Precise physics of simple atoms

Abstract

Abstract. We give a review of experimental and theoretical results on the precision study of hydrogen-like atoms with low value of the nuclear charge Z.The simplicity of "simple" atoms has been for a while a challenge to precision theory and experiment. Are the hydrogen-like atomic systems simple enough to be calculated with an accuracy, appropriate to compete with the best experimental results? That is a question, that theorists have tried to answer. The simplest atoms are different two-body bound systems with a low value of the nuclear charge: Z = 1 (hydrogen, deuterium, muonium and positronium) and Z = 2 (ions of helium-3 and helium-4) etc. We do not try to review theoretical calculations (if necessary details can be found in Ref. [1]), but present state of art in physics of simple atoms and discuss in detail the theoretical and experimental status of studying such atoms. LOW-ENERGY TESTS OF QEDThe precise physics of simple atom is the most interesting part of the so-called low-energy tests of Quantum Electrodynamics (QED). Low energy tests of QED offer a number of different options:• A study with free particles provides the possibility of testing the QED Lagrangian for free particles. The most accurate data arise from anomalous magnetic moments of the electron (Kinoshita †2 ) and the muon [2].• However, one knows that the bound problem makes all calculations more complicated. Bound state QED is not a well-established theory. It involves different effective approaches to solve a two-body problem. These approaches can be essentially checked with low Z atomic systems like for e. g. hydrogen 1) Summer address 2) References marked with † correspond to presentations at a satellite meeting to ICAP named Hydrogen atom, 2: Precision physics of simple atomic system and its Proceedings will be published by Springer in 2001.

Precision physics of simple atoms: QED tests, nuclear structure and fundamental constants

“…Our conservative estimation of the theoretical uncertainty in Fig. 9 is related to [36,60] R p (conservative) = 0.88(3) fm .…”

“…The bound state problem is complicated by itself even in the case of classical mechanics. The hydrogen atom is the simplest atomic system; however, a theoretical result for the energy levels is expressed as a complicated function (often a perturbation expansion) of a number of small parameters [60] (see review [16] for a collection of theoretical contributions):…”

“…In particular, the latter involves large logarithms (ln(1/Zα) ≃ 5, ln 2 (1/Zα) ≃ 24 and ln 3 (1/Zα) ≃ 120 at Z = 1) [60,61] and big coefficients. Comparing α and Zα we note that in the relativistic case, when the energy transfer k 0 = ∆E/c is of the same order as the momentum transfer k, the parameter is rather α/π.…”

Hyperfine structure of the ground and first excited states in light hydrogen-like atoms and high-precision tests of QED

“…[34] (see also Refs. [37,32,18]) and we follow consideration there. The hadronic contribution is taken from Ref.…”

Precision study of positronium and precision tests of the bound state quantum electrodynamics

“…It faces a lack of pure QED description of the nucleon structure, hadronic vacuum polarization and other hadronic effects. Such effects are unavoidable while calculating the spectrum of hydrogen, muonium and most of other simple atoms [1]. For some applications the weak interaction is also involved into calculations, but in such a case it can often be done ab initio, while strong interaction effects require model-dependent evaluations, experimental data and phenomenological approaches.…”