Registration of hydrogen-like leptonic bound states (e^- mu^+) and (e^+ mu^-) in reactions of high-energy scattering of polarized electrons and positrons by nuclei with Z ~ 100 and analysis of CPT invariance

The cross sections for the reactions of muonium(anti-muonium) production in high energy electron(positron) scattering by nuclei e^-(e^+) + Z -> Z + M^0(anti-M^0) + mu^-(mu^+) are calculated in dependence on an energy and polarization of an initial electron(positron) and a polarization of a final mu^-(mu^+)-meson. Due to coherent phenomenon the cross sections are proportional to Z^2. For Z ~ 100 due to the factor Z^2 the cross sections are large enough to be measured at energies available at the HERA Collider in DESY. The results are discussed in connection with a test of CPT invariance.