The electronic spectra of light one-electron quasi-molecular compounds H-H$^+$, He$^+$-He$^2+$ and He$^+$-H$^+$ are analyzed. To this end, the two-center Dirac equation is solved by the dual-kinetically balanced finite-basis-set method for axially symmetric systems termed as A-DKB. This method allows a complete relativistic consideration of these systems at fixed internuclear distances. A comparison of the obtained results with the nonrelativistic and relativistic calculations presented in the literature is performed. The advantages and disadvantages of the approach are discussed in details.

Homonuclear molecules have emerged as a crucial component in the pursuit of frequency standards, offering a promising avenue for the discovery of new physics phenomena that transcend the standard model. They also provide a unique approach to constraining variations in fundamental constants over time, thereby complementing the capabilities of atomic clocks. A notable challenge faced by molecular and single atomic quantum systems is the management of blackbody radiation (BBR), which introduces significant systematic errors and is challenging to regulate effectively. To address this issue, we perform ab initio quantum chemical calculations to accurately determine the potential energy curve and the polarizability tensor for the ground state of the N+2 molecular ion, one of the most promising candidates for searching for variation of me/mp and creating frequency standards. We then calculate the BBR shifts affecting the vibrational levels of the ground electronic X2Eg+ state, marking a substantial contribution towards the precise experimental measurements.

Spectroscopic measurements of transition frequencies in various atomic systems are a significant part of modern physics. They enable the testing of fundamental interactions, the determination of physical constants, and the study of fundamental symmetries that occur in nature with unprecedented accuracy. Studies based on two-photon spectroscopy of simple atoms represent some of the most accurate experiments to date. The verification of precision experimental results is largely supported by theoretical analysis, which is most rigorous for light, nonrelativistic atoms and ions. In the last decade, much attention in the literature has been paid to the study of the quantum interference effect (QIE) in hydrogen and hydrogenlike atomic systems. This has made it possible to significantly reduce the experimental error in determining the appropriate transition frequency. The theoretical description of the QIE corresponds to the consideration of similar pathways arising for close-lying resonant states into which the transition frequency is measured. In the present work, the influence of the emission process on the absorption profile formation is investigated. The results of the studies carried out in this work show the need to take into account the effect of quantum interference in cascade radiation for the precise determination of the absorption transition frequency to highly excited states in two-photon spectroscopic experiments.

This paper discusses some features of the spectral line profile theory used in the treatment of measured atomic transitions. It is shown that going beyond the established linear approximation for the spectral line contour in the case of its nonresonant extension, the potential for a more accurate extraction of atomic characteristics from experimental data arises. Using the example of the Lyman-α (Ly_α) transition in hydrogen, a simple analysis of the observed spectral line distorted by a possible interfering transitions is given. In particular, the results obtained in the present work clearly demonstrate that the processing of the same experimental data at different settings can provide an accurate determination of the transition frequency, the centre of gravity as well as the hyperfine splitting of the ground state in hydrogen-like atomic systems. The latter is especially important for setting up precision spectroscopic experiments on the antihydrogen atom.

In this study, we reexamine the long-range interaction between two atoms placed in an equilibrium thermal radiation environment. Employing the formalism of quantum electrodynamics at finite temperatures, we derive an expression for the thermal correction to the interaction potential and explore various asymptotic behaviors. The numerical calculations of temperature-dependent dispersion coefficients for both the ground and highly excited states of the hydrogen atom are performed. We proceed from the first principles of the theory to derive the dipole-dipole interaction at finite temperature. The analysis presented in this work reveals that the expressions established earlier in the context of phenomenological extrapolation from zero- to finite-temperature scenarios exhibit disparate asymptotic behavior and lead to overestimated results to those of the rigorous quantum electrodynamics approach.

In this paper we investigate higher-order corrections to the energies of bound states in hydrogen subjected to the external blackbody radiation field. In particular, within the framework of thermal quantum electrodynamics and $S$-matrix approach we analyze combined type of two-loop self-energy corrections, including one zero-vacuum and one loop at finite temperature. By utilizing the method of dimensional regularization, we derive closed analytical expressions for the energy shifts of atomic levels. Our numerical calculations demonstrate that even at room temperature these corrections can be significant for excited states, reaching the magnitude of the thermal induced Stark contribution.

The effect of a constant magnetic field in combination with a field induced by an external thermal environment on atomic decay rates is studied. For this purpose, radiative corrections including magnetic interaction are considered for hydrogen and hydrogen-like ions with a small nuclear charge Z . Corrections to the decays of the metastable state 2 s and the excited state 2 p were calculated at various magnetic field strengths suitable for the conditions of the laboratory experiments. It is found that the combination of the magnetic field and thermal environment can lead to a broadening close to the level of experimental error, which makes it necessary to take them into account in the near future.

The paper discusses the line profile asymmetry of the photon scattering process that arises naturally in quantum electrodynamics (QED). Based on precision spectroscopic experiments conducted on hydrogen atoms, we focus our attention on the two-photon 1s - 2s transition. As one of the most precisely determined transition frequencies, it is a key pillar of optical frequency standards and is used in determining fundamental physical constants, testing physical principles, and searching constraints on new fundamental interactions. The results obtained in this work show the need to take into account the natural line profile asymmetry in precision spectroscopic experiments.

Modern resonant spectroscopic experiments to measure transition frequencies in atoms have reached a level where a meticulous description of all aspects of the processes under study has become obligatory. The precision achieved in the experiments of A. Beyer, et al., Science 358, 79 (2017), has led to the fact that the determination of the transition frequency based on measured data is significantly refined by theoretical treatment of the observed spectral line profile. As it was predicted theoretically, a great impact of effects arising beyond the resonance approximation was found experimentally. These findings marked the beginning of the upcoming epoch in the resonant atomic spectroscopy when many commonly understood ideas became invalid. For example, the atomic transition may be characterized by several different but equally acceptable frequencies. Furthermore, we show that the picture becomes even more complicated when the observed spectral line profile is "identified" with one of the processes - emission or absorption. Precise determination of the transition frequency requires a description of the absorption line profile inseparable from the emission process and vice versa. The theoretical aspects discussed in this work provide prerequisites for more accurate and yet simpler experiments than those reported in Science 358, 79 (2017). Implementing the new physics expected in atomic resonance spectroscopy in the near future beyond the resonance approximation is unfeasible without resolving these issues.

In the present work, two quasi-molecular compounds each involving one antiproton and one electron (p̄), He+−p̄ and H−p̄, are investigated. Using completely relativistic calculations within the finite-basis method adapted to systems with axial symmetry, the adiabatic potential curves are constructed by numerically solving the two-center Dirac equation. The binding energies of electron are obtained as a function of the inter-nuclear distance and compared with the corresponding nonrelativistic values and relativistic leading-order corrections calculated in the framework of other approaches. A semantic analysis of antiproton quasi-molecular ions with compounds containing a proton (p) instead of an antiproton is given. The advantages of the A-DKB method are demonstrated.

Thermal corrections, including relativistic effects, for the positronium atom are discussed. The theoretical description of thermal corrections is carried out within the framework of relativistic quantum electrodynamics. As a result, thermal corrections to atomic energy levels with a fine and hyperfine structure and to the probabilities of annihilation of a positronium atom placed in a thermal environment (blackbody radiation) are taken into account. Numerical results are discussed throughout the paper in view of modern experiments and theoretical searches for verification of fundamental interactions.

Atomic spectroscopy experiments have reached a level where the transition line profile has become measurable with high precision. One of the most important task of such experiments is the determination of the transition frequency and an accurate comparison with the corresponding theoretical value. However, a detailed theoretical description of the line profile requires consideration of increasingly tiny effects which can play a crucial role in determining fundamental physical constants. In particular, it was shown recently that the nonresonant corrections arising in the description of the scattering processes of photon by atoms can lead to significant changes in the determination of the transition frequency. In present work, an adaptive method of moments for extracting the transition frequency from the experimental spectral data is discussed. (C) 2022 Elsevier B.V. All rights reserved.

The influence of the blackbody radiation field on the $g$-factor of light hydrogenlike ions is considered within the framework of quantum electrodynamics at finite temperature for bound states. One-loop thermal corrections are examined for a wide range of temperatures. The numerical results for $1s$, $2s$, $2p_{1/2}$, and $2p_{3/2}$ states are presented. It is shown that for excited states finite temperature corrections to the bound-electron $g$-factor are close to the level of current experimental uncertainty even at room temperatures and can be discerned within the measurements anticipated in the near future.

In this work, we consider the thermal correction to the hyperfine interaction in hydrogen, deuterium, and the $^3$He$^+$ ion. This correction is effectively described by one-loop Feynman graphs in the framework of the quantum electrodynamics theory for bound states at a finite temperature. A simple analysis shows the importance of the obtained results for future prospects for measuring hyperfine splitting. In addition, the application for testing the time variation of fundamental constants is briefly discussed.

It is well known that the 4-rotation in four-dimensional space-time is equivalent to the CPT transformation (C is the charge conjugation, P is the space inversion, and T is the time reversal). The standard definition of the T reversal includes the change of the sign of the time variable and replacement of the initial state of the particle (system of particles) by the final state and vice versa. Since the time-reversal operation changes the state of a particle, the particle's wave function cannot be the eigenfunction of the corresponding operator with a certain eigenvalue, as in the case of space parity. Unlike the CPT transformation, the separate P, T, or C transformations cannot be reduced to any 4-rotation. The extended Lorentz group incorporates all the separate C, P, or T transformations which do not bring the time axis out of the corresponding light cone. The latter restriction is included in the standard definition of the time reversal. In the present Letter, we ignore this restriction. This allows us to introduce the "time arrow" operator and characterize every particle by the new quantum number-the "time arrow" value. The wave functions of all particles are eigenfunctions of this operator with eigenvalues equal to time arrow values. The particles with the time arrow values opposite to the time arrow value in our universe form another universe (antiuniverse). The existence of an antiuniverse can be confirmed, in principle, by laboratory (atomic) experiments. The antiuniverse may be also considered as a candidate for the role of dark matter.

In this review, we have investigated the asymmetry of the line profile in precision one- and two-photon spectroscopy of hydrogen and helium atoms within the framework of a rigorous QED approach. A detailed analysis of the angular correlations of the quantum interference effect has been carried out using various examples. Nonresonant effects are also considered in relation to some astrophysical problems. In particular, a rigorous QED derivation of the nonresonant extension for the Lorentz line profile is given using the Ly_α transition as an example; such a QED derivation has been lacking in the literature.

In the present paper, we study nonresonant corrections for experimental measurements of the transition frequencies in the helium atom. Having attracted more attention, such effects can make a significant contribution to experiments based on one- and two-photon atomic spectroscopy. The quantum interference effects in the measurements of n 3 S 1 − 33 D 1 (n = 3, 4, 5) transition frequencies based on Doppler-free two-photon spectroscopy, are considered as a possible source of current discrepancy between the experimental and theoretical data. We demonstrate that line profile asymmetry caused by the quantum interference of fine sub-levels of the DJ3(J=1,2,3) state can reach tenths of a megahertz for different experimental conditions. Thus, previously unaccounted nonresonant corrections should be taken in next-generation experimental measurements of transitions frequencies in helium. However, they could not completely eliminate the current imbalance in the study of helium spectra and the question is still open.

A discrepancy of 4σ (σ is the standard deviation) between the proton radii obtained by measuring transition frequencies in electron (H) and muonic (µH) hydrogen atoms has been actively discussed in the last decade. Theoretical and experimental efforts are focused on the test of this discrepancy and search for effects removing it. Recent measurements of the 2s–4p transition and the Lamb shift in the electron hydrogen atom approach the solution of the “proton radius puzzle.” The rms proton radius rp calculated from these experimental data is 0.8335(95) fm, which is in agreement within the indicated errors with a value of 0.84087(39) fm obtained from experiment with muon hydrogen. This agreement between the results has been achieved by including interference effects appearing in the processes of single-photon scattering on the hydrogen atom, whereas experiments on muonic hydrogen are insensitive to these effects. However, the charge radius of the proton cannot be calculated taking into account only single-photon transitions and measured frequencies corresponding to two-photon transitions should be taken into account. In this work, it has been shown that interference effects in the 2s–nd transitions in the hydrogen atom can make a significant contribution to the determination of the charge radius of the proton and Rydberg constant.

This paper discusses relativistic corrections to the thermal Coulomb potential for simple atomic systems. The theoretical description of the revealed thermal corrections is carried out within the framework of relativistic quantum electrodynamics. As a result, thermal corrections to the fine and hyperfine structures of atomic levels are introduced. The theory presented in this paper is based on the assumption that the atom is placed in a thermal environment created by the blackbody radiation. The numerical results allow us to expect their significance for modern experiments and testing the fundamental interactions.

Thermal corrections to the one-photon spontaneous and induced transition probabilities for hydrogen and hydrogen-like ions are evaluated. The found thermal corrections are given by the vertex Feynman graph, where the vertex represents the thermal interaction between the bound electron and the nucleus. All derivations of thermal corrections to bound–bound transitions for an atom exposed to blackbody radiation are made in a fully relativistic approach within the framework of the adiabatic S -matrix formalism. It is found that the vertex-type radiative corrections to the transition rates can be at the level of a few percent to corresponding spontaneous rates for highly excited states in the hydrogen atom. A comprehensive analysis of the vertex-type thermal corrections for hydrogen-like atomic systems is presented.