Contrary to the muonic atoms case, it is well known that the self-energy correction to the solutions of the Dirac equation dominates vacuum-polarization in electronic atoms. However, having precise results for the latter contribution is crucial to obtaining accurate numerical results on the first-order QED corrections to the Dirac equation. Accounting for the vacuum polarization effect is...
In the framework of the perturbation theory we consider the fine structure of the energy levels of few-electron atoms and ions in the states with the dominant configuration containing one or two $p$-electrons (or one $d$-electron). Using highly accurate expansions
of the nonrelativistic wave functions in terms of all-particle explicitly correlated Gaussians, we derived analytical expressions...
Variational, nonrelativistic energies of eight states of the carbon atom have been calculated with high precision. The states of interest include two low-lying singlet P and D states, as well as triplet P and D states, all of even parity. The wave functions are expanded in the basis of products of Explicitly Correlated Gaussians and bipolar harmonics.
Major progress in spectroscopy of ro-vibrational transitions of hydrogen molecular ions (HMI) has been achieved in the past few years, and the precision of these measurements can still be pushed further. In conjunction with further developments in the theory, this would yield tighter constraints on physics beyond the standard model and improved determinations of fundamental constants.
The...
Precision measurement of positronium, the bound-state of an electron and a positron, can be used to probe fundamental theories and place constraints on physics beyond the standard model [1]. Previous spectroscopic studies [2, 3] of the n=2 fine-structure intervals using slow-moving clouds of positronium have achieved only mediocre precision compared with studies of simple atomic systems (e.g....
We present a recent progress towards experiments with hydrogen atoms at ultra-low energies, nearly at rest. This work is a part of an international collaboration GRASIAN (Gravity, Spectroscopy and Interferometry with Atoms and Neutrons) [1]. The motivation for the work proposed here is associated with weak short-range forces exerted by yet undiscovered light bosons, direct checking of the...
The investigation on high-precision calculations of molecular ions emerges as a captivating and fascinating domain of research. The meticulous exploration of molecular ions necessitates a comprehensive understanding of their structural, electronic and dynamic properties. In a molecular system, unlike in an atomic system, describing nuclear motion is significantly more complicated due to the...
This project aims to perform spectroscopy of H_2 above the n=2 and n=3 dissociation limits to observe its photofragments utilizing velocity map imaging (VMI) and study the competition between predissociation and autoionization by measuring the energy and angular distribution of the H^+ and H_2^+ ions [1]. To this end, the molecule is first excited via a one-photon transition to the B state...
The reason why there is no primordial antimatter in the Universe remains a mystery. Measurements with antimatter [1][2] show full compatibility with its matter counterparts at high precision and that the antimatter feels Earth's gravitational attraction similarly to matter [3] at low precision.
Antihydrogen (Hbar) is produced by trapping antiprotons and positrons in neighboring wells in a...
Rigorous tests of QED and precise measurements of the proton-to-electron mass ratio are compelling applications for high precision spectroscopy of the dihydrogen cation. We propose to carry out millimeter-wave spectroscopy in the Lamb-Dicke regime on $H_2^+$ in a radiofrequency ion trap. This technique enables Doppler-free spectroscopy with a high signal-to-noise ratio, when used in...
Hydrogen molecule and hydrogen molecular ion remain important for test of QED and the determination of fundamental constants. For both of them both the leading ($\alpha^3$) and next-to-leading ($\alpha^4$) QED corrections have been computed in the Born-Oppenheimer approximation. We present extremely accurate calculation of the asymptotic behavior of the QED correction for large inter-nuclear...
The extreme ultraviolet (XUV) frequency comb is an indispensable tool for extending optical frequency metrology into the unexplored wavelength range below 200 nm. With XUV frequency combs, precision spectroscopy for fundamental physics, optical clocks and laser cooling can be extended into the XUV regime for the first time. This includes applications in the spectroscopy of hydrogen-like ions...
The ionisation energies of many atoms and molecules lie in the vacuum ultraviolet (VUV) and extreme ultraviolet (XUV) parts of the electromagnetic spectrum, which correspond to wavelengths (frequencies) of light of $<200~\mathrm{nm}$ $(>1.5 \times 10^{15}~\mathrm{Hz})$ and $<105~\mathrm{nm}$ $(>2.9 \times 10^{15}~\mathrm{Hz})$, respectively [1]. Laser radiation generated at these wavelengths...
Atomic spectroscopy experiments at the precision frontier allow us to study low-energy nuclear structure, test bound-state QED, refine fundamental constants, and potentially find New Physics.
As experimental precision is continuously improved, it is a timely task to re-examine the sensitivity of specific bound states to New Physics scenarios. Depending on their Bohr radii, hydrogen-like...
The equal-time Bethe–Salpeter (Salpeter–Sucher) equation is the exact QED wave equation for a two-fermion system $[1, 2, 3, 13, 14]$. The equation containing only the instantaneous part of the interaction is the with-pair Dirac–Coulomb(–Breit) equation (wpDC(B)), which includes the double-pair correction to the no-pair DC(B) equation (npDC(B)). The numerical results for these equations can be...
XUV comb has leads to a joint frontier of precision spectroscopy and ultrafast science since its first demonstration in 2005 [1-2]. On one hand, it provides a coherent light source in the XUV region with narrow band width for the first time. This advance paves the way for measuring important atomic transitions in the XUV region [3-4]. On the other hand, ultrafast processes on the...
Drachmann's regularization approach is implemented for floating explicitly correlated Gaussians (fECGs) and molecular systems. Earlier applications of Drachmannized relativistic corrections for molecular systems were hindered due to the unknown analytic matrix elements of $1/r_{ix}1/r_{jy}$-type operators with fECGs. In the present work, one of the $1/r$ factors is approximated by a linear...
The ASACUSA collaboration carries out laser spectroscopy of metastable antiprotonic helium atoms ($\bar{p}He^+=\bar{p}+He^{2+}+e^-$) at CERN’s Antiproton Decelerator facility [1-5]. This is a three-body Coulomb system composed of a helium nucleus, an electron, and orbital antiproton. CERN has recently commissioned the ELENA ring, which produced cooled beams of antiprotons with >100 times...
The Swiss Federal Institute of Metrology METAS and its Photonics, Time and Frequency laboratory are responsible for realizing, maintaining and disseminating the Swiss Coordinated Universal Timescale UTC(CH), and is thus contributing to the realization of UTC at the international level. The realization of UTC(CH) is based on an ensemble of atomic clocks, jointly with our own primary frequency...
Among the leading Quantum Electrodynamical (QED) corrections to atomic-molecular energy levels, the effect of one-loop electron self-energy has proven to be one of the most challenging to compute.
There are well-established techniques to calculate it in two extreme cases (for predominantly non-relativistic[1] and highly relativistic[2] systems, like low-charged and highly charged ions,...
