  Earlier work showed how a nucleon optical model wave function could be
defined as a projection of a many-nucleon scattering state within a
translationally invariant second quantised many-body theory. In this paper an
optical potential operator that generates this optical model wave function is
defined through a particular off-shell extension of the elastic transition
operator. The theory is express explicitly in terms of the many-nucleon
Hamiltonian in a mixed representation in which localised target nucleus states
feature. No reference to a mean-field concept is involved in the definition. It
is shown that the resulting optical model operator satisfies the requirements
of rotational and translational invariance and has standard behaviour under the
time reversal transformation.
  The contributions to the optical potential from two different exchange
mechanisms are expressed in terms of an effective Hamiltonian involving a
nucleon-number conserving one-body interaction. In the weak-binding limit the
method reduces to a a version of Feshbach's projection operator formulation of
the optical potential with a truncated nucleon-nucleon potential including
exchange terms and recoil corrections.
  Definitions of the nucleon single-particle Green's function and the
corresponding Dyson self-energy modified by corrections for translational
invariance are presented and different definitions of the optical potential
operator are compared.
