The Relativistic Theory of Electromagnetic Interactions

Abstract

Quantum – mechanical problem on electron motion in Coulomb field plays the fundamental role in the modern physics, because solution of this problem provides the most realistic model of atomic structure. In nowadays the model of meson atom is of the same importance. Indeed, the mesoatom is unstable, hence the study of interaction of mesons with atomic nuclei can provide the valuable information on the nature of hadronic interactions and structure of atomic nucleus. The mesoatoms arise in the process of scattering of the negatively charged pions in matter. The pions captured by the target atoms populate initially the highly excited atomic orbits and then go down to 2p and 1s atomic states via cascade of radiative transitions. As far as the meson mass exceeds the electron mass for the two orders of magnitude then the mesonic atom orbit radius is much smaller than the radius of electron atom orbits. For example, the radius of the lowest mesonic orbits becomes comparable with the atomic nucleus size in the case of nucleus charge 12 Z [1]. As a result, for meson in 2p state the probability to annihilate on atomic nucleus is higher than the probability to decay radiatively in 2 1 p s transition. In the atoms with the nucleus charge 40 Z the radiative transitions disappear before the cascade reaches the 2p state. In the case of atoms with more heavy nuclei even the 3d states can not often be occupied. Thus the study of the cascade x-ray spectra of mesonic atoms provides the information on the efficiency of meson interaction with the different nuclei. The nonrelativistic Schredinger theory produces the atomic spectrum in zero-order approximation which does not include fine and hyperfine structure. The atomic spectrum calculated in the frames of the Dirac relativistic theory includes the fine structure. The hyperfine atomic structure can be calculated with the help of the invariant perturbation theory methods, which are based on the field quantization theory. The smallness parameter of invariant perturbation theory is the product of the hyperfine structure constant and nucleus charge, Z . Hence, the atoms with the nucleus charge of 1 Z are out of the frames of the perturbation theory and therefore they are of special interest. This interest is due to a number of reasons: Firstly, the precise mathematical calculations of hyperfine atomic structure can be based on the non-perturbative theory which is valid for arbitrary value of parameter Z . Secondly, the Dirac theory predicts that at 1 Z the energy eigenvalues become complex. It means that the corresponding atomic states are unstable, i.e. the lifetime of these states is finite [2-4].