# Precise calculations of atomic spectra and tests of fundamental physics

**Advisor:** Vojtěch Patkóš & Jaroslav Zamastil (MFF CUNI)

**Funding:** Basic scholarship

**Website:** http://quantum.karlov.mff.cuni.cz/~vpatkos/

As the "nightmare scenario" at LHC, namely the discovery of the Higgs particle and nothing more, became reality, the fundamental physics has started facing a serious problem. On one hand, we know for sure that the Standard Model (SM) of fundamental constituents and interactions is incomplete, yet on the other hand, we do not know even the scale where to search for physics beyond the SM. In this situation, precise low-energy tests of the SM offer one of the viable possibilities how to proceed further in our exploration of fundamental physical laws.

In present time the atomic spectroscopic measurements achieved such a high accuracy that if they are accompanied by precise theoretical calculations they can provide bounds on the hypothetical new particles and forces that exceed those obtained at LHC (see e.g. https://www.nature.com/articles/d41586-018-00106-5, https://www.nature.com/articles/s41586-018-0599-8).

Comparison of the theory and experiment for muonic and ordinary hydrogen recently generated the so called radius proton-puzzle (R. Pohl et al., Nature 466, 213 (2010), for recent review see J.-P. Karr and D. Marchand, Nature 575, 61 (2019)). Also, there is an inconsistency concerning various determinations of charge radii of helium nuclei from different experiments, see [4] for review.

The goal of the project is to improve the accuracy of theoretical determination of atomic spectra for the lightest of atoms, i.e. hydrogen and helium.

For hydrogen, we have developed a method for calculation of the one-loop self-energy [1,2]. Using this method, we were able to calculate the self-energy of hydrogen-like atoms with the accuracy matching, or even better than, that of other approaches. The aim is to extend this method to two-loops self-energy that constitutes the greatest present uncertainity in theoretical calculation [3].

In the case of the helium atom, the most effective way to calculate atomic
spectra is to use the so called Nonrelativistic QED (NRQED) method. In this
method, energy levels are expressed as a series in the powers of the fine
structure constant α. At the present time, the energy levels are evaluated up
to the order α^{6}*m*/*M* where *m* is the mass of
electron and *M* is the mass of the nucleus [4]. Our aim is to calculate
the next order correction which is of the order α^{7}.

References:

- J. Zamastil, V. Patkóš: "Self-energy of an electron bound in a Coulomb field", Phys. Rev. A 88, 032501 (2013).
- V. Patkóš, J. Zamastil: "Lamb shift for states with j=1/2", Phys. Rev. A 91, 062511 (2015).
- V. A. Yerokhin, K. Pachucki, V. Patkóš: "Theory of the Lamb Shift in Hydrogen and Light Hydrogen‐Like Ions", Ann. Phys. (Berl.), 1800324 (2019).
- K. Pachucki, V. Patkóš, V. A. Yerokhin: "Testing fundamental interactions on the helium atom", Phys. Rev. A 95, 062510 (2017).