  We have studied the residual interaction effects theoretically on the deeply
bound pionic states in Pb and Sn isotopes. We need to evaluate the residual
interaction effects carefully in order to deduce the nuclear medium effects for
pion properties, which are believed to provide valuable information on nuclear
chiral dynamics. The s- and p-wave $\pi-N$ interactions are used for the
pion-nucleon residual interactions. We show that the complex energy shifts are
around [(10-20)+i(2-7)]keV for 1s states in Sn, which should be taken into
account in the analyses of the high precision data of deeply bound pionic $1s$
states in Sn isotopes.

Nuclear Theory