International Conference on Precision Physics of Simple Atomic Systems

Non-adiabatic, relativistic, and QED corrections to the rovibrational intervals of $\text{He}_2\ (\text{a}\ ^3\Sigma_\text{u}^+)$ and $\text{He}_2^+\ (\text{X}\ ^2\Sigma_\text{u}^+)$

18 May 2026, 17:47

1m

Aula (ÖAW)

Poster Poster Session 1

Speaker

Dr Ádám Margócsy (ELTE, Eötvös Loránd University)

Description

Spectroscopists have been interested in the low-lying electronically excited states of $\text{He}_2$ (the lowest being $^3\Sigma_\text{u}^+$, denoted as "a") and their cation (ground state $^2\Sigma_\text{u}^+$, denoted as "X") for decades. These excited states are strongly bound compared to the $^1\Sigma_\text{g}^+$ ground state and, therefore, have much richer rovibrational spectra. The accuracy of the experiment has improved drastically over the years for this system$^{1,2}$, the uncertainty of measured rotational intervals or vibrational spacings being on the order of $\sim10^{-4} \, \text{cm}^{-1}$ or even less. At the same time, theoretical predictions lag behind in many respects. While there are recent computations for the rotational-vibrational levels of the cation$^3$, only older results are available for $\text{He}_2 \ \text{a}$, which show a non-negligible discrepancy with experiment.

I present the joint effort of our group$^{4,5,6,7}$ towards the accurate computation of rovibrational and fine-structure levels of $\text{He}_2 \ \text{a}$, and improved computations for $\text{He}_2^+ \ \text{X}$. Using an explicitly correlated Gaussian basis representation, we computed variationally the non-relativistic Born-Oppenheimer potential energy curves (PEC). Along each PEC, diagonal Born-Oppenheimer correction and non-adiabatic mass corrections$^8$ were computed, as well as accurate leading-order relativistic and quantum-electrodynamical (QED) corrections using regularization techniques$^{9,10,11,4}$; higher-order QED corrections and nuclear finite size effects were approximately taken into account. Accurate rotational-vibrational energies were found by solving the Schrödinger equation of the nuclei with the corrected PEC. In the case of $\text{He}_2 \ \text{a}$, the magnetic dipole interaction gives rise to zero-field splitting and the fine-structure splitting of rotational energy levels. This splitting was also obtained by computing the relativistic and QED couplings between the $M_S=-1,0,+1$ components of the $\text{He}_2 \ \text{a}$ state.

Our work improves significantly on previous theoretical results for the rotational intervals, as well as the vibrational spacings. When QED corrections are properly taken into account, the computed fine-structure intervals are in similarly excellent agreement with available experimental data$^{12}$.

References

1. Semeria, Jansen, Merkt, J. Chem. Phys. 145 204301 (2016)
2. Semeria, Jansen, Camenisch, Mellini, Schmutz, Merkt, Phys. Rev. Lett. 124 213001 (2020)
3. Ferenc, Korobov, Mátyus, Phys. Rev. Lett. 125 213001 (2020)
4. Mátyus, Margócsy, Mol. Phys. e2611409 (2026)
5. Margócsy, Rácsai, Jeszenszki, Mátyus, J. Chem. Theory Comput. 22 5 2405 (2026)
6. Rácsai, Jeszenszki, Margócsy, Mátyus, J. Chem. Phys. 163 081102 (2025)
7. Jeszenszki, Hollósy, Margócsy, Mátyus, ACS Phys. Chem. Au 5 6 618 (2025)
8. Mátyus, Teufel, J. Chem. Phys. 151 014113 (2019)
9. Ferenc, Mátyus, J. Phys. Chem. A 127 627 (2023)
10. Pachucki, Cencek, Komasa, J. Chem. Phys. 122 184101 (2005)
11. Rácsai, Ferenc, Margócsy, Mátyus, J. Chem. Phys. 160 211102 (2024)
12. Focsa, Bernath, Colin, J. Mol. Spectr. 191 209 (1998)