arXiv subjects

A. V. Malyshev

Publications and source records attributed to A. V. Malyshev.

At least 19 recordsLinked to original sources

arXiv2026

Quadratic Zeeman effect in light boron-like ions

The quadratic Zeeman effect is calculated for the ground $^2P_{1/2}$ state of light boron-like ions in the range of nuclear-charge numbers $Z = 10-24$. The calculations are performed in the Furry picture using three models for the zeroth-order approximation potential: pure nuclear Coulomb potential and two effective screening potentials $-$ core-Hartree and Kohn-Sham. First-order perturbation-theory contributions are considered: the one-photon-exchange correction and the radiative corrections associated with the self-energy and vacuum-polarization diagrams. The dominant contributions from the self-energy diagrams are calculated within a rigorous QED approach. The vacuum polarization corrections are obtained within the electric-loop approximation in the leading order, which is given by the Uehling potential. As a result, theoretical predictions for the contribution of the quadratic Zeeman effect to the binding energy of the valence electron in the $^2P_{1/2}$ state are obtained. The results can be used for the analysis of high-precision $g$-factor and fine-structure splitting measurements in boron-like highly charged ions.

physics.atom-ph↗

arXiv2026

Self-energy corrections to the ionization energies in sodium-like ions: comparison of the \textit{ab initio} QED and model-QED-operator approaches

Calculations of the self-energy corrections to ionization energies of the $3s$, $3p_{1/2}$, and $3p_{3/2}$ states in sodium-like ions with nuclear-charge numbers $Z=30$, $50$, $70$, and $92$ are presented. The calculations are performed using two approaches: the rigorous bound-state QED formalism and the model-QED-operator method. Within the first method, the first and second orders of the QED perturbation theory formulated in the Furry picture are evaluated. Various screening potentials are included into the initial approximation to partially take into account the electron-electron interaction effects already at the lowest order, thereby accelerating the convergence of perturbation series. Within the second approach, different implementations of the model-QED operator, including its incorporation into the relativistic configuration-interaction calculations, are considered. A detailed comparison of the results obtained by these two independent methods is presented, demonstrating good agreement and thus validating the accuracy and efficiency of the model-QED-operator approach for many-electron systems.

physics.atom-ph↗

arXiv2026

Bound-electron self-energy calculations in Feynman and Coulomb gauges: detailed analysis

The energy correction associated with the self-energy diagram is the leading (in magnitude) and fundamental (in significance) contribution to the Lamb shift in highly charged ions. Conventional approaches to this correction rely on partial-wave expansions, which is a stumbling block limiting accuracy. To elucidate the issue, we perform a comprehensive comparative analysis of partial-wave-expansion convergence between two gauges: Feynman and Coulomb. Some tricks for improving the convergence are discussed as well.

physics.atom-ph↗

arXiv2025

QED calculations of intra-$L$-shell doubly excited states in Be-like ions

The rigorous QED approach is employed to calculate the energies of the $2p2p\,^3P_{0,1,2}$, $2p2p\,^1D_2$, and $2p2p\,^1S_0$ states of selected Be-like highly charged ions over a wide range of nuclear-charge numbers, $18 \leqslant Z \leqslant 92$. Combined with the previously reported energies of the $2s2p \, ^3P_{0,1,2}$ and $2s2p \, ^1P_1$ states [A. V. Malyshev et al., Phys. Rev. A 110, 062824 (2024)], the obtained results are used to study various intra-$L$-shell transition energies. Strong level mixing, caused by the proximity of states with the same symmetry, is overcome by means of the QED perturbation theory for quasi-degenerate levels. The applied approach merges a rigorous perturbative QED treatment up to the second order with the consideration of electron-electron correlation contributions of the third and higher orders evaluated within the Breit approximation. The higher-order screened QED effects are estimated using the model-QED-operator approach. The nuclear-recoil and nuclear-polarization effects are also taken into account. The obtained predictions represent the most accurate theoretical description of the electronic structure of Be-like ions to date and demonstrate good agreement with available experimental data.

physics.atom-ph↗

arXiv2025

QED effects in quadratic Zeeman splitting in highly charged hydrogen-like ions

We present ab initio calculations of one-electron quantum electrodynamical corrections to the second-order Zeeman splitting for the $1s_{1/2}$, $2s_{1/2}$, and $2p_{1/2}$ states in highly charged hydrogen-like ions. The self-energy correction is evaluated using the rigorous QED approach. The vacuum polarization correction is evaluated within the electric-loop approximation. Calculations are performed for the wide range of nuclear charge number: $Z = 14 - 92$.

physics.atom-ph↗

arXiv2025

Study of atomic effects on electron spectrum in bound-muon decay process

For the bound-muon decay process, the study of atomic effects on the electron spectrum near its endpoint is performed within the framework of the Fermi effective theory. The analysis takes into account for corrections due to finite-nuclear-size, nuclear-deformation, electron-screening, and vacuum-polarization effects, all of which are incorporated self-consistently into the Dirac equation. Furthermore, the nuclear-recoil correction to the muon binding energy is included. Calculations are carried out for the isotopes of C, Al, and Si, which are of a particular importance for forthcoming experiments aimed at search for the charged-lepton flavor-violating process of muon-to-electron conversion in a nuclear field.

physics.atom-ph↗

arXiv2025

$g$ factor of the $2p_j$ excited states in lithium-like ions

Relativistic calculations for the $g$ factor of the lowest excited states $2p_{1/2}$ and $2p_{3/2}$ of lithium-like ions over a wide range of the nuclear charge numbers $Z=10-92$ are presented. Interelectronic interaction is considered within the perturbation theory up to the second order. One-loop QED contributions are calculated to all orders in $αZ$. Leading contributions of the nuclear recoil effects are taken into account. The quadratic and cubic terms in magnetic field are considered as well. A set of screening potentials is used in all calculations to estimate the unknown higher-order correlation effects.

physics.atom-ph↗

arXiv2024

QED calculations of intra-$L$-shell singly excited states in Be-like ions

The \textit{ab initio} approach is used to evaluate the excitation energies of the $2s2p \, ^{2S+1}P_J$ states from the ground state as well as the $2s2p \, ^3P_1 \rightarrow 2s2p \, ^3P_0$ and $2s2p \, ^3P_2 \rightarrow 2s2p \, ^3P_1$ transition energies for selected Be-like highly-charged ions over a wide range: from ${\rm Ar}^{14+}$ to ${\rm U}^{88+}$. The issue of a strong level mixing due to the proximity of states with the same symmetry is addressed by applying the QED perturbation theory for quasidegenerate levels. The employed approach combines a rigorous perturbative QED treatment up to the second order with electron-electron correlation contributions of the third and higher orders calculated in the Breit approximation. The higher-order QED effects are estimated using the model-QED-operator approach. The nuclear-recoil and nuclear-polarization effects are taken into account as well. The performed calculations are accompanied with a thorough analysis of uncertainties due to uncalculated effects. The most accurate theoretical predictions for the excitation and transition energies in Be-like ions are obtained, which, in general, are in perfect agreement with the available experimental data.

physics.atom-ph↗

arXiv2024

Convergence-acceleration approach to partial-wave expansion of two-electron self-energy contributions to the Lamb shift

Methods of bound-state QED that treat the self-energy contributions to the Lamb shift within the partial-wave expansion usually face the problem of slow convergence of the latter. Inspired by an approach formulated in [J. Sapirstein and K. T. Cheng, Phys. Rev. A 108, 042804 (2023)], we propose a modification of the standard procedure for calculating the contributions of two-electron self-energy diagrams. The performance of the method is studied by evaluating the corresponding corrections to the binding energies of He-like ions and by comparing the obtained results with the state-of-the-art values available in the literature: our calculations involving a much smaller number of partial waves show an improvement in accuracy.

physics.atom-ph↗

arXiv2024

Orbital collapse and dual states of the $5g$ electrons in superheavy elements

The problem of orbital collapse of the $5g$ and $6f$ electrons in atoms of superheavy elements (SHE) is considered. Previously, the presence of the orbital collapse was established for the $4f$ and $5f$ elements of the periodic table. Because of the large centrifugal term for the $f$ and $g$ electrons, the effective radial potential has two wells, one narrow and deep and the other wide but shallow. Depending on the external parameters, the electron can be either localized in the outer well with low binding energy and large average radius or in the inner one with higher energy and smaller radius. In this work, we demonstrate the existence of the orbital collapse for the $5g$ electrons when changing the total angular momentum $J$ of the atom. We also found that for some SHE elements, two different solutions of the same Dirac-Fock equations may coexist, with the $5g$ electron localized either in the inner or outer well. In both cases, the radial wave functions are nodeless. The problem of the dual-state coexistence is studied by the configuration-interaction method in the Dirac-Fock-Sturm orbital basis as well.

physics.atom-ph↗

arXiv2023

Ab initio calculations of the $2p_{3/2} \rightarrow 2s$ transition in He-, Li-, and Be-like uranium

The bound-state QED approach is applied to calculations of the $2p_{3/2} \rightarrow 2s$ transition energies in He-, Li-, and Be-like uranium. For U$^{90+}$ and U$^{89+}$, standard perturbation theory for a single level is employed, while the calculations of U$^{88+}$ have required its counterpart for quasidegenerate levels. The utilized approach merges the rigorous QED treatment up to the second order of perturbation theory with the higher-order electron-correlation contributions evaluated within the Breit approximation. The higher-order screened QED effects are estimated by means of the model-QED operator. The nuclear recoil, nuclear polarization, and nuclear deformation effects are taken into account as well. Along with the transition energies, their pairwise differences are calculated. The comprehensive analysis of the uncertainties due to uncalculated effects is carried out, and the most accurate theoretical predictions, which are in perfect agreement with available experimental data, are obtained.

physics.atom-ph↗

arXiv2023

Relativistic calculations of the energies of the low-lying $1sns$, $1snp$, $1snd$ states and the probabilities of the one-photon $1snl\to 1sn'l'$ transitions in heliumlike uranium

For heliumlike uranium, the energies of the singly-excited $1sns$, $1snp$, and $1snd$ states with $n\leq 4$ and the probabilities of the one-photon $1s3d\to 1s2p$, $1s3p\to 1s2s$, $1s3p\to 1s2p$ and $1s4d\to 1s2p$ transitions are evaluated. The calculations are performed within the Breit approximation using the configuration-interaction method in the basis of the Dirac-Fock-Sturm orbitals. The QED corrections to the energy levels are calculated employing the model-QED-operator approach. The nuclear recoil, frequency-dependent Breit-interaction, nuclear polarization, and nuclear deformation corrections are taken into account as well.

physics.atom-ph↗

arXiv2023

Model-QED-operator approach to relativistic calculations of the nuclear recoil effect in many-electron atoms and ions

A model-operator approach to fully relativistic calculations of the nuclear recoil effect on energy levels in many-electron atomic systems is worked out. The one-electron part of the model operator for treating the normal mass shift beyond the Breit approximation is represented by a sum of semilocal and nonlocal potentials. The latter ones are constructed by employing the diagonal and off-diagonal matrix elements rigorously evaluated for hydrogenlike ions to first order in the electron-to-nucleus mass ratio. The specific mass shift beyond the lowest-order relativistic approximation has a form which can be directly employed in calculations. The capabilities of the method are probed by comparison of its predictions with the results of ab initio QED calculations. The proposed operator can be easily incorporated into any relativistic calculation based on the Dirac-Coulomb-Breit Hamiltonian.

physics.atom-ph↗

arXiv2023

Ground state of superheavy elements with $120 \leq Z \leq 170$: systematic study of the electron-correlation, Breit, and QED effects

For superheavy elements with atomic numbers $120\leq Z \leq 170$, the concept of the ground-state configuration is being reexamined. To this end, relativistic calculations of the electronic structure of the low-lying levels are carried out by means of the Dirac-Fock and configuration-interaction methods.The magnetic and retardation parts of the Breit interaction as well as the QED effects are taken into account. The influence of the relativistic, QED, and electron-electron correlation effects on the determination of the ground-state is analyzed.

physics.atom-ph↗

arXiv2022

Complex-scaled ab initio QED approach to autoionizing states

Ab initio method based on a complex-scaling approach and aimed at a rigorous QED description of autoionizing states is worked out. The autoionizing-state binding energies are treated nonperturbatively in $αZ$ and include all the many-electron QED contributions up to the second order. The higher-order electron correlation, nuclear recoil, and nuclear polarization effects are taken into account as well. The developed formalism is demonstrated on the $LL$ resonances in heliumlike argon and uranium. The most accurate theoretical predictions for the binding energies are obtained.

physics.atom-ph↗

arXiv2022

Model-QED operator for superheavy elements

The model-QED-operator approach [Phys. Rev. A 88, 012513 (2013)] to calculations of the radiative corrections to binding and transition energies in atomic systems is extended to the range of nuclear charges $110 \leqslant Z \leqslant 170$. The self-energy part of the model operator is represented by a nonlocal potential based on diagonal and off-diagonal matrix elements of the ab initio self-energy operator with the Dirac-Coulomb wave functions. The vacuum-polarization part consists of the Uehling contribution which is readily computed for an arbitrary nuclear-charge distribution and the Wichmann-Kroll contribution represented in terms of matrix elements similarly to the self-energy part. Performance of the method is studied by comparing the model-QED-operator predictions with the results of ab initio calculations. The model-QED operator can be conveniently incorporated in any numerical approach based on the Dirac-Coulomb-Breit Hamiltonian to account for the QED effects in a wide variety of superheavy elements.

physics.atom-ph↗

arXiv2022

Ionization potentials and electron affinities of Rg, Cn, Nh, and Fl superheavy elements

The successive ionization potentials (IPs) and electron affinities (EAs) for superheavy elements with $111 \leq Z \leq 114$, namely, Rg, Cn, Nh, and Fl are reexamined using the relativistic Fock-space coupled-cluster method with nonperturbative single (S), double (D), and triple (T) cluster amplitudes (FS-CCSDT). For the most of considered quantities, the triple-amplitude contributions turn out to be important. The Breit and frequency-dependent Breit corrections are evaluated by means of the configuration-interaction method. The quantum-electrodynamics corrections to the IPs and EAs are taken into account within the model-QED-operator approach. The obtained results are within 0.10 eV uncertainty.

physics.atom-ph↗

arXiv2021

Electron affinity of oganesson

The electron affinity (EA) of superheavy element Og is calculated by the use of the relativistic Fock-space coupled cluster (FSCC) and configuration interaction methods. The FSCC cluster operator expansion included single, double, and triple excitations treated in a non-perturbative manner. The Gaunt and retardation electron-electron interactions are taken into account. Both methods yield the results that are in agreement with each other. The quantum electrodynamics correction to EA is evaluated using the model Lamb-shift operator approach. The electron affinity of Og is obtained to be 0.076(4) eV.

physics.atom-ph↗