Negative Meson Absorption in Liquid Hydrogen

A theoretical study has been made of the atomic processes involved in the absorption of ${\ensuremath{\pi}}^{\ensuremath{-}}$ and ${K}^{\ensuremath{-}}$ mesons in liquid hydrogen, with the main purpose of setting an upper limit on the fraction of $K$ mesons that react with the proton from the $P$ state. The principal mode of de-excitation of the mesonic atom, Auger ionization of neighboring hydrogen atoms, was calculated in Born approximation for all the appropriate initial and final values of $n$. The Stark mixing process discussed by Day, Snow, and Sucher, which allows $S$-state reaction from high $n$ orbitals, was calculated quantitatively using an impact parameter method and including the effect of the $S$-state energy shift. In agreement with Day et al., it was found that practically all of the ${K}^{\ensuremath{-}}$ mesons react from the $S$ state; the actual fraction of $P$-state reactions is less than 1%. In addition, the calculated cascade time for ${\ensuremath{\pi}}^{\ensuremath{-}}$ in liquid hydrogen is compatible with the experimental value.