  Previous studies of $(d,p)$ reactions in three-body (proton, neutron, nuclear
core) systems revealed a nontrivial effect of the core excitation: the transfer
cross section cannot be factorized into the spectroscopic factor and the
single-particle cross section obtained neglecting the core excitation. This
observable, up to a kinematic factor, is the angular distribution of the core
nucleus in the $(p,d)$ reaction. The study of the core excitation effect for
the most closely related observable in the $(p,pn)$ three-body breakup, i.e.,
the core angular distribution, is aimed in the present work. Breakup of the
one-neutron halo nucleus in the collision with the proton is described using
three-body Faddeev-type equations extended to include the excitation of the
nuclear core. The integral equations for transition operators are solved in the
momentum-space partial-wave representation. Breakup of 11Be nucleus as well as
of model $A=11$ $p$-wave nuclei is studied at beam energies of 30, 60, and 200
MeV per nucleon. Angular and momentum distributions for the 10Be core in ground
and excited states is calculated. In sharp contrast to $(p,d)$ reactions, the
differential cross section in most cases factorizes quite well into the
spectroscopic factor and the single-particle cross section. Due to different
reaction mechanisms the core excitation effect in the breakup is very different
from transfer reactions. A commonly accepted approach to evaluate the cross
section, i.e., the rescaling of single-particle model results by the
corresponding spectroscopic factor, appears to be reliable for breakup though
it fails in general for transfer reactions.
