  The relativistic amplitude for the direct knock-out contribution to $\left(
\gamma, p \right)$ reactions on nuclei is reduced to a nonrelativistic form
using an effective Pauli reduction scheme. The reduction is carried out to
second order in the inverse nucleon mass. It is found that the interaction
Hamiltonian appearing in the nonrelativistic amplitude has significant
dependence, starting at second order, on the vector and scalar mean nuclear
potentials. These strong medium modifications are absent in traditional
nonrelativistic calculations. Detailed comparisons show that these
modifications are crucial to understanding the differences between relativistic
and nonrelativistic models. These differences are also examined through
reduction of the relativistic amplitude via the Foldy-Wouthuysen
transformation. Similar medium modifications are obtained in this case as well.
We discuss the implications of these medium modifications for the consistency
of existing nonrelativistic calculations.
