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"

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

Coherent and incoherent atomic scattering: Formalism and application to pionium interacting with matter

The experimental determination of the lifetime of pionium provides a very important test on chiral perturbation theory. This quantity is determined in the DIRAC experiment at CERN. In the analysis of this experiment, the breakup probabilities of of pionium in matter are needed to high accuracy as a theoretical input. We study in detail the influence of the target electrons. They contribute through screening and incoherent effects. We use Dirac-Hartree- Fock-Slater wavefunctions in order to determine the corresponding form factors. We find that the inner-shell electrons contribute less than the weakly bound outer electrons. Furthermore, we establish a more rigorous estimate for the magnitude of the contributions form the transverse current (magnetic terms thus far neglected in the calculations).Comment: Journal of Physics B: Atomic, Molecular and Optical Physics; (accepted; 22 pages, 6 figures, 26 references) Revised version: more detailed description of DIRAC experiment; failure of simplest models for incoherent scattering demonstrated by example

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.

First measurement of the π+π−\pi^+\pi^- atom lifetime

The goal of the DIRAC experiment at CERN (PS212) is to measure the $\pi^+\pi^-$ atom lifetime with 10% precision. Such a measurement would yield a precision of 5% on the value of the $S$-wave $\pi\pi$ scattering lengths combination $|a_0-a_2|$. Based on part of the collected data we present a first result on the lifetime, $\tau=[2.91 ^{+0.49}_{-0.62}]\times 10^{-15}$ s, and discuss the major systematic errors. This lifetime corresponds to $|a_0-a_2|=0.264 ^{+0.033}_{-0.020} m_{\pi}^{-1}$.Comment: 18 pages, 6 figure

Sca calculations of the proton induced alignment using relativistic hartree-fock wavefunctions

Proton-induced differentia] and total alignment is reviewed and some calculations presented. A density matrix formalism is employed as the theoretical framework and a more efficient expansion into state multipoles used. The collision T-matrix elements entering the expression for the alignment tensor are calculated in the semiclassical approximation to first order. A coordinate space formulation including classical hyperbolic trajectories for the projectile path is adopted here, to take proper account of deflection. Relativistic Hartree-Fock orbital wavefunctions for bound and continuum electronic states in the partial-wave expansion cover both screening and relativistic effects in the atom in a unifying scheme. The continuum orbitals are calculated iteratively until the frozen core VN-1 potential converges. © 1995 IOP Publication Ltd

SCA calculations of the inner shell ionization with Dirac-Fock electronic wave functions

The theory of inner shell ionization for arbitrary atomic shells is reviewed. Emphasis is on L- and M-shells in order to show how the proper screening formalism entering the electronic form factor affects the ionization probabilities. The radial wavefunctions in the form factor are computed as relativistic Hartree-Fock orbitals for both bound and continuum states. The continuum orbitals were evaluated in the V(N-1) potential with correct exchange. These results are then compared with the previous ones using screened hydrogen-like wavefunctions and also with the experimental data in some cases

Continuum wavefunction solver for GRASP

Relativistic VN-1 continuum orbitals are solved numerically within the framework of the GRASP code [K. Dyall et al., Comput. Phys. Commun. 55 (1989) 425]. Normalization is accomplished with a relativistic WKB method or curve fitting, depending on whether the core is an ion or is neutral. In the normalization, the phase shift (relative to hydrogen) is also calculated. The spacing of the radial grid at large distances is automatically determined to provide at least 10 grid points per half cycle of the wavefunction. Lagrange multipliers are automatically determined. © 1993