Ratio of productions of pi+pi-atoms to free pi+pi- pairs with account of the strong interaction in final states

The ratio of productions of pi+pi- atoms to free pi+pi- pairs is calculated with account of the strong interaction in final states. It is shown that this ratio is expressed via a squared ratio of the well-known Coulomb wave functions and thus can be calculated with a high accuracy.Comment: 3 page

Sum Rules for Total Interaction Cross Sections of Relativistic Elementary Atoms with Atoms of Matter Up to Terms of Order α2\alpha^2

It is shown that $\alpha^2$-term of sum rules for the total cross sections of interaction of elementary atoms with matter ones, obtained in ref.[Denisenko K. and Mrowczynski S., Phys. Rev. D36 (1987) 1529] is wrong. New sum rules valid up to terms of order $\alpha^2$ are derived.Comment: 3 page

Dynamics of the Pionium with the Density Matrix Formalism

The evolution of pionium, the $\pi^+ \pi^-$ hydrogen-like atom, while passing through matter is solved within the density matrix formalism in the first Born approximation. We compare the influence on the pionium break-up probability between the standard probabilistic calculations and the more precise picture of the density matrix formalism accounting for interference effects. We focus our general result in the particular conditions of the DIRAC experiment at CERN.Comment: 14 pages, 2 figures, submitted to J. Phys. B: At. Mol. Phy

Density Matrix Kinetic Equation Describing a Passage of Fast Atomic Systems Through Matter

The quantum-mechanical consideration of a passage of fast dimesoatoms through matter is given. A set of quantum-kinetic equations for the density matrix elements describing their internal state evolution is derived. It is shown that probabilistic description of internal dynamics of hydrogen-like atoms is impossible even at sufficiently low energies because of the ``accidental'' degeneracy of their energy levels.Comment: 12 pages, LATEX, submitted to J. Phys.

Contribution of α2\alpha^2-terms to the total interaction cross sections of relativistic elementary atoms with atoms of matter

It is shown that the corrections of $\alpha^2$ order to the total cross sections for interaction of elementary hydrogen-like atoms with target atoms, reported in the previously published paper [S.Mrowczynski, Phys.Rev. D36, 1520 (1987)], do not include some terms of the same order of magnitude. That results in a significant contribution of these corrections in particular cases. The full $\alpha^2$-corrections have been derived and it is shown that they are really small and could be omitted for most practical applications.Comment: 5 page

A Complete Version of the Glauber Theory for Elementary Atom - Target Atom Scattering and Its Approximations

A general formalism of the Glauber theory for elementary atom (EA) - target atom (TA) scattering is developed. A second-order approximation of its complete version is considered in the framework of the optical-model perturbative approach. A `potential' approximation of a second-order optical model is formulated neglecting the excitation effects of the TA. Its accuracy is evaluated within the second-order approximation for the complete version of the Glauber EA-TA scattering theory.Comment: PDFLaTeX, 10 pages, no figures; an updated versio

Direct calculation of the probability of pionium ionization in the target

We performed the first direct calculation of the probability of pionium (pi+pi- atom) ionization in the target. The dependence of the probability of pionium ionization in the target as a function of the pionium lifetime is established. These calculations are of interest of the DIRAC experiment at CERN, which aims to measure the pionium lifetime with high precision.Comment: 11 pages, 4 figures; submitted to "Physics of Atomic Nuclei" ("Yadernaya Fizika"

The electromagnetic effects in Ke4K_{e4} decay

The final state interaction of pions in $K_{e4}$ decay allows one to obtain the value of the isospin and angular momentum zero $\pi\pi$ scattering length $a_0^0$.We take into account the electromagnetic interaction of pions and isospin symmetry breaking effects caused by different masses of neutral and charged pions and estimate the impact of these effects on the procedure of scattering length extraction from $K_{e4}$ decay.Comment: 8 pages,1 figur