new data from Kr to Xe. We then calculated the old and new coefficients of determination, and the difference between them. Due to their common use in modeling, exponential, sinusoidal, and quadratic regressions were tested to model the data. The data supported the hypothesis that the scatter plots had non-linear correlations. Sinusoidal and quadratic regressions had higher initial coefficients, suggesting higher viability, while sinusoidal regressions also had the highest average final coefficients, and the lowest change in coefficients. The data indicated that of the three regressions, sinusoidal regressions most aptly modeled the scatter plots.

The universality of Rydberg constant is investigated with concern for ethics

Bearing in mind the unintended restriction of the Rydberg constant to atomic properties, there is a need to defend the universality of the Rydberg constant beyond atomic physics against the backdrop of the demands of ethics in research and publishing. The objectives of the research were:1) to show that the Rydberg constant is not just a composite fundamental physical constant applicable to the field of atomic physics but also nuclear matter physics; and 2) to examine the burning issues of the need for ethics in research, critique, or evaluation, and publishing. The methods were theoretical and calculational. The derivational and calculational results gave equations and values that were positive and verifiable; the calculation of the Rydberg constant using the derived equation after substituting the calculated mass radius of proton in this research and other literature values and the well-known physical constants reproduced the Rydberg constant to between 99.88 and 104.26 % of the 2016 CODATA value. Calculations based on charge radii from electron-proton scattering experiments produced results ranging from 72.53 to 75.34% of the CODATA value. Specifically, the calculation using the calculated mass radius of the proton in this research yielded approximately 1.096049145 exp. (+7)/m. Unethical behaviors in research, critique/evaluation review, and publishing were identified and discussed, and pieces of advice given accordingly. In conclusion, the universality of the Rydberg constant as a composite constant, applicable to both atomic and nuclear physics remains undisputable. The role of the Rydberg constant in the determination of periodic parameters of multi-electron atom is recommended for future research.

Relative energies without electronic perturbations via alchemical integral transform.

We show that the energy of a perturbed system can be fully recovered from the unperturbed system's electron density. We derive an alchemical integral transform by parametrizing space in terms of transmutations, the chain rule, and integration by parts. Within the radius of convergence, the zeroth order yields the energy expansion at all orders, restricting the textbook statement by Wigner that the p-th order wave function derivative is necessary to describe the (2p + 1)-th energy derivative. Without the need for derivatives of the electron density, this allows us to cover entire chemical neighborhoods from just one quantum calculation instead of single systems one by one. Numerical evidence presented indicates that predictive accuracy is achieved in the range of mHa for the harmonic oscillator or the Morse potential and in the range of machine accuracy for hydrogen-like atoms. Considering isoelectronic nuclear charge variations by one proton in all multi-electron atoms from He to Ne, alchemical integral transform based estimates of the relative energy deviate by only few mHa from corresponding Hartree-Fock reference numbers.

Calculation of high-order harmonic generation of atoms and molecules by combining time series prediction and neural networks.

High-order harmonic generation (HHG) from the interaction of ultra-intense laser pulses with atoms is an important tabletop short-wave coherent light source. Accurate quantum simulations of it present large computational difficulties due to multi-electron multidimensional effects. In this paper, the time-dependent response of hydrogen atoms is calculated using a time-series prediction scheme, the HHG spectrum is reconstructed very accurately. The accuracy of the forecasting is further improved by using a neural network scheme. This scheme is also applied to the simulation of the harmonic emission on multi-electron systems, and the applicability of the scheme is confirmed by the harmonic calculation of complex systems. This method is expected to simulate the nonlinear dynamic process of multi-electron atoms and molecules irradiated by intense laser pulses quickly and accurately.

Recent Progress in Low-Energy Electron Elastic-Collisions with Multi-Electron Atoms and Fullerene Molecules

We briefly review recent applications of the Regge pole analysis to low-energy 0.0 ≤ E ≤ 10.0 eV electron elastic collisions with large multi-electron atoms and fullerene molecules. We then conclude with a demonstration of the sensitivity of the Regge pole-calculated Ramsauer–Townsend minima and shape resonances to the electronic structure and dynamics of the Bk and Cf actinide atoms, and their first time ever use as novel and rigorous validation of the recent experimental observation that identified Cf as a transitional element in the actinide series.

ATOM Program System and Computational Experiment

The article is devoted to a brief description of the ATOM computer program system, designed to study the structure, transition probabilities and cross sections of various processes in multielectron atoms. The theoretical study was based on the concept of a computational experiment, the main provisions of which are discussed in the article. The main approximate methods used in the system of programs for taking many-electron correlations into account and determining their role in photoionization processes, elastic and inelastic electron scattering, the decay of vacancies, and many others are presented. The most significant results obtained with this software are listed.

On Semi-Classical Approach to Materials Electronic Structure

Materials atomic structure, ground-state and physical properties as well as their chemical reactivity mainly are determined by electronic structure. When first-principles methods of studying the electronic structure acquire good predictive power, the best approach would be to design new functional materials theoretically and then check experimentally only most perspective ones. In the paper, the semi-classical model of multi-electron atom is constructed, which makes it possible to calculate analytically (in special functions) the electronic structure of atomic particles themselves and materials as their associated systems. Expected relative accuracy makes a few percent, what is quite acceptable for materials science purposes.

How to Calculate Condensed Matter Electronic Structure Based on Multi-Electron Atom Semi-Classical Model

Atoms are proved to be semi-classical electronic systems in the sense of closeness of their exact quantum electron energy spectrum with that calculated within semi-classical approximation. Introduced semi-classical model of atom represents the wave functions of bounded in atom electrons in form of hydrogen-like atomic orbitals with explicitly defined effective charge numbers. The hydrogen-like electron orbitals of constituting condensed matter atoms are used to calculate the matrix elements of the secular equation determining the condensed matter electronic structure in the linear-combination-of-atomic-orbitals (LCAO) approach. Preliminary test calculations are conducted for boron B atom and diboron B2 molecule electron systems.