Related papers: A Simple approach for precision calculation of Bet…
The Bethe logarithm for a large set of states of the helium atom is calculated with a precision of 12-14 significant digits. The numerical data is obtained for the case of infinite mass of a nucleus. Then we study the mass dependence and…
We describe the calculation of hydrogenic (one-loop) Bethe logarithms for all states with principal quantum numbers n <= 200. While, in principle, the calculation of the Bethe logarithm is a rather easy computational problem involving only…
In this work we develop and implement a method for calculation of the Bethe logarithm for many-electron atoms. This quantity is required to evaluate the leading-order quantum electrodynamics correction to the energy and properties of atomic…
A general computational scheme for the (non-relativistic) Bethe logarithm is developed opening the route to `routine' evaluation of the leading-order quantum electrodynamics correction (QED) relevant for spectroscopic applications for small…
The efficient and simple B-splines variational method of calculating the hydrogen atom Bethe logarithms in the acceleration gauge [Y-B Tang et.al., Phys. Rev. A $\mathbf{87}$, 022510 (2013)] is successfully applied to other gauges. The…
We calculate the two-loop Bethe logarithm correction to atomic energy levels in hydrogen-like systems. The two-loop Bethe logarithm is a low-energy quantum electrodynamic (QED) effect involving multiple summations over virtual excited…
We develop a numerical method to calculate the Bethe logarithm for resonant states. We use the Complex Coordinate Rotation (CCR) formalism to describe resonances as time-independent Schr\"odinger solutions. To get a proper expression for…
In this work, we report an application of Hylleraas-$B$-spline basis set to the nonrelativistic Bethe logarithm calculation of helium. The Bethe logarithm for $n\ ^1S$, $n$ up to 10, states of helium are calculated with a precision of 7-9…
We present a variational approach to evaluate relativistic corrections of order \alpha^2 to the Bethe logarithm for the ground electronic state of the Coulomb two center problem. That allows to estimate the radiative contribution at…
We have computed the Bethe logarithms for the 1 singlet S, 2 singlet S and 2 triplet S states of the helium atom to about seven figure-accuracy using a generalization of a method first developed by Charles Schwartz. We have also calculated…
This document provides reference data for all Bethe logarithms of hydrogenic bound states with principal quantum numbers n <= 200.
Two-loop Bethe logarithms are calculated for excited P and D states in hydrogenlike systems, and estimates are presented for all states with higher angular momenta. These results complete our knowledge of the P and D energy levels in…
We report a calculation of relativistic corrections of order $m\alpha^7$ to the Bethe logarithm for the $2^3S$ and $2^3P$ states of helium-like ions. The calculation is required for improving the accuracy of theoretical energies of…
We consider a general procedure to evaluate the Bethe logarithm for a general few-body atomic or molecular system. As benchmarks we use calculation for the ground states of a helium atom and H_2^+ molecular ion. The obtained values are:…
We introduce a method for computing corrections to Bethe approximation for spin models on arbitrary lattices. Unlike cluster variational methods, the new approach takes into account fluctuations on all length scales. The derivation of the…
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…
In this work, we consider the numerical computation of ground states and dynamics of single-component Bose-Einstein condensates (BECs). The corresponding models are spatially discretized with a multiscale finite element approach known as…
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.
We calculate the one- and two-loop corrections of order alpha(Zalpha)^6 and alpha^2(Zalpha)^6 respectively, to the Lamb shift in hydrogen-like systems using the formalism of nonrelativistic quantum electrodynamics. We obtain general results…
In this work, we generalize the numerical approach to Gaudin models developed earlier by us to degenerate systems showing that their treatment is surprisingly convenient from a numerical point of view. In fact, high degeneracies not only…