arXiv subjects

Vojtěch Patkóš

Publications and source records attributed to Vojtěch Patkóš.

At least 19 recordsLinked to original sources

arXiv2026

Hydrogenic rotational levels with spin-0 or spin-1/2 constituent particles

We employ nonrelativistic quantum electrodynamics with a unified description of two-body systems with spin-0 or spin-1/2 constituents, arbitrary masses, and arbitrary magnetic moments in rotational states with $L>1$, to present state-of-the-art theoretical predictions for muonic, kaonic, and antiprotonic atoms that have recently been measured or are targeted by upcoming experiments. We show that the theoretical accuracy can further be improved, opening the possibility of using precision spectroscopy of muonic and hadronic atoms for high-accuracy determinations of nuclear charge radii and nuclear electric dipole polarizabilities, and for testing the existence of hypothetical long-range hadronic interactions.

physics.atom-ph↗

arXiv2026

Two-body $P$-state energies at $α^6$ order

We present an analytical calculation of the complete $α^6$ correction to energies of $nP$-levels of two-body systems consisting of the spin-$0$ or $1/2$ extended-size particles with arbitrary masses and magnetic moments. The obtained results apply to a wide class of two-body systems such as hydrogen, positronium, muonium, and pionic or aniprotonic helium ion. We found an additional $α^6$ correction for $nP$-levels of positronium, which was previously overlooked. Our results are also relevant for light muonic atoms, whose accurate theoretical predictions are required for extracting the nuclear charge radii.

physics.atom-ph↗

arXiv2025

QED nuclear recoil effect in helium isotope shift

We present a detailed investigation of the leading-order $mα^5$ QED correction with inclusion of the finite-nuclear-mass effects. Previously, this correction had been calculated within an expansion in the electron-nucleus mass ratio $m/M$ up to the first order. In this work, we derive formulas for the $mα^5$ QED contribution that are valid up to the second order in $m/M$, and perform its calculation for the $^3$He$-$$^4$He isotope shift, leading to an improved determination of the nuclear charge-radius difference.

physics.atom-ph↗

arXiv2025

Recoil corrections with finite nuclear size in hydrogenic systems

Formulas for the combined nuclear-recoil and finite-nuclear-size effects of order $(Z\,α)^5$ and $(Z\,α)^6$ are derived without any expansion in the nuclear charge radius $r_C$, making them applicable to both electronic and muonic atoms. The obtained results are particularly relevant for high-precision determinations of root-mean-square charge radii from muonic atom spectroscopy. We demonstrate that calculations of the atomic isotope shift based on the widely used Breit approximation give rise to an unphysical nuclear-size contribution that is linear in the nuclear charge radius $r_C$ at order $(Z\,α)^5$. This spurious term vanishes in a full QED treatment, leaving the correct contribution quadratic in $r_C$. For electronic atoms, this quadratic term is significantly smaller than the spurious linear contribution.

physics.atom-ph↗

arXiv2024

Second-order hyperfine correction to H, D, and $^3$He energy levels

The complete second-order hyperfine-interaction correction is calculated for centroid energy levels of H, D, and $^3$He atoms. For $^3$He, the corrections of $-2.075$~kHz and $-0.305$~kHz beyond the leading hyperfine-mixing contribution are obtained for the $2^1S$ and $2^3S$ states, respectively. These results shift the nuclear charge radii difference derived from the $^3$He -$^4$He isotope shift and largely resolve the previously reported disagreement between the muonic and electronic helium determinations [van der Werf et al., arXiv:2306.02333 (2023); Schuhmann et al., arXiv:2305.11679 (2023)].

physics.atom-ph↗

arXiv2024

Radiative corrections of the order $α\,(Z\,α)^6$ for rotational states of two-body systems

The analytical calculation of the complete $α\,(Z\,α)^6$ one-loop radiative correction to energies of two-body systems with the angular momenta $l>0$, consisting of a pointlike particle and an extended-size nucleus with arbitrary masses and spin 1/2, is presented. The obtained results apply to a wide variety of two-body systems, such as hydrogen, muonium, positronium, and antiprotonic atoms.

physics.atom-ph↗

arXiv2023

Hyperfine splitting in $^{6,7}$Li$^+$

We present a detailed derivation of the QED effects of order $α^7\,m$ to the hyperfine structure (hfs) of the $^3S$ states of helium-like ions and perform numerical calculations for $^6$Li$^+$ and $^7$Li$^+$. By comparing the theoretical point-nucleus results with the measured hfs of Li$^+$, we determine the nuclear-structure contribution parameterized in terms of the effective Zemach radius. Using the experimental hfs results for Li$^+$, we obtain accurate predictions for the hfs of $^6$Li$^{2+}$ and $^7$Li$^{2+}$, for which no experimental data is available so far. By examining the normalized differences of the hfs of Li$^{+}$ and Li and of the corresponding isotope-shift differences, we test the consistency of the hfs measurements in $^{6,7}$Li$^{+}$ and $^{6,7}$Li.

physics.atom-ph↗

arXiv2023

Higher-order QED corrections to the hyperfine splitting in $^3$He

We present a calculation of the hyperfine splitting of the $2^3S$ state in the $^3$He atom with inclusion of all QED effects up to $α^3E_F$, where $E_F$ is the Fermi splitting. Using the experimental value of the $1S$ hyperfine splitting in $^3$He$^+$, we obtain the theoretical prediction for $^3$He of $ν_\mathrm{hfs}= -6\,739\,701\,181(41)$ Hz, which is in perfect agreement with the experimental value $-6\,739\,701\,177(16)$ Hz [S. D. Rosner and F. M. Pipkin, Phys. Rev. A ${\bf 1}$, 571 (1970)]. This result constitutes a 40-fold improvement in precision as compared to the previous value and is the most accurate theoretical prediction ever obtained for a non-hydrogenic system.

physics.atom-ph↗

arXiv2023

Accurate determination of $^{6,7}$Li nuclear magnetic moments

We report an accurate determination of the nuclear magnetic dipole moments of $^{6,7}$Li from the measured ratio of the nuclear and the electron $g$-factors in atomic Li. The obtained results significantly improve upon the literature values and stress the importance of reliable theoretical calculations of the nuclear shielding corrections.

physics.atom-ph↗

arXiv2023

Nuclear polarizability effects in $^3$He$^+$ hyperfine splitting

The nuclear polarizability effects in hyperfine splitting of light atomic systems are not well known. The only system for which they were previously calculated is the hydrogen atom, where these effects were shown to contribute about 5\% of the total nuclear correction. One generally expects the polarizability effects to become more pronounced for composite nuclei. In the present work we determine the nuclear polarizability correction to the hyperfine splitting in He$^+$ by comparing the effective Zemach radius deduced from the experimental hyperfine splitting with the Zemach radius obtained from the electron scattering. We obtain a surprising result that the nuclear polarizability of the helion yields just 3\% of the total nuclear correction, which is smaller than for the proton.

physics.atom-ph↗

arXiv2022

QED $mα^7$ effects for triplet states of helium-like ions

We perform ab initio calculations of the QED effects of order $mα^7$ for the $2^3S$ and $2^3P$ states of He-like ions. The computed effects are combined with previously calculated energies from [V. A. Yerokhin and K. Pachucki, Phys. Rev. A 81, 022507 (2010)], thus improving the theoretical accuracy by an order of magnitude. The obtained theoretical values for the $2^3S$-$2^3P_{0,2}$ transition energies are in good agreement with available experimental results and with previous calculations performed to all orders in the nuclear binding strength parameter $Zα$. For the ionization energies, however, we find some inconsistency between the $Zα$-expansion and all-order calculations, which might be related to a similar discrepancy between the theoretical and experimental results for the ionization energies of helium [V. Patkóš et al., Phys. Rev. A 103, 042809 (2021)].

physics.atom-ph↗

arXiv2022

Quantum electrodynamics of two-body systems with arbitrary masses

We perform a calculation of quantum electrodynamics effects in excited states with $l>1$ of arbitrary two-body systems up to $α^6\,μ$ order. The obtained results are valid for hadronic atoms, as long as the strong interaction effects are negligible. We demonstrate that for circular states with $l\sim n$, the effective expansion parameter is $Z\,α/n$, which extends the applicability of the derived formulas to heavy ions. Moreover, inclusion of higher-order terms is feasible, which indicates that accurate measurements of excited states of, for example, muonic or antiprotonic hydrogenic ions can be used to determine the fundamental constants and to search for the existence of yet unknown long-range interactions.

physics.atom-ph↗

arXiv2022

Relativistic Bethe logarithm for triplet states of helium-like ions

We report a calculation of relativistic corrections of order $mα^7$ to the Bethe logarithm for the $2^3S$ and $2^3P$ states of helium-like ions. The calculation is required for improving the accuracy of theoretical energies of helium-like ions and for checking the evaluation of the $mα^7$ effects in helium performed in [V. Patkóš, V. A. Yerokhin, K. Pachucki, Phys. Rev. A 103, 042809 (2021)], where a significant discrepancy with experimental results was found. The large-$Z$ limit of the relativistic Bethe logarithm is determined numerically, in excellent agreement with the analytical results obtained from the hydrogen theory.

physics.atom-ph↗

arXiv2022

QED calculations of energy levels of helium-like ions with $5 \leq Z \leq 30$

A calculation of two-electron QED effects to all orders in the nuclear binding strength parameter $Zα$ is presented for the ground and $n = 2$ excited states of helium-like ions. After subtracting the first terms of the $Zα$ expansion from the all-order results, we identify the higher-order QED effects of order $mα^7$ and higher. Combining the higher-order remainder with the results complete through order $mα^6$ from [V. A. Yerokhin and K. Pachucki, Phys. Rev. A 81, 022507 (2010)], we obtain the most accurate theoretical predictions for the ground and non-mixing $n=2$ states of helium-like ions with $Z = 5-30$. For the mixing $2^1 P_1$ and $2^3 P_1$ states, we extend the previous calculation by evaluating the higher-order mixing correction and show that it defines the uncertainty of theoretical calculations in the $LS$ coupling for $Z > 10$.

physics.atom-ph↗

arXiv2021

Complete $α^7\,m$ Lamb shift of helium triplet states

We have derived the complete formula for the $α^7\,m$ contribution to energy levels of an arbitrary triplet state of the helium atom, performed numerical calculations for the $2^3S$ and $2^3P$ states, and thus improved the theoretical accuracy of ionization energies of these states by more than an order of magnitude. Using the nuclear charge radius extracted from the muonic helium Lamb shift, we obtain the theoretical prediction in excellent agreement with the measured $2^3S - 2^3P$ transition energy [X.~Zheng et al., Phys. Rev. Lett. {\bf 199}, 263002 (2017)]. At the same time we observe significant discrepancies with experiments for the $2^3S- 3^3D$ and $2^3P - 3^3D$ transitions.

physics.atom-ph↗

arXiv2021

Nonradiative $α^7m$ QED effects in Lamb shift of helium triplet states

Theoretical predictions for the Lamb shift in helium are limited by unknown quantum electrodynamic effects of the order $α^7m$, where $α$ is the fine-structure constant and $m$ is the electron mass. We make an important step towards the complete calculation of these effects by deriving the most challenging part, which is induced by the virtual photon exchange between all three helium particles, the two electrons, and the nucleus. The complete calculation of the $α^7m$ effect including the radiative corrections will allow comparing of the nuclear charge radii determined from the electronic and muonic helium atoms and thus provide a stringent test of the Standard Model of fundamental interactions.

hep-ph↗

arXiv2021

Relativistic corrections to the Bethe logarithm for the $2^3S$ and $2^3P$ states of He

With this work we start a project of calculating the QED contribution of order $α^7m$ to the $2^3P$-$2^3S$ transition energy in helium, aiming for an accurate determination of the nuclear charge radius $r_E$ from measurements of the corresponding transition frequency. Together with the complementary determination of $r_E$ from muonic helium, this project will provide a stringent test of universality of electromagnetic interactions of leptons in the Standard Model. We report a calculation of the relativistic corrections to the Bethe logarithm for the $2^3S$ and $2^3P$ states, which is the most numerically demanding part of the project.

physics.atom-ph↗

arXiv2021

Radiative $\bm{α^7m}$ QED contribution to the helium Lamb shift

We present a derivation of the last unknown part of the $α^7m$ contribution to the Lamb shift of a two-electron atom, induced by the radiative QED effects beyond the Bethe logarithm. This derivation is performed in the framework of nonrelativistic quantum electrodynamics and is valid for the triplet (spin $S = 1$) atomic states. The obtained formulas are free from any divergences and are suitable for a numerical evaluation. This opens a way for a complete numerical calculation of the $α^7m$ QED effects in helium, which will allow an accurate determination of the nuclear charge radius from measurements of helium transition frequencies.

physics.atom-ph↗