  Three-body nuclear reactions in two-nucleon plus core systems are described
in the framework of exact scattering equations including the core excitation. A
nucleon-core optical potential is constructed that can be easily adjusted to
the reference potential and thereby to the experimental two-body data, if
available. This constitutes an important improvement over the simple
deformation of the potential used previously that violated the original fit to
the data. Predictions for elastic, inelastic, and transfer reactions involving
$^{10}{Be}$ and $^{24}{Mg}$ nuclear cores are obtained. The new optical
potential leads to a moderate increase of cross sections.
