arXiv subjects

Krzysztof Pachucki

Publications and source records attributed to Krzysztof Pachucki.

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

Recoil corrections to $μ$H hyperfine splitting

This work attempts to present a complete theory of the $μ$H hyperfine splitting, including all contributions above 1 ppm. Quantum electrodynamic and recoil corrections are calculated directly, while the proton structure correction is obtained with the help of the H hyperfine splitting. The resulting theoretical prediction for the ground state of $μ$H is $E_\mathrm{hfs} = 182\,626(5)$ $μ$eV.

physics.atom-ph↗

arXiv2026

Relativistic nuclear recoil effects in hyperfine splitting of hydrogenic systems

Finite nuclear mass $(Z\,α)^2\,m/M\,E_F$ corrections to the hyperfine splitting in hydrogenic systems are calculated using a combined relativistic heavy particle and nonrelativistic quantum electrodynamics. The obtained results are in disagreement with previous calculations by Bodwin and Yennie [Phys. Rev. D {\bf 37}, 498 (1988)]. The comparison of improved theoretical predictions with the corresponding measurements in hydrogen reveals $2\,σ$ discrepancy, which may indicate problems with the proton structure corrections.

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↗

arXiv2026

Nonadiabatic corrections to electric quadrupole transition rates in H$_2$

We derive formulas and perform calculations of nonadiabatic corrections to rates of electric quadrupole transitions in the hydrogen molecule. These corrections can be represented in terms of the quadrupole moment curve $D^{(1)}(R)$, similarly to the Born-Oppenheimer one, $D^{(0)}(R)$, derived originally by Wolniewicz. Numerical results change E2 transition rates for the fundamental band by as much as 0.4 - 12\% depending on rotational quantum numbers.

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

Magnetic shielding in the atomic hydrogen anion

The atomic hydrogen anion H$^-$ is the lightest stable anion and its bound states and resonances are well studied in the literature. Due to the planned comparison of the bare antiproton to H$^-$ in a Penning trap, we study the magnetic shielding of H$^-$ using the nonrelativistic quantum electrodynamics theory, by accurately calculating the non-relativistic shielding, as well as finite nuclear mass, relativistic, and partially QED corrections. We find that the finite nuclear mass correction is quite significant in H$^-$ contributing about $0.1\%$ of the total shielding, which is more than twice as much as the relativistic correction. Our final result for the shielding constant has a nine-parts-per-trillion accuracy and paves the way for direct comparison of the antiproton-to-proton magnetic moments.

physics.atom-ph↗

arXiv2025

Radiative corrections to the nuclear size and polarizability effects in atomic systems

We perform a complete calculation of $α\,(Z\,α)^5\,m$ radiative corrections to the finite nuclear size, the recoil finite size and the nuclear polarizability effects in atomic systems. Results confirm very good agreement for the mean square charge radii difference $r_d^2-r_p^2$ between the deuteron and the proton, as measured in {\em electronic} and muonic isotope shifts.

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

Heavy-particle quantum electrodynamics

The quantum electrodynamic formalism is presented for the systematic and exact in $Z\,α$ derivation of nuclear recoil corrections in hydrogenic systems.

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↗

arXiv2024

Finite nuclear mass correction to the hyperfine splitting in hydrogenic systems

A general quantum electrodynamic method for derivation of nuclear recoil corrections in hydrogenic systems, which are exact in the nuclear charge parameter $Z\,α$, is introduced. The exemplary derivation is presented for the $O(m/M)$ nuclear pure recoil correction to the hyperfine splitting. The obtained result is verified by comparison to the known $(Z\,α)^5$ contribution

physics.atom-ph↗

arXiv2024

Nuclear magnetic shielding in heliumlike ions

Ab initio QED calculations of the nuclear magnetic shielding constant in helium-like ions are presented. We combine the nonrelativistic QED approach based on an expansion in powers of the fine-structure constant $α$ and the so-called ``all-order'' QED approach which includes all orders in the parameter $Zα$ but uses a perturbation expansion in the parameter $1/Z$ (where $Z$ is the nuclear charge number). The combination of the two complementary methods makes our treatment applicable both to low-$Z$ and high-$Z$ ions. Our calculations confirm the presence of a rare antiscreening effect for the relativistic shielding correction and demonstrate the importance of the inclusion of the negative-energy part of the Dirac spectrum.

physics.atom-ph↗

arXiv2024

Integrals for relativistic nonadiabatic energies of H$_2$ in exponential basis

Accurate predictions for hydrogen molecular levels require the treatment of electrons and nuclei on an equal footing. While nonrelativistic theory has been effectively formulated this way, calculation of relativistic and quantum electrodynamic effects using an exponential basis with explicit correlations that ensure well-controlled numerical precision is much more challenging. In this work, we derive a complete set of integrals for the relativistic correction and demonstrate their application to several of the lowest rovibrational levels. Together with similar advancements for quantum electrodynamic corrections, this will improve the accuracy beyond $10^{-9}$ and hopefully explain discrepancies with recent experimental values.

physics.chem-ph↗

arXiv2023

Nuclear mass and size corrections to the magnetic shielding

We derive finite nuclear mass and finite nuclear size corrections to the magnetic shielding in light ions. These corrections are important for the accurate determination of nuclear magnetic moments. We correct several previous formulas for the nuclear mass corrections and present improved results for the magnetic shielding in $^1$H, $^3$He$^+$, and $^3$He. Finally, we obtain an $^3$He atomic magnetic moment, which serves as an accurate probe to measure magnetic fields.

physics.chem-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↗