arXiv subjects

Z. Harman

Publications and source records attributed to Z. Harman.

At least 19 recordsLinked to original sources

arXiv2026

Testing New Scalar Interactions in Few-Electron Highly Charged Ions

We investigate how a hypothetical scalar boson mediating an interaction between electrons as well as between electrons and nucleons would affect the g factor of lithium-like highly charged ions. In such ions, the strong nuclear Coulomb fields enhance electron-electron interactions, making them ideal systems for detecting subtle new physics signatures. Exceptionally accurate quantum electrodynamic predictions and experimental data in such few-electron systems allow for sensitive probes, thereby enabling bounds on the boson's coupling strength. Exploiting the enhanced sensitivity of highly charged ions to short-range interactions, we combine g-factor measurements and quantum electrodynamic theory predictions of lithium- and hydrogen-like ions with the free-electron magnetic moment and an isotope-shift measurement to constrain simultaneously the electron-proton, electron-neutron, and electron-electron coupling combinations as functions of the scalar mass. We find that precision g-factor spectroscopy provides competitive constraints on scalar interactions over a broad mass range and, in particular, yields bounds on electron-electron interactions from bound-state QED observables.

hep-ph↗

arXiv2026

Higher-order corrections to the field shift in atomic systems

Differences in nuclear charge distributions between isotopes lead to small changes in atomic spectra known as the field shift. While largely proportional to the change in the mean-square nuclear radius, the field shift also contains higher-order contributions with different dependencies on nuclear moments. Their knowledge is required in searches for new physics using King plots, as they can induce deviations from King-plot linearity. We present a systematic expansion of the field-shift energies in terms of nuclear parameters and test its validity against direct numerical calculations for H-like ions. We also compute leading- and higher-order field-shift corrections for alkali-like systems from Li-like to Rb-like ions, and find that their ratio is nearly independent of the ionic charge state, agreeing with the corresponding hydrogenic $1s$ ratios on a sub-percent level. Motivated by this observation, we introduce an approximation in which these fractional contributions are assumed to be independent of the electronic configuration. We show that within this approximation, higher-order field-shift corrections do not contribute to King-plot nonlinearities.

physics.atom-ph↗

arXiv2026

Wichmann-Kroll Correction to the Interelectronic Interaction in He- and Li-Like Ions

We present a theoretical study of the higher-order QED contribution to the interelectronic interaction in He- and Li-like ions, where a virtual electron-positron loop is inserted into the photon line of the one-photon exchange diagram. Our approach is based on the Dirac-Coulomb Green's function and accounts for the interaction of the virtual $e^+e^-$ pair with the electric field of the nucleus to all orders in $\alpha Z$, with $\alpha$ being the fine-structure constant and $Z$ the atomic charge number. We show that the numerical convergence of the involved integrals can be significantly improved by explicitly subtracting the non-gauge-invariant spurious contributions from the integrands. We present improved numerical values for this contribution to the Lamb shift over a wide range of nuclear charge numbers $Z$. Our calculations agree well with previous results by Artemyev and co-workers [Phys. Rev. A 56, 3529 (1997); Phys. Rev. A 60, 45 (1999)] for He-like ions, but we find a discrepancy in the Li-like case. Moreover, we calculate the finite nuclear size correction to this diagram, which can reduce its size by more than 5% for heavy ions. The improved QED calculations not only decrease the uncertainty of theoretical predictions for the interelectronic interaction in few-electron ions but the methods could also be used in the future to improve calculations of closely related one-electron two-loop QED diagrams.

physics.atom-ph↗

arXiv2025

Two-loop electron self-energy in bound-electron $g$ factor: diagrams in momentum-coordinate representation

The two-loop electron self-energy correction is one of the most problematic QED effects and, for a long time, was the dominant source of uncertainty in the theoretical prediction of the bound-electron $g$ factor in hydrogen-like ions. A major breakthrough was recently achieved in [B. Sikora et al. Phys. Rev. Lett. 134, 123001 (2025)], where this effect was calculated without any expansion in the nuclear binding strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and $\alpha$ is the fine-structure constant). In this paper, we describe our calculations of one of the most difficult parts of the two-loop self-energy, represented by Feynman diagrams that are treated in the mixed momentum-coordinate representation.

physics.atom-ph↗

arXiv2025

Two-loop vacuum polarization in a Coulomb field

The leading-order two-loop vacuum-polarization potential, linear in the Coulomb field of a nucleus, was first derived in the seminal 1955 work of K\"all\'en-Sabry. The higher-order two-loop vacuum-polarization corrections, however, have remained unknown until now. In this work, we compute Coulomb corrections to the K\"all\'en-Sabry potential, specifically those involving three, five, and seven Coulomb interactions inside the vacuum-polarization loop. The potentials are evaluated in momentum space and subsequently used to calculate one-electron energy shifts. Our results drastically reduce the theoretical uncertainty of the two-loop vacuum-polarization contribution to transition energies, which is required for next-generation tests of bound-state QED in heavy one and few-electron ions as well as for the determination of nuclear charge radii.

physics.atom-ph↗

arXiv2025

QED calculations of the $2p$-$2s$ transition energies in Li-like ions

Systematic QED calculations of ionization energies of the $2s$, $2p_{1/2}$, and $2p_{3/2}$ states, as well as the $2p_{1/2}$--$2s$ and $2p_{3/2}$--$2p_{1/2}$ transition energies are performed for Li-like ions with the nuclear charge numbers $Z = 10$--$100$. The convergence of QED perturbative expansion is improved by using the extended Furry picture, which starts from the Dirac equation with a local screening potential. An ab initio treatment is accomplished for one- and two-photon electron-structure QED effects and the one-photon screening of the self-energy and vacuum-polarization corrections. This is complemented with an approximate treatment of the two-photon QED screening and higher-order (three or more photon) electron-structure effects. As a result, the obtained theoretical predictions improve upon the accuracy achieved in previous calculations. Comparison with available experimental data shows a good agreement between theory and experiment. In most cases, the theoretical values surpass the experimental results in precision, with only a few exceptions. In the case of uranium and bismuth, the comparison provides one of the most stringent tests of bound-state QED in the strong-field regime. Alternatively, the obtained results can be employed for high-precision determinations of nuclear charge radii.

physics.atom-ph↗

arXiv2025

$g$ Factor of Boron-like Tin

In the ALPHATRAP experiment, the $g$ factor of boron-like $^{118}\mathrm{Sn}^{45+}$ has been measured with a $0.5$ parts-per-billion uncertainty. This is the first high-precision measurement of a heavy boron-like $g$ factor. The measured value of $0.644\,703\,826\,5(4)$ is consistent with the presented \textit{ab initio} state-of-the-art theory calculations, which predict a value of $0.644\,702\,9(8)$. So far, the only boron-like $g$ factor measured with high precision has been $^{40}\mathrm{Ar}^{13+}$. The measurement presented here therefore tests quantum electrodynamics as well as many-electron interactions at much higher $Z$. Furthermore, we discuss the potential for an independent determination of the fine-structure constant $\alpha$, which can be achieved with a specific difference of $g$ factors, combining the presented results with the recent electron $g$-factor measurement of hydrogen-like tin.

physics.atom-ph↗

arXiv2025

Testing strong-field QED to second-order in the highly correlated atomic system berylliumlike Pb78+ by electron-ion recombination spectroscopy

A low-energy storage ring with an ultracold electron cooler has been coupled with a heavy-ion accelerator facilitating high-resolution electron-ion collision spectroscopy of the heaviest few-electron ions. In the present work resonant electron-ion recombination of berylliumlike Pb$^{78+}$ ions was measured in the collision-energy range 9.3-16.5eV and a value of 244.937(30) eV is derived for the Pb$^{78+}$($2s^2\;^1S_0 - 2s\,2p\;^3P_1$) excitation energy. This result agrees with the most recent (less accurate) theoretical value of 244.942(52) eV [Malyshev et al., Physical Review A 110, 062824 (2024)], which has been calculated by applying strong-field QED rigorously up to the second order. The present investigation suggests that further technical improvements can potentially increase the experimental accuracy by an order of magnitude.

physics.atom-ph↗

arXiv2025

Two-loop electron self-energy with accelerated partial-wave expansion

Calculations of the two-loop electron self-energy for the $n = 1$ and $n = 2$ states of hydrogen-like ions are reported, performed to all orders in the nuclear binding strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and $\alpha$ is the fine structure constant). The presented approach features an accelerated convergence of the partial-wave expansion and allows calculations to be accomplished for nuclear charges lower than previously possible and with a higher numerical accuracy.

physics.atom-ph↗

arXiv2025

Dielectronic recombination studies on Fe$^{2+}$

Dielectronic recombination resonance strengths, energy-differential cross sections, and recombination rate coefficients are calculated fully relativistically for Fe$^{2+}$ ions. The ground-state and resonance energies are determined using the multiconfiguration Dirac-Hartree-Fock method. Radiative and auto-ionization rates are computed with a relativistic configuration interaction method. For the calculation of Auger widths and resonance strengths, the continuum electron is treated within the framework of the relativistic distorted-wave model. Notably, the calculated level energies for Fe$^{2+}$ not only align well with experimental results but also show improvements compared to earlier theoretical studies. These fully relativistic calculations provide a more accurate and comprehensive understanding of the recombination process. This is particularly important in astrophysics and plasma physics, especially for studying phenomena such as kilonova events.

physics.atom-ph↗

arXiv2024

Nonlinear calcium King plot constrains new bosons and nuclear properties

Nonlinearities in King plots (KP) of isotope shifts (IS) can reveal the existence of beyond-Standard-Model (BSM) interactions that couple electrons and neutrons. However, it is crucial to distinguish higher-order Standard Model (SM) effects from BSM physics. We measure the IS of the transitions ${{}^{3}P_{0}~\rightarrow~{}^{3}P_{1}}$ in $\mathrm{Ca}^{14+}$ and ${{}^{2}S_{1/2} \rightarrow {}^{2}D_{5/2}}$ in $\mathrm{Ca}^{+}$ with sub-Hz precision as well as the nuclear mass ratios with relative uncertainties below $4\times10^{-11}$ for the five stable, even isotopes of calcium (${}^{40,42,44,46,48}\mathrm{Ca}$). Combined, these measurements yield a calcium KP nonlinearity with a significance of $\sim 900 \sigma$. Precision calculations show that the nonlinearity cannot be fully accounted for by the expected largest higher-order SM effect, the second-order mass shift, and identify the little-studied nuclear polarization as the only remaining SM contribution that may be large enough to explain it. Despite the observed nonlinearity, we improve existing KP-based constraints on a hypothetical Yukawa interaction for most of the new boson masses between $10~\mathrm{eV/c^2}$ and $10^7~\mathrm{eV/c^2}$.

physics.atom-ph↗

arXiv2024

One-loop electron self-energy with accelerated partial-wave expansion in Coulomb gauge

Numerical calculations of the electron self-energy without any expansion in the binding nuclear field are required in order to match the rapidly advancing precision of experimental spectroscopy. For the lightest elements, particularly hydrogen, these computations are complicated by large numerical cancellations and the slow convergence of the partial-wave expansion. Methods with accelerated convergence of the partial-wave expansion have been recently put forward [V. A. Yerokhin, K. Pachucki, V. M. Shabaev, Phys. Rev. A 72, 042502 (2005); J. Sapirstein and K. T. Cheng, Phys. Rev. A 108, 042804 (2023)]. In our work we extend the accelerated-convergence methods to the previously hardly accessible region of nuclear charges $Z < 5$ and higher excited states.

physics.atom-ph↗

arXiv2024

Two-loop electron self-energy for low nuclear charges

Calculations of the two-loop electron self-energy for the $1S$ Lamb shift are reported, performed to all orders in the nuclear binding strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and $\alpha$ is the fine structure constant). Our approach allows calculations to be extended to nuclear charges lower than previously possible and improves the numerical accuracy by more than an order of magnitude. Extrapolation of our all-order results to hydrogen yields a result twice as precise as the previously accepted value [E. Tiesinga et al. Rev. Mod. Phys. 93, 025010 (2021)], differing from it by 2.8 standard deviations. The resulting shift in the theoretical prediction for the $1S$-$2S$ transition frequency in hydrogen decreases the value of the Rydberg constant by one standard deviation.

physics.atom-ph↗

arXiv2023

Stringent test of QED with hydrogenlike tin

Inner-shell electrons naturally sense the electric field close to the nucleus, which can reach extreme values beyond $10^{15}\,\text{V}/\text{cm}$ for the innermost electrons. Especially in few-electron highly charged ions, the interaction with the electromagnetic fields can be accurately calculated within quantum electrodynamics (QED), rendering these ions good candidates to test the validity of QED in strong fields. Consequently, their Lamb shifts were intensively studied in the last decades. Another approach is the measurement of $g$ factors in highly charged ions. However, so far, either experimental accuracy or small field strength in low-$Z$ ions limited the stringency of these QED tests. Here, we report on our high-precision, high-field test of QED in hydrogenlike $^{118}$Sn$^{49+}$. The highly charged ions were produced with the Heidelberg-EBIT (electron beam ion trap) and injected into the ALPHATRAP Penning-trap setup, where the bound-electron $g$ factor was measured with a precision of 0.5 parts-per-billion. For comparison, we present state-of-the-art theory calculations, which together test the underlying QED to about $0.012\,\%$, yielding a stringent test in the strong-field regime. With this measurement, we challenge the best tests via the Lamb shift and, with anticipated advances in the $g$-factor theory, surpass them by more than an order of magnitude.

physics.atom-ph↗

arXiv2022

Direct measurement of the $^3$He$^+$ magnetic moments

Helium-3 has nowadays become one of the most important candidates for studies in fundamental physics [1, 2, 3], nuclear and atomic structure [4, 5], magnetometry and metrology [6] as well as chemistry and medicine [7, 8]. In particular, $^3$He nuclear magnetic resonance (NMR) probes have been proposed as a new standard for absolute magnetometry [6, 9]. This requires a high-accuracy value for the $^3$He nuclear magnetic moment, which, however, has so far been determined only indirectly and with a relative precision of $12$ parts per billon (p.p.b.) [10,11]. Here we investigate the $^3$He$^+$ ground-state hyperfine structure in a Penning trap to directly measure the nuclear $g$-factor of $^3$He$^+$ $g'_I=-4.255\, 099\, 606\, 9(30)_{stat}(17)_{sys}$, the zero-field hyperfine splitting $E_{\rm HFS}^{\rm exp}=-8\, 665\, 649\, 865.77(26)_{stat}(1)_{sys}$ Hz and the bound electron $g$-factor $g_e^\text{exp}=-2.002\, 177\, 415\, 79(34)_{stat}(30)_{sys}$. The latter is consistent with our theoretical value $g_e^\text{theo}=-2.002\, 177\, 416\, 252\, 23(39)$ based on parameters and fundamental constants from [12]. Our measured value for the $^3$He$^+$ nuclear $g$-factor allows for the determination of the $g$-factor of the bare nucleus $g_I=-4.255\, 250\, 699\, 7(30)_{stat}(17)_{sys}(1)_{theo}$ via our accurate calculation of the diamagnetic shielding constant [13] $\sigma_{^3He^+}=0.000\,035\,507\,38(3)$. This constitutes the first direct calibration for $^3$He NMR probes and an improvement of the precision by one order of magnitude compared to previous indirect results. The measured zero-field hyperfine splitting improves the precision by two orders of magnitude compared to the previous most precise value [14] and enables us to determine the Zemach radius [15] to $r_Z=2.608(24)$ fm.

physics.atom-ph↗

arXiv2022

Mass-difference measurements on heavy nuclides with at an eV/c2 accuracy level with PENTATRAP

First ever measurements of the ratios of free cyclotron frequencies of heavy highly charged ions with Z>50 with relative uncertainties close to 1e-11 are presented. Such accurate measurements have become realistic due to the construction of the novel cryogenic multi-Penning-trap mass spectrometer PENTATRAP. Based on the measured frequency ratios, the mass differences of five pairs of stable xenon isotopes, ranging from 126Xe to 134Xe, have been determined. Moreover, the first direct measurement of an electron binding energy in a heavy highly charged ion, namely of the 37th atomic electron in xenon, with an uncertainty of a few eV is demonstrated. The obtained value agrees with the calculated one using two independent different implementations of the multiconfiguration Dirac-Hartree-Fock method. PENTATRAP opens the door to future measurements of electron binding energies in highly charged heavy ions for more stringent tests of bound-state quantum electrodynamics in strong electromagnetic fields and for an investigation of the manifestation of Light Dark Matter in isotopic chains of certain chemical elements.

physics.ins-det↗

arXiv2021

$\text{Direct}~Q\text{-Value Determination of the}~\beta^-~\text{Decay of} ~^{187}\text{Re}$

The cyclotron frequency ratio of $^{187}\mathrm{Os}^{29+}$ to $^{187}\mathrm{Re}^{29+}$ ions was measured with the Penning-trap mass spectrometer PENTATRAP. The achieved result of $R=1.000\:000\:013\:882(5)$ is to date the most precise such measurement performed on ions. Furthermore, the total binding-energy difference of the 29 missing electrons in Re and Os was calculated by relativistic multiconfiguration methods, yielding the value of $\Delta E = 53.5(10)$ eV. Finally, using the achieved results, the mass difference between neutral $^{187}$Re and $^{187}$Os, i.e., the $Q$ value of the $\beta^-$ decay of $^{187}$Re, is determined to be 2470.9(13) eV.

nucl-ex↗

arXiv2021

Two-photon exchange corrections to the $g$ factor of Li-like ions

We report calculations of QED corrections to the $g$ factor of Li-like ions induced by the exchange of two virtual photons between the electrons. The calculations are performed within QED theory to all orders in the nuclear binding strength parameter $Z\alpha$, where $Z$ is the nuclear charge number and $\alpha$ is the fine-structure constant. In the region of low nuclear charges we compare results from three different methods: QED, relativistic many-body perturbation theory, and nonrelativistic QED. All three methods are shown to yield consistent results. With our calculations we improve the accuracy of the theoretical predictions of the $g$ factor of the ground state of Li-like carbon and oxygen by about an order of magnitude. Our theoretical results agree with those from previous calculations but differ by 3-4 standard deviations from the experimental results available for silicon and calcium.

physics.atom-ph↗