Precise Physics of Simple Atoms

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 QED The 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) 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. and deuterium (Hänsch), neutral helium (Drake) and helium ions, muonium (Jungmann), positronium (Conti), muonic hydrogen and helium etc. We consider here most of the low–Z atoms. • Study of high–Z ions (Myers, Stölker) cannot further the test of the bound state QED because of large contributions due to the nuclear structure. Rather such an investigation is useful for trying different nuclear models. However, in some particular cases, atomic systems with a not too high Z can give some important information on higher order terms of the QED Zα expansion. • There are some other two–body atoms under investigation. They contain a hadron as an orbiting particle. Different antiprotonic (Yamazaki) and pionic (Nemenov) atoms provide a unique opportunity to study particle property with spectroscopic means with a high precision. In some sense it is not possible to have low precision: if a signal is detected the accuracy is granted. The precision study of the simple atoms is not only limited by experiments with simple atoms. The theory is not able to predict anything to be comparable to the experimental data. What theory can do is to express a measurable quantity in terms of fundamental constants and particle (or nuclear) properties. First of all we need to determine somehow the Rydberg constant (R∞), the fine structure constant (α) and the electron mass in some appropriate units (e. g. in atomic units or in terms of the proton mass (me/mp)). Uncertainties arising from these constants are sometimes compatible with other items of the uncertainty budget or they are even sometimes the most important source of inaccuracy. One should remember that the electron is the most fundamental particle for physics, chemistry, and metrology and the constants associated with its properties go through any atomic spectroscopic effects and any quantum electromagnetic effects. Due to that a number of different studies, which are very far from the spectroscopy of simple atoms (like e. g. Watt balance experiment (see Mohr for detail)), are really strongly connected with the precision physics of simple atoms. However, a knowledge of the universal fundamental constants is not enough for precision theoretical predictions and we need to learn also some more specific constants like for e. g. the muon mass or the proton electric charge radius. The former is important for the muonium hyperfine structure, while the latter is for calculating the hydrogen Lamb shift. SPECTRA OF SIMPLE ATOMS Let us discuss the spectrum of simple atoms in more detail. The gross structure of atomic levels in a hydrogen–like atom comes from the Schödinger equation with the Coulomb potential and the result is well–known En = −(Zα) me. There are a number of different corrections: the relativistic ones (one can find them from 3) We use the relativistic units in which h̄ = c = 1. 2p1/2 2s1/2 Lamb splitting fine structure