Modern high-precision experiments with highly charged ions require equivalent accuracy intheoretical calculations within bound-state quantum electrodynamics (QED). Measurements of the $g$-factor in hydrogen-like ions demonstrate record accuracy up to 10^-11 [1], necessitating the account of quantum-electrodynamic corrections to atomic characteristics.

Among QED corrections, the self-energy contribution plays a key role, being critical for calculating energy levels, the g-factor, hyperfine splitting, and the quadratic Zeeman effect. Theoretical calculations for highly charged ions must consider all orders of the electron–nucleus coupling parameter, with the main uncertainty arising from the slow convergence of partial-wave expansions [2, 3]. Green's function of an electron in a central potential, computed through solutions of systems of differential equations, serves as an effective tool for high-precision calculations [4, 5].

In this work, Green's function method is applied to analyze single and double interactions with an external field. General expressions for radial Green functions with potentials that change angular quantum numbers have been obtained. The developed approach allows for the calculation of one- and two-potential self-energy corrections. The method is applied to hyperfine structure calculations, showing its high accuracy compared to alternative computational methods. The quadratic Zeeman effect in hydrogen-like ions is also calculated.

This research was supported by the Theoretical Physics and Mathematics Advancement Foundation ``BASIS'' (Grant No. 24-1-2-74-3).

[1] H. Haffner et al., Phys. Rev. Lett. 85, 5308 (2000).
[2] V. A. Yerokhin et al., Phys. Rev. A 60, 3522 (1999).
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[4] P. Mohr et al., Phys. Rep. 293, 227 (1998).
[5] V. A. Yerokhin, A. V. Maiorova, Symmetry 12, 800 (2020).

In this study, we examine the applicability of the Dirac–Fock plus Core-Polarization (DFCP) method to atomic characteristics calculations [1]. We present results for static electric-dipole polarizability, the thermal Stark shift and the Bethe logarithm [2]. The evaluation of these quantities requires summation over intermediate discrete states and integration over continuum states. While such summations can be carried out directly and with controlled convergence in exactly solvable systems (e.g., hydrogen-like atoms and ions), the situation becomes significantly more complex for many-electron atoms and ions due to the difficulty of reproducing the complete atomic spectrum.

To solve this problem, there are approximate approaches, including the use of model potentials, which are especially effective for monovalent atoms and ions of the alkaline group. In our work, we employ the DFCP method, which based a local form of the Dirac–Hartree–Fock potential [3] (LDFCP). We solve the radial part of the Dirac equation using a finite basis based on B-splines using the dual kinetic balance (DKB) method [4]. In this framework, the complete spectrum—discrete, continuum, and negative continuum—is replaced by a discrete pseudo-spectrum enabling summation over intermediate states (the so-called «sum-over-states» method). The pseudo-spectrum is constructed so that the lowest positive-energy states accurately reproduce the experimental low-lying bound states of the valence electron. The valence electron is considered in the self-consistent field of a frozen core, while core–valence correlation effects are described using a semi-empirical core-polarization potential.

We have obtained a complete spectrum of the energies and wave functions of the effective one-particle Hamiltonian using the LDFCP method. This allowed us to calculate some properties of atoms.This allowed us to calculate some properties of atoms such as polarizability, the thetmal Stark shift, the Bethe logarithm.

A comparison of the results obtained with the data from the literature calculated by other methods shows a good correspondence.

Abstract:

Scattering is one of the most powerful tools for studying the dynamics of particle interactions in the presence of external fields such as laser or magnetic fields. The objective of this work is to investigate the scattering dynamics of an electron interacting with the Yukawa potential in the presence of bichromatic polarized laser fields. For this purpose, the Kroll–Watson approximation, the Volkov wave equation, and the Yukawa potential are used [1-2]. The S-matrix is determined, and, using the Kronecker delta condition, the transition matrix is developed, which is directly related to the differential cross-section (DCS) for different polarizations. The transition matrix, along with the initial and final momentum of the electron, is used to analyze the scattering dynamics by computing the developed equations. The result shows that the DCS is highly sensitive to the screening parameter, momentum transfer, separation distance, and scattering angle. Distinct peaks emerge for different screening strengths, with their positions and intensities varying systematically with changes in the scattering angle and screening effect. When the change in momentum is minimum, the high and low peaks of the DCS are most pronounced; conversely, they decrease as the momentum change increases. The DCS attains its maximum value when the screening parameter is minimal, and this behavior is similarly observed in the variation of DCS with respect to separation and screening parameters. The developed theoretical model provides new insights into multiphoton processes and resonance mechanisms in laser-assisted scattering.

[1]Liu, P., Wang, Q., & Li, X. (2009). Studies on CdSe/L-cysteine quantum dots synthesized in aqueous solution for biological labeling. Journal of Physical Chemistry C, 113(18),7670–7676.

[2]Maurer, J., and Keller, U. (2021). Ionization inintense laser fields beyond the electric dipoleapproximation: concepts, methods, achieVementsand future directions. Journal of Physics B: Atomic,Molecular and Optical Physics, 54(9), 40-45.

Introduction

Significant advances in high-precision measurements of Zeeman splitting in highly charged ions have been achieved over the past quarter century. The corresponding leap in measurement precision, together with theoretical research, made it possible to determine the most accurate up-to-date electron mass determination. It is expected that in the near future high-precision g-factor measurements in hydrogen-, lithium- and boronlike ions will provide a high-precision tool for independent fine structure constant determination. New experiments on the g-factor of excited p-states enable separate measurement of the quadratic Zeeman effect. The quadratic Zeeman effect, studied for over eight decades, gains renewed importance in ultra-strong magnetic fields of magnetars and precision atomic clocks. Theoretical understanding of interelectronic interactions remains crucial for accurate interpretation of experimental data from projects like ALPHATRAP and ARTEMIS.

Methods

We present theoretical calculations of two-photon exchange corrections to the quadratic Zeeman effect in boron-like ions within the Breit approximation. This work extends previous theoretical treatments that established foundational calculations including leading-order terms, one-loop QED corrections, and one-photon-exchange contributions. The computational approach systematically addresses the dominant sources of uncertainty in quadratic Zeeman effect calculations for middle-Z boron-like systems.

Results and Discussion

Our calculations reveal that the two-photon exchange correction constitutes a significant contribution to the quadratic Zeeman effect in middle-Z boron-like ions. The results demonstrate that interelectronic interactions substantially influence the quadratic Zeeman splitting.

Conclusions

The two-photon exchange correction represents an advancement in the theoretical description of quadratic Zeeman effects in boron-like systems. Our results substantially reduce the theoretical uncertainty in quadratic Zeeman splitting calculations. These findings have direct implications for ongoing experiments with boron-like ions and contribute to improved understanding of atomic structure in magnetic fields.

Introduction:

The interaction of a two-level atom with an electromagnetic field inside a cavity is described by the Jaynes–Cummings model. It predicts an interesting feature, namely, the collapse and revival of atomic population inversion especially when an atom interacts with the coherent state |α>.

Methods:

In this study, we consider the Jaynes–Cummings Hamiltonian H=ω₀σ_z/2 + ω_ca⁺a + g(σ_{_}a⁺ + σ₊a). The atomic population inversion is defined as W(t)=<Ψ(t)|σ_z|Ψ(t)>, where |Ψ(t)> is the time-evolved state calculated through |Ψ(t)>= e^-iHt |Ψ(0)>. The initial state is defined as follows: the atom is in its excited state and the field is in a number-state filtered coherent state (NSFCS). NSFCS is obtained by filtering out a number state (for example, |m> from a coherent state).

Results and Discussion:

We observed the following: (i) The atomic population inversion no longer exhibits the collapse feature; instead, it displays micro-Rabi oscillations with small amplitudes, indicating a washout of perfect destructive interference. (ii) The amplitude can be tuned by filtering an appropriate number state. (iii) The amplitude is maximum when m is |α|². (iv) The number of oscillations present in the collapse region is
given by k=√m+1 gΔt_c/ Π, where g is the atom–cavity coupling strength.

Conclusion: We studied the effect of number-state filtration from an initial coherent state on the temporal dynamics of atomic population inversion. We observed the emergence of micro-oscillations in the collapse region due to washout of destructive
interference.

In this study, we investigate electron interactions with the magnesium sulfide (MgS) [1] molecule, the first metallic sulfide molecule detected in the interstellar medium (ISM). Its presence in the ISM is significant because metal-containing molecules in the gas phase are generally rare due to the refractory nature of metals. It is observed near the Galactic Centre, known as G+0.693-0.027 [1]. Its vertical ionisation threshold is reported at 7.64 eV [1], while the dipole moment is given as 7.07 Debye [1], which is quite high. A study of electron interactions with MgS is important, as it has applications in astrophysics, plasma physics, and interstellar chemistry. To understand how MgS interacts with electrons in astrochemistry modelling, scattering cross-sections are required. To determine various cross-sections, we employed the R-Matrix method [2] for low energies (below 15 eV) and used the spherical complex optical potential (SCOP) along with the complex scattering potential–ionisation contribution (CSP-ic) [3] for the energy range of 15–5000 eV. Low-energy electron interaction cross-sections are calculated using three models: static exchange (SE), static exchange and polarisation (SEP), and configuration interaction (CI). During the meeting, we will report the electron impact elastic, ionisation, total, excitation, and dissociative electron attachment cross-sections of MgS. The molecular structure is optimised for MgS, and different properties, such as dissociation energy, bond length, polarisability, and ionisation potential, are reported using the software Avogadro [4] and ORCA [5].

References

[1] Marta Rey-Montejo et al. Discovery of MgS and NaS in the Interstellar Medium and Tentative Detection of CaO. ApJ, 975, 174, 2024

[2] Tomer et al. Low-Energy Electron Scattering from Pyrrole and Its Isomers J Phys Chem A. 127, 12, 2023

[3] Yadav et al. Investigation of Electron Collisions with Organic Phosphates. J Phys Chem A. 129, 34, 2025

[4] M. D. Hanwell et al. Avogadro: an advanced semantic chemical editor, visualisation, and analysis platform. J. Cheminform, 4:22889332, 2012.

[5] F. Neese et al. The orca quantum chemistry program package. J. Chem. Phys., 152:224108, 2020.

To solve the strong CP problem in QCD, a global U(1) Peccei–Quinn symmetry is postulated [1, 2]. Its spontaneous breaking gives rise to a pseudo-Nambu–Goldstone boson, the axion, which eliminates CP violation in strong interactions [3, 4]. Extensions of the Standard Model predict the emergence of new particles [5]. For example, additional U(1) gauge symmetries can lead to the appearance of a dark photon—a massive vector particle that acts as a mediator of interactions within the dark sector. As the dark matter problem remains one of the key issues in modern physics, the study of axions and dark photons opens new possibilities for reconciling cosmological data with experimental results [6].

Despite the success of the Standard Model, its incompleteness drives the development of precision methods, with measurements of the bound-electron g factor and energy spectra in highly charged ions (HCIs) playing a central role. Significant progress has been achieved in HCI research in these areas [7, 8]. The strong Coulomb field of the HCI nucleus enhances relativistic and quantum electrodynamic effects, while their simple electronic structure enables high-precision calculations. High-precision measurements of the HCI g factor [9-12], when compared with theoretical predictions, provide opportunities to detect deviations arising from new physics [13-15].

In this work, we investigate the interaction of bound electrons, mediated by new physics models (such as axions, dark photons, and others), and its impact on the energy levels and g factors of few-electron ions. The study is devoted to assessing the contribution of these effects that emerge from the exchange of virtual axions or dark photons between electrons. This approach opens up the possibility of establishing stringent constraints on the parameters of the considered models. We also examine systems and configurations in which corrections associated with new physics are enhanced.

In hadrontherapy, reference dosimetry relies on air-filled ionization chambers [1]. Converting chamber readings to absorbed doses in water requires knowledge of the stopping power and the W-value in air (Wₐ), defined as the mean energy needed to produce an electron–ion pair. Experimental data for Wₐ for fast ions are limited, while theoretical calculations are highly demanding, as they must account for ion pairs generated by both the primary ion and all secondary electrons. Therefore, international protocols recommend a constant W-value, independent of beam quality, which represents a major source of uncertainty. This study aims to calculate these parameters for ion interactions in air to reduce uncertainties in reference dosimetry.

Calculations were performed with the MDM-Ion Monte Carlo code, extended to the studied media and ion projectiles [2,3,4], and with an analytical model based on the Continuous Slowing Down Approximation [5]. The adopted cross sections include relativistic corrections for projectile kinetic energy and consider the contribution from Auger electron emission.

The stopping power results obtained with the relativistic approximation show excellent agreement with the reference data reported in ICRU90. For the w-values, a good consistency is observed with other theoretical models and recommended data when post-collisional effects are taken into account. Moreover, this parameter exhibits a strong sensitivity to the choice of excitation cross sections employed in the calculations.

Stopping power is strongly influenced by relativistic corrections. In contrast, the w-values are mainly affected by the selection of excitation cross sections and post-collision effects, while remaining largely independent of the projectile type, approaching a constant value at high energies.

[1] IAEA TRS-398. (2000) http://www-naweb.iaea.org/nahu/DMRP/documents/CoP_V12_2006-06-05.pdf

[2] Tessaro (2019), NIMB doi:10.1016/j.nimb.2018.11.031.

[3] Tessaro (2021), Physica Medica, doi:10.1016/j.ejmp.2021.06.006.

[4] Tessaro (2022) Cotutelle Phd thesis: Universidad Nacional de Rosario (Argentina) and Universidad de Lyon 1 (Francia).

[5] Inokuti (1975), Radiation Research 64(1):6–22.

The description of molecular ionisation processes by electron impact represents a challenging scenario in the field of atomic collisions, given their relevance in both astrophysical and biological contexts. In particular, water (H₂O) and tetrahydrofuran (C₄H₈O or THF) have been considered biological system prototypes in radiation processes; hence, fully differential cross-sections have been recently measured for the electron impact single ionisation of these molecules [1, 2]. From a theoretical point of view, perturbative models have been the reasonable choice to analyse these processes, since the inherent complexity of these targets makes difficult the implementation of numerical intensive methods.
In this work we calculate and analyse fully differential cross-sections of the electron impact single ionisation of H₂O and THF by means of two single-centre approximations to the final state of the collisional process, which are variants of the perturbative method CDW-EIS. The first one approximates the molecular ion as a single centre of charge +1, while the second one spherically averages the anisotropic interaction with the residual ion. We benchmark our results with recent experimental data reported in the literature, where we observe good overall agreement for the impact energies considered [3]. In addition, we discuss different difficulties that arise by modelling multi-centre targets with single-centre wave functions.

[1] J. Zhou, E. Ali, M. Gong, S. Jia, Y. Li, Y. Wang, Z. Zhang, X. Xue, D. V. Fursa, I. Bray, X. Chen, D. Madison, A. Dorn, and X. Ren, Phys. Rev. A 104, 012817 (2021).
[2] X. Xue, D. M. Mootheril, E. Ali, M. Gong, S. Jia, J. Zhou, E. Wang, J.-X. Li, X. Chen, D. Madison, A. Dorn, and X. Ren, Phys. Rev. A 106, 042803 (2022).
[3] E. Acebal and S. Otranto, Phys. Rev. A 109, 062807 (2024).

This work aims to study the scattering dynamics of electron–H₂⁺ molecules under the influence of self-generated laser and thermal fields in a Proton Exchange Membrane Fuel Cell (PEMFC). The system is modeled considering that one electron of the hydrogen molecule participates in an exothermic reaction that is catalyzed by platinum, while the other electron remains non-reactive, forming –H₂⁺ . The reaction generates localized temperature rise and motion of charged particles, which produce a spectrum of electromagnetic wavelengths, contributing to a laser-like field within the PEMFC. To analyze this system, thermal Volkov wavefunctions and the hydrogen ion potential were employed to calculate the scattering and transition matrices, which were then used to determine the differential cross-section (DCS) of electron–H₂⁺ interactions near the PEMFC electrode. This approach is significant, because although numerous studies focus on material selection, design, and simulations, few address the microscopic scattering processes affecting PEMFC performance. The computed results reveal that the DCS decreases with increasing incident electron energy [1], increases with thermal conductivity, and rises with temperature, showing oscillatory sinusoidal behavior. As the DCS is directly related to the temperature, and the temperature is inversely related to the cell voltage, an increase in temperature leads to a decrease in voltage and overall performance of the PEMFC. Therefore, understanding electron–H₂⁺ scattering dynamics is essential for improving PEMFC efficiency and thermal management. These findings highlight the importance of incorporating microscopic scattering analysis alongside conventional approaches for optimizing fuel cell operation .

[1] Dhobi, S. H., Gupta, S. P., Yadav, K., & Jha, A. K. (2025). Scattering Dynamics in Thermal Environments Around PEMFC Electrode. International Energy Journal, 25(1A).