arXiv subjects

Maen Salman

Publications and source records attributed to Maen Salman.

6 recordsLinked to original sources

arXiv2026

One-loop self-energy using a numerical Green function

We calculate the one-loop self-energy in hydrogenlike atoms using a numerical Green function obtained by solving the radial Dirac equation in an exponential basis set. The self-energy correction in the ground state of hydrogenlike uranium is obtained with about $10^{-5}$ relative uncertainty in the Feynman gauge. Using a convergence acceleration scheme, we extend our calculations to the region of low nuclear charges. Our results allow calculating the self-energy correction for the hydrogen atom with $10^{-4}$ relative uncertainty. Calculations in the Coulomb gauge are also presented, improving the precision to $10^{-5}$. Present limitations and possible improvements of our method are discussed.

physics.atom-ph↗

arXiv2026

Photodetachment energy of negative hydrogen ions

We report a high-precision calculation of the photodetachment energy of the hydrogen anion \mathrm{H}^{-}. The nonrelativistic bound-state energy is obtained using an exact three-body approach, and supplemented by leading relativistic, quantum-electrodynamic, finite-nuclear-size, and hyperfine corrections. Our result is 6083$.$06447(68)\mathrm{cm}^{-1} for the detachment to the hydrogen ground-state hyperfine level \mathit{(F=0)}, which is 220 times more precise than the best experimental determination to date, 6082$.$99(15)\mathrm{cm}^{-1}, as reported by Lykke \mathit{et al.} Beyond their intrinsic interest, these results provide critical input for antihydrogen physics, where controlled photodetachment of \bar{\mathrm{H}}^{+} offers a path to producing ultracold antihydrogen (and its isotopes) for precision experiments. Corresponding calculations for the negative deuterium and tritium ions yield 6086$.$70676(68)\mathrm{cm}^{-1} for ^{2}\mathrm{H}^{-}(F=1/2) and 6087$.$87924(68)\mathrm{cm}^{-1} for ^{3}\mathrm{H}(F=0).

physics.atom-ph↗

arXiv2025

Wichmann-Kroll vacuum polarization density in a finite Gaussian basis set

This work further develops the calculation of QED effects in a finite Gaussian basis. We focus on the non-linear $α(Zα)^{n\ge 3}$ contribution to the vacuum polarization density, computing the energy shift of 1s$_{1/2}$ states of hydrogen-like ions. Our goal is to improve the numerical computations to achieve a precision comparable to that of Green's function methods reported in the literature. To do so, an analytic expression for the linear contribution to the vacuum polarization density is derived using Riesz projectors. Alternative formulations of the vacuum polarization density and their relation is discussed. The convergence of the finite Gaussian basis scheme is investigated, and the numerical difficulties that arise are characterized. In particular, an error analysis is performed to assess the method's robustness to numerical noise. We then report a strategy for computing the energy shift with sufficient precision to enable a sensible extrapolation of the partial-wave expansion. A key feature of the procedure is the use of even-tempered basis sets, allowing for an extrapolation towards the complete basis set limit.

quant-ph↗

arXiv2025

Gaussian basis set approach to one-loop self-energy

We report a method for the evaluation of the one-loop self-energy, to all orders in the external binding field, using a Gaussian basis set expansion. This choice of basis is motivated by its widespread use in molecular calculations. For a one-electron atom, our results show excellent agreement with those obtained using the exact Dirac--Coulomb wave functions. The developed method can be of interest for high-precision studies of heavy few-electron molecular systems, where the rigorous computation of QED corrections is currently a formidable task.

quant-ph↗

arXiv2023

Calculating the many-potential vacuum polarization density of the Dirac equation in the finite-basis approximation

In this work, we propose an efficient and accurate computational method to evaluate the many-potential $α\left(Zα\right)^{n\ge3}$ vacuum polarization density of hydrogen-like atoms within the finite-basis approximation of the Dirac equation. To prove the performance of our computational method, we choose to work with the one-electron $_{\,\,\,92}^{238}\text{U}$ atom. In summary, we find that compliance with charge conjugation symmetry is a priori required to obtain physical results that are in line with our knowledge of the analytical problem. We also note that the final numerical results are found to be in excellent agreement with previous formal analytical (and numerical) evaluations that are limited to a few simple nuclear distribution models. Our technique can be efficiently implemented and evaluated in codes that solve the radial Dirac equation in the finite basis set framework and allows the use of arbitrary (radial) nuclear charge distribution. The obtained numerical results of the non-perturbative vacuum polarization density automatically account for the extended nuclear size effect. This method is hence of special importance for atomic Dirac problems whose analytical Green's functions expressions are not at hand or have relatively complicated analytical forms. Furthermore, we propose a vacuum polarization density formula that forces compliance with charge conjugation symmetry and can be used in cases where the relativistic basis violates this symmetry, as is the case in most relativistic basis set programs. In addition, we have shown that vector components of the vacuum polarization four-current vanish in the case where the Dirac Hamiltonian is symmetric under time-reversal symmetry.

physics.atom-ph↗

arXiv2022

4-component relativistic Hamiltonian with effective QED potentials for molecular calculations

We report the implementation of effective QED potentials for all-electron 4-component relativistic molecular calculations using the DIRAC code. The potentials are also available for 2-component calculations, proper picture-change being mandatory. Specificially, we have implemented the Uehling potential [E. A. Uehling, Phys. Rev. 48 , 55 (1935)] for vacuum polarization and two effective potentials [P. Pyykkö and L.-B. Zhao, J. Phys. B 36 , 1469 (2003); V. V. Flambaum and J. S. M. Ginges, Phys. Rev. A 72 , 052115 (2005)] for electron self-energy. We provide extensive theoretical background for these potentials. We report the following sample applications: i) we confirm the conjecture of Pyykkö that QED effects are observable for the AuCN molecule by directly calculating ground-state rotational constants $B_0$ of the three isotopomers studied by MW spectroscopy; QED brings the corresponding substitution Au-C bond length $r_s$ from 0.23 to 0.04 pm agreement with experiment, ii) spectroscopic constants of van der Waals dimers M$_2$ (M=Hg, Rn, Cn, Og) iii) there is a significant change of valence s population of Pb in the reaction PbH$_4$ -> PbH$_2$ + H$_2$, which is thereby a good candidate for observing QED effects in chemical reactions, as proposed in [K. G. Dyall et al., Chem. Phys. Lett. 348 , 497 (2001)]. QED contributes 0.32 kcal/mol to the reaction energy, thereby reducing its magnitude by -1.27 %. For corresponding hydrides of superheavy flerovium, the electronic structures are quite similar. Interestingly, the QED contribution to the reaction energy is of quite similar magnitude (0.35 kcal/mol), whereas the relative change is significantly smaller (-0.50 %). This curious observation can be explained by the faster increase of negative vacuum polarization over positive electron self-energy contributions as a function of nuclear charge.

physics.chem-ph↗