Related papers: Bethe logarithm for the helium atom
The Lagrange-mesh method has the simplicity of a calculation on a mesh and can have the accuracy of a variational method. It is applied to the study of a confined helium atom. Two types of confinement are considered. Soft confinements by…
Spectroscopic measurements of the helium atom are performed to high precision using an atomic beam apparatus and electro-optic laser techniques. These measurements, in addition to serving as a test of helium theory, also provide a new…
The total energies and various bound state properties of the excited $2^1S(L = 0)-$states in two-electron helium atoms, including the ${}^{\infty}$He, ${}^4$He and ${}^3$He atoms, are determined to very high numerical accuracy. The…
We analyze the conditions for producing atomic number states in a one-dimensional optical box using the Bethe ansatz method. This approach provides a general framework, enabling the study of number state production over a wide range of…
Topological data analysis has emerged as a powerful tool for analyzing large-scale data. An abstract simplicial complex, in principle, can be built from data points, and by using tools from homology, topological features could be…
Ultracold dilute gases provide ideal settings for measurements of atomic structure. Helium has an internal structure sufficiently simple to permit highly accurate predictions of its resonances and transition rates. Precise laser…
High-precision measurements of the fine-structure splittings in helium high Rydberg states have been reported, yet corresponding ab initio benchmarks for direct comparison remain unavailable. In this work, we extend the correlated B-spline…
The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schr\"odinger equation and account for relativistic and QED effects by perturbation…
In order to explain discrepancies between theoretical predictions and experimental data for the helium fine structure, we check and recalculate all theoretical contributions up to orders m\alpha^7 and m^2/M\alpha^6. The previous result for…
A sensitive laser spectroscopic method has been applied to the quantitative determination of the isotope ratio of helium at the level of 3He/4He = 10^-7 - 10^-5. The resonant absorption of 1083 nm laser light by the metastable 3He atoms in…
Improvements in both theory and frequency metrology of few-electron systems such as hydrogen and helium have enabled increasingly sensitive tests of quantum electrodynamics (QED), as well as ever more accurate determinations of fundamental…
The Bethe approximation is a well-known approximation of the partition function used in statistical physics. Recently, an equality relating the partition function and its Bethe approximation was obtained for graphical models with binary…
The method and status of a study to provide numerical, high-precision values of the self-energy level shift in hydrogen and hydrogen-like ions is described. Graphs of the self energy in hydrogen-like ions with nuclear charge number between…
We describe a method for deriving logarithmic corrections in the mass ratio to the S-level of a hydrogen-like atom. With this method, a number of new corrections of this type are calculated analitically for the first time.
The Faddeev equations for the atomic helium-trimer systems are solved numerically with high accuracy both for the most sophisticated realistic potentials available and for simple phenomenological potentials. An efficient numerical procedure…
A recent 15 parts-per-million (ppm) experiment on muonic hydrogen found a major discrepancy with QED and independent nuclear size determinations. Here we find a significant discrepancy in a different type of exotic atom, a medium-Z nucleus…
The helium ground state nonrelativistic energy with 24 significant digits is presented. The calculations are based on variational expansion with randomly chosen exponents. This data can be used as a benchmark for other approaches for many…
It is shown that the non-relativistic ground state energy of helium-like and lithium-like ions with static nuclei can be interpolated in full physics range of nuclear charges $Z$ with accuracy of not less than 6 decimal digits (d.d.) or 7-8…
The theoretical treatment of Rydberg states in one-electron ions is facilitated by the virtual absence of the nuclear-size correction, and fundamental constants like the Rydberg constant may be in the reach of planned high-precision…
We derive a full formula for the energy level of a heavy quarkonium state identified by the quantum numbers $n$, $\ell$, $s$ and $j$, up to ${\cal O}(\alpha_s^5 m)$ and ${\cal O}(\alpha_s^5 m \log \alpha_s)$ in perturbative QCD. The QCD…