The isotopic effects in the scattering and the kinetics of the atomic cascade

TL;DR

This paper presents ab initio quantum-mechanical calculations of scattering cross sections and atomic cascade kinetics for muonic hydrogen and deuterium, revealing isotopic effects that align well with experimental data.

Contribution

It introduces a unified close-coupling approach for scattering processes and incorporates detailed cascade modeling with initial state distributions and target motion.

Findings

Calculated cross sections show isotopic differences.

Kinetic energy distributions match experimental observations.

Results confirm isotopic effects are experimentally observable.

Abstract

{\it Ab initio} quantum-mechanical calculations of the differential and integrated cross sections of the elastic scattering, Stark transitions, and Coulomb de-excitation at collisions of excited $\mu^- p$ and $\mu^- d$ 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 $n_{\rm max}=20$. 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 $\mu^- p$ and $\mu^- d$ atoms are studied in a wide range of relative target densities ($\varphi = 10^{-8} -1$) within the improved version of the extended cascade model. 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, kinetic energy distributions at the instant of the $np\to 1s$ 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.