  We study the kaonic atom and kaonic nucleus formation by the in-flight ($K^-,
p$) reactions for C, O, Si and Ca target cases theoretically. Deeply bound
kaonic atoms were predicted to exist as quasi-stable states and were expected
to be observed in some proper experimental methods. Kaonic nuclear states are
also expected to exist with large decay widths. We evaluate the formation cross
sections of the kaonic atoms and kaonic nuclei using an effective number
approach. We show that the indications of the kaonic bound states can be
observed in the outgoing proton energy spectra.
