Diabatic-state treatment of negative-meson moderation and capture. I. The hydrogen atom

A new formulation of the moderation and capture of negative mesons by atoms has been developed. The scattering is described by a complex potential with a real part given by a diabatic interaction potential and an imaginary part given by the ionization width of the diabatic state embedded in the electronic continuum. Results are presented for collisions of μ-, π-, K-, and p- with the hydrogen atom. The differential energy-loss cross sections and stopping powers obtained are large. The energy spectrum of stopped mesons is determined and most captures are found to occur at collision energies below or near the ionization potential. The principal--quantum-number distributions of the initially formed mesic atoms peak close to the orbital giving optimal overlap with the displaced electronic orbital. The angular-momentum distributions are not too different from statistical, except that they tend to cut off at l significantly smaller than n-1 in the case of large n. Comparison to a very recent experiment is made in a note added