  The eXtended Continuum Discretized Coupled Channel (XCDCC) method is
developed to treat reactions where core degrees of freedom play a role. The
projectile is treated as a multi-configuration coupled channels system
generated from a valence particle coupled to a deformed core which is allowed
to excite. The coupled channels initial state breaks up into a coupled channels
continuum which is discretized into bins, similarly to the original CDCC
method. Core collective degrees of freedom are also included in the interaction
of the core and the target, so that dynamical effects can occur during the
reaction. We present results for the breakup of $^{17}$C=$^{16}$C+n and
$^{11}$Be=$^{10}$Be+n on $^{9}$Be. Results show that the total cross section
increases with core deformation. More importantly, the relative percentage of
the various components of the initial state are modified during the reaction
process through dynamical effects. This implies that comparing spectroscopic
factors from structure calculations with experimental cross sections requires
more detailed reaction models that go beyond the single particle model.
