  One important ingredient for many applications of nuclear physics to
astrophysics, nuclear energy, and stockpile stewardship are cross sections for
reactions of neutrons with rare isotopes. Since direct measurements are often
not feasible, indirect methods, e.g. (d,p) reactions, should be used. Those
(d,p) reactions may be viewed as three-body reactions and described with
Faddeev techniques. Faddeev equations in momentum space have a long tradition
of utilizing separable interactions in order to arrive at sets of coupled
integral equations in one variable. Optical potentials representing the
effective interactions in the neutron (proton) nucleus subsystem are usually
non-Hermitian as well as energy-dependent. Including excitations of the nucleus
in the calculation requires a multichannel optical potential. The purpose of
this paper is to introduce a separable, energy-dependent multichannel
representation of complex, energy-dependent optical potentials that contain
excitations of the nucleus and that fulfill reciprocity exactly. Momentum space
Lippmann-Schwinger integral equations are solved with standard techniques to
obtain the form factors for the separable representation. Starting from
energy-dependent multichannel optical potentials for neutron and proton
scattering from $^{12}$C, separable representations based on a generalization
of the Ernst-Shakin-Thaler (EST) scheme are constructed which fulfill
reciprocity exactly. Applications to n$+^{12}$C and p$+^{12}$C scattering are
investigated for energies from 0 to 50~MeV.
