arXiv subjects

V. M. Shabaev

Publications and source records attributed to V. M. Shabaev.

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↗

arXiv2025

A relativistic coupled-cluster treatment of magnetic hyperfine structure of the $X^2\Pi$ and $A^2\Sigma^+$ states of OH isotopologues

$\textit{Ab initio}$ calculations of the parallel component of the magnetic dipole hyperfine structure (HFS) constant have been carried out for hydroxyl radical isotopologues ($^{16,17}$OH(D)) over the internuclear distance range $R \in [0.6, 1.8]$ \r{A}. For the ground electronic state $X^2\Pi$, the HFS functions were evaluated for contributions induced by both oxygen and hydrogen nuclei. In addition, the hydrogen-induced HFS curve was calculated for the excited $A^2\Sigma^+$ state. The quantum-chemistry study employs a four-component relativistic coupled-cluster (CC) method, including excitations up to the triple level, namely: the contribution of triple-cluster amplitudes was studied both perturbatively (CCSD(T)) and through fully iterative calculations (CCSDT). The resulting oxygen- and hydrogen-induced HFS functions represent the most accurate and reliable theoretical predictions to date exhibiting excellent agreement with semiempirical curve for hydrogen-induced HFS derived from high-resolution spectroscopic data for the lowest vibrational levels ($v\in [0,2]$) of the electronic $X^2\Pi$ state. Vibrationally averaged $\textit{ab initio}$ values are consistent with experimental values within $1\%$ for all states considered. Furthermore, the internuclear distance range over which the HFS curves are defined has been extended beyond that of previous studies, thereby providing a robust foundation for accurate HFS treatments of higher-lying rovibrational levels of OH isotopologues within both adiabatic and non-adiabatic frameworks.

physics.chem-ph↗

arXiv2025

Influence of the nuclear magnetic field on electron-positron pair production in low-energy heavy-nuclei collisions

Total and energy-angle differential probabilities of positrons created in slow collisions of two identical nuclei are calculated within relativistic two-center approach. The time-dependent Dirac equation is solved in the rotating frame using the generalized pseudospectral method in modified prolate spheroidal coordinates. The magnetic interaction induced by the motion of the nuclei is included in the Hamiltonian. The rotational coupling term is also taken into account. Angle-integrated and angle-resolved energy spectra of the emitted positrons are calculated by projecting the propagated wave function onto positive-energy plane-wave states. Our results show that the magnetic interaction leads to a slight increase in the critical internuclear distance and enhances the total positron yield by up to several percent. However, it does not qualitatively alter the energy or angular distributions of emitted positrons. The angular distributions remain nearly isotropic. The characteristic supercritical regime signatures, found in previous works, are preserved.

hep-ph↗

arXiv2025

Ionization potential and electron affinity of superheavy element 119: relativistic high-order coupled cluster study with QED corrections

We report a highly accurate \textit{ab initio} study of the ionization potential (IP) and electron affinity (EA) of element 119. Electronic correlation are treated within the relativistic coupled cluster theory including excitations up to quadruples. The Gaunt electron--electron interaction and quantum electrodynamic (QED) corrections are taken into account. The role of high-order correlation effects is analyzed in detail. Our recommended values for the IP and EA are 4.7839(56) eV and 0.6750(71) eV, respectively. These results tighten previous estimates and provide a reference point for future experiments probing periodic-law trends beyond oganesson.

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

The influence of electron-electron interaction on pair production in supercritical collisions of highly charged ions

The effect of electron-electron interaction on positron emission in supercritical collisions of highly charged ions is studied within the monopole approximation using the time-dependent density functional theory and the time-dependent Hartree-Fock-Slater methods. Positron production probabilities and energy spectra are calculated for U-U, U-Cm, and Cm-Cm collision systems, considering both bare nuclei and highly charged ions with partially filled electron shells. The results demonstrate that electron screening substantially reduces positron production and suppresses the characteristic signatures of spontaneous vacuum decay, previously found in collisions of bare nuclei.

hep-ph↗

arXiv2024

Three-dimensional calculations of positron creation in supercritical collisions of heavy nuclei

Energy--angle differential and total probabilities of positron creation in slow supercritical collisions of two identical heavy nuclei are calculated beyond the monopole approximation. The time-dependent Dirac equation (TDDE) for positrons is solved using the generalized pseudospectral method in modified prolate spheroidal coordinates, which are well-suited for description of close collisions in two-center quantum systems. In the frame of reference where the quasimolecular axis is fixed, the rotational coupling term is added to the Hamiltonian. Unlike our previous calculations, we do not discard this term and retain it when solving the TDDE. Both three-dimensional angle-resolved and angle-integrated energy distributions of outgoing positrons are obtained. Three-dimensional angle-resolved distributions exhibit a high degree of isotropy. For the collision energies in the interval 6 to 8 MeV/u, the influence of the rotational coupling on the distributions and total positron creation probabilities is quite small.

hep-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

Schwinger pair production in counterpropagating laser pulses: Identifying volume factors

We investigate the nonperturbative process of vacuum pair production in a combination of two counterpropagating linearly polarized laser pulses of a finite spatial extent. By means of the locally-constant field approximation (LCFA), we calculate the total particle yield for the corresponding four-dimensional setup and compare it with the estimates obtained for simplified low-dimensional scenarios. Within the domain where the LCFA is well justified, we examine a combination of two plane-wave pulses, a standing electromagnetic wave, and a spatially uniform oscillating field and demonstrate that at each of these three levels of approximation, one can accurately predict the actual particle number by multiplying the results by properly chosen volume factors depending on the field parameters. We present closed-form expressions for these factors providing universal prescriptions for evaluating the particle yield. Our final formula connecting the spatially uniform setup with the four-dimensional scenario has a relative uncertainty of the level of $10\%$. The explicit correspondences deduced in this study not only prove the relevance of the approximate predictions, but also allow one to quickly estimate the number of pairs for various realistic scenarios without performing multidimensional LCFA integrations.

hep-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

Excitation of the $^{229}$Th nucleus by the hole in the inner electronic shells

The $^{229}$Th nucleus has a long-lived isomeric state $A^*$ at 8.338(24) eV [Kraemer et al, Nature, \textbf{617}, 706 (2023)]. This state is connected to the ground state by an M1 transition. For a hydrogenlike Th ion in the $1s$ state the hyperfine structure splitting is about 0.7 eV. This means that the hyperfine interaction can mix the nuclear ground state with the isomeric state with a mixing coefficient $β$ about 0.03. If the electron is suddenly removed from this system, the nucleus will be left in the mixed state. The probability to find the nucleus in the isomeric state $A^*$ is equal to $β^2\sim 10^{-3}$. For the $2s$ state the effect is roughly two orders of magnitude smaller. An atom with a hole in the $1s$ or $2s$ shell is similar to the hydrogenlike atom, only the hole has a short lifetime $τ$. After the hole is filled, there is a non-zero probability to find the nucleus in the $A^*$ state. Estimates of this probability are presented along with a discussion of possible experiments on Th-doped xenotime-type orthophosphate crystals and other broad band gap materials.

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↗

arXiv2024

Positron supercritical resonances and spontaneous positron creation in slow collisions of heavy nuclei

We present a theoretical and computational study of positron supercritical resonances in systems consisting of two highly-charged bare nuclei. The resonance positions and widths depending on the internuclear separation are calculated with the help of the complex-scaling generalized pseudospectral method in modified prolate spheroidal coordinates. The results are applied to estimate the probability of spontaneous positron creation in slow U$^{92+}$--U$^{92+}$ and Cm$^{96+}$--Cm$^{96+}$ collisions.

hep-ph↗

arXiv2023

The ground-state potential and dipole moment of carbon monoxide: contributions from electronic correlation, relativistic effects, QED, adiabatic, and non-adiabatic corrections

The ground X1Σ+ state potential energy curve (PEC) and dipole moment curve (DMC) of CO molecule have been revisited within the framework of the relativistic coupled-cluster approach, which incorporates non-perturbative single, double, and triple cluster amplitudes (CCSDT) in conjunction with a finite-field methodology. The generalized relativistic pseudo-potential model was used for the effective introducing the relativity in all-electron correlation treatment and accounting the quantum-electrodynamics (QED) corrections within the model-QED-operator approach. The diagonal Born-Oppenheimer correction to PEC has been evaluated using the CCSD approach. The sensitivity of resulting PEC and DMC to variations in basis set parameters and regular intramolecular perturbations were considered as well. The present ab initio results are in a reasonable agreement with their most accurate semi-empirical counterparts.

physics.chem-ph↗

arXiv2023

Angular and energy distributions of positrons created in subcritical and supercritical slow collisions of heavy nuclei

Positron creation probabilities as well as energy and angular distributions of outgoing positrons in slow collisions of two identical heavy nuclei are obtained within the two-center approach beyond the monopole approximation. The time-dependent Dirac equation for positron wave functions is solved with the help of the generalized pseudospectral method in modified prolate spheroidal coordinates adapted for variable internuclear separation. Depending on the nuclear charge, the results are obtained for both subcritical and supercritical regimes of the positron creation. The signatures of transition to the supercritical regime in the total positron creation probabilities and energy spectra are discussed. The angular distributions of emitted positrons demonstrate a high degree of isotropy.

hep-ph↗

arXiv2023

Relativistic Stark energies of hydrogen-like ions

The relativistic energies and widths of hydrogen-like ions exposed to the uniform electric field are calculated. The calculations are performed for the ground and lowest excited states using the complex scaling technique in combination with a finite-basis method. The obtained results are compared with the non-relativistic values. The role of relativistic effects is investigated.

physics.atom-ph↗