  The $^{12}$C(p,2p)$^{11}$B reaction at $E_p =98.7$ MeV proton beam energy is
analyzed using a rigorous three-particle scattering formalism extended to
include the internal excitation of the nuclear core or residual nucleus. The
excitation proceeds via the core interaction with any of the external nucleons.
We assume the $^{11}$B ground and low-lying excited states [$\frac32^-$ (0.0
MeV), $\frac52^-$ (4.45 MeV), $\frac72^-$ (6.74 MeV)] and the excited states
[$\frac12^-$ (2.12 MeV), $\frac32^-$ (5.02 MeV)] to be members of $K=\frac32^-$
and $K=\frac12^-$ rotational bands, respectively. The dynamical core excitation
results in a significant cross section for the reaction leading to the
$\frac52^-$ (4.45 MeV) excited state of $^{11}$B that cannot be populated
through the single-particle excitation mechanism. The detailed agreement
between the theoretical calculations and data depends on the used optical model
parametrizations and the kinematical configuration of the detected nucleons.
