Schwinger variational principle in charged particle scattering by mesic atoms and atoms

The way for solving the strong channel coupling method equation with the use of the Shcwinger variational method is proposed. The equation obtained is valid for atomic and mesoatomic physics when the account of the large number of closed channels is necessary and virtual transitions in continuum. In this variational method the trial functions are chosen in the form of expansion into eigenfunctions. The region of the equation validity is found. The problems of the e+H and p-dμ scattering are studied. The e+H scattering length turns out to be 1.8 a. u. which is in accordance with other results. The scattering cross section for p-dμ scattering is equal to 5.7x10-21 cm-2 which also qualitatively is in agreement with results obtained elsewhere. The bound state which is stable relative to the decay into a positron and hydrogen atom is found for the e+H system