Auger-capture of μ mesons by He atoms in the Hartree-Fock approximation

Auger capture of muons by He atoms is calculated in the nonrelativistic Hartree-Fock approximation. The calculation is carried out for the muon capture into states having the principle quantum number n>=4, the radiational capture being small for these states to be neglected. The atom polarization by a projectile and the correlations in the initial states which contributions for helium atom being small, are also neglected. The initial meson energy amounts from 1 to 175 eV. The following values are calculated: the meson capture cross sections G into the definite n states as a function of the orbital moment l, G as a function of l summed over n, G as a function of n summed over l, the total capture cross section depending on the meson energy E. The G approximately (2l+1) low is found to be valid only for small l and l>10. The most probable capture occurs into the states with n=14-20. With an increase in n, G quickly decreases as n-3. When E exceeds the atom excitation threshold G quickly drops. At E higher than the ionization potential I, the elastic and inelastic cross sections (>1015 cm-2) exceeds the capture cross section by an order of the magnitude. Meson capture is best probable at E< or approximately I