  Background. 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. Purpose. 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. Potential matrix elements as well as
transition matrix elements calculated with them must fulfill the reciprocity
theorem. The purpose of this paper is to introduce a separable,
energy-dependent representation of complex, energy-dependent optical potentials
that fulfill reciprocity exactly. Results. Starting from a separable,
energy-independent representation of global optical potentials based on a
generalization of the Ernst-Shakin-Thaler (EST) scheme, a further
generalization is needed to take into account the energy dependence.
Applications to n$+^{48}$Ca, n$+^{208}$Pb, and p$+^{208}$Pb are investigated
for energies from 0 to 50~MeV with special emphasis on fulfilling reciprocity.
Conclusions. We find that the energy-dependent separable representation of
complex, energy-dependent phenomenological optical potentials fulfills
reciprocity exactly. In addition, taking into account the explicit energy
dependence slightly improves the description of the $S$ matrix elements.
