Related papers: Calculation of Hydrogenic Bethe Logarithms for Ryd…
This document provides reference data for all Bethe logarithms of hydrogenic bound states with principal quantum numbers n <= 200.
We investigate relativistic and quantum electrodynamic effects for highly-excited bound states in hydrogenlike systems (Rydberg states). In particular, hydrogenic one-loop Bethe logarithms are calculated for all circular states (l = n-1) in…
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…
In this article we propose a simple approach for the precision calculation of Bethe logarithm. The leading contributions are obtained using specific operators, while the remaining terms are eliminated by adjusting the parameter $\lambda$.…
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 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…
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 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…
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…
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…
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…
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 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 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…
In the realm of statistical physics, the number of states in which a system can be realized with a given energy is a key concept that bridges the microscopic and macroscopic descriptions of physical systems. For quantum systems, many…
We consider the $1s$ Lamb shift in hydrogen and helium ions, a quantity, required for an accurate determination of the Rydberg constant and the proton charge radius by means of hydrogen spectroscopy, as well as for precision tests of the…
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…
The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical…
The hydrogen atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the…
We compare recently proposed methods to compute the electronic state energies of the water molecule on a quantum computer. The methods include the phase estimation algorithm based on Trotter decomposition, the phase estimation algorithm…