  Background: Separable interactions have a long history in nuclear physics. In
the last few years, separable expansions have been used to represent the
optical potential between a nucleon (proton or neutron) and a target. Purpose:
We explore the non-local properties of these separable optical potentials as
well as their convergence behavior. Method: For a couple of cases, we use the
generalized Ersnt-Shakin-Thaler scheme to generate separable interactions
starting from local optical potentials. We study the variation of the
interaction with energy range and rank. Results: We find that, overall the
off-diagonal behavior of the converged separable interaction deviates from the
Gaussian form assumed by Perey and Buck. However, in the region surrounding the
maximum depth the Gaussian form works quite well. Focusing on this region, we
study potentials describing neutron elastic scattering on $^{16}$O and
$^{48}$Ca for beam energies in the range of $ E=$10-50 MeV and explore several
measures of non-locality of the separable interactions. Conclusions: When the
energy range considered for generating the separable interaction is $0\le
E_{range}\le 50$ MeV, the resulting non-locality is large and target dependent.
Contrarily, the nonlocality obtained including larger energy ranges in the
separable procedure is independent of the target and other details of the
original local potential. We find that, even when including in the expansion
many support points with energy ranges $0\le E_{range}\le 2400$ MeV, the
resulting potential retains non-local behavior. Connections with microscopic
optical potentials as well as other transformations used in the nucleon-nucleon
domain are made.
