Isotopic effects in scattering and kinetics of the atomic cascade of excited μ−p and μ−d atoms

Abstract

The isotopic effects in the scattering and the kinetics of the atomic cascade of excited µ − p and µ − d atoms The quantum-mechanical calculations of the differential and integrated cross sections of the elastic scattering, Stark transitions, and Coulomb de-excitation at collisions of excited µ − p and µ − d atoms with hydrogen isotope atoms in the ground state are performed. The scattering processes are treated in a unified manner in the framework of the close-coupling approach. The used basis includes both open and closed channels corresponding to all exotic atom states with principal quantum numbers from n = 1 up to nmax = 20. The energy shifts of ns states due to electron vacuum polarization and finite nuclear size are taken into account. The kinetics of atomic cascade of µ − p and µ − d atoms are studied in a wide range of relative target densities (ϕ = 10 −8 − 1) within the improved version of the extended cascade model, in which the results of the numerical quantum-mechanical calculations of the cross sections for quantum numbers and kinetic energies of muonic atoms, that are of interest for the detailed cascade calculations, are used as input data. Initial (n, l, E)-distributions of muonic atoms at the instant of their formation and the target motion are taken into account explicitly in present cascade calculations. The comparison of the calculated cross sections, the kinetic energy distributions of muonic atoms at the instant of their np → 1s radiative transitions as well as the absolute and relative x-ray yields for both muonic hydrogen and muonic deuterium reveals the isotopic effects, which, in principal, may be observed experimentally. The present results are mainly in very good agreement with experimental data available in the literature.PACS numbers: I. INTRODUCTIONThe muonic and hadronic hydrogen-like atoms (µ) are formed in highly-excited states, when a heavy negatively charged particle (µ − , π − , K − , etc.) is slowed down in the gaseous or liquid hydrogen target and captured on the atomic orbit. After the exotic atom formation, its initial distributions in quantum numbers and kinetic energy are changed during the so-called atomic cascade through a number of processes: radiative and Stark transitions, elastic scattering, external Auger effect, Coulomb de-excitation (CD), weak decay, and strong absorption in the case of hadronic atoms.The general features of these exotic atoms are similar to ones of ordinary hydrogen atoms, because their level structure is mainly determined by the static Coulomb interaction. However, due to significant differences of exotic particle and electron masses, the distance scale in the exotic atom case is much smaller, while the energy scale is much larger in comparison with the usual atomic scale. These scale effects make possible to realize the processes of external Auger effect and CD and open additional opportunities for study of the quantum electrodynamics, weak or strong interactions (in the case of hadronic atoms), and scattering processes in collisions of the...

Pionic hydrogen and deuterium

“…It is worth mentioning that no Doppler contribution could be identified in pionic deuterium within the experimental uncertainties [7]. A theoretical explanation for such behavior is provided by cascade theory [20].…”

Collision-induced radiative quenching and other disintegration modes of the $2S$ state of muonic hydrogen and deuterium atoms

“…In our paper [5], the cross sections of all processes at collisions of the excited µ − p and µ − d atoms with hydrogen isotope atoms in the ground state have been presented. In these calculations, performed in the framework of the close-coupling approach, the radiative widths or instability of the excited states of muonic atoms and the possibility of the collision-induced radiative transitions were not taken into account.…”

“…in (µ − p) 2s + H and (µ − d) 2s + D collisions calculated earlier [4,5] at energies below the 2s − 2p threshold were recalculated taking into account the radiation width or the instability of the 2p state. Calculations were performed in the framework of the closed coupling approach by using the propagation matrix method described in details in our paper [4].…”

“…During this deexcitation cascade a fraction of µ − p or µ − d atoms reaches the 2s state. The value of this fraction is determined by several factors: the initial (n, l, E)-distributions (e.g., see [4,5]), the competition of collisional processes and radiative transitions during the deexcitation cascade, as well as a target temperature and density.…”

“…The theoretical description of the collisional processes and kinetics of the atomic cascade was improved significantly in our papers (e.g., see [4,5,[25][26][27][28][29][30] and refs. therein).…”