  The nuclear optical model potential (OMP) is generally assumed to be
independent of the orbital angular momentum, $l$, of the interacting nuclei.
Nucleon-nucleus and nucleus-nucleus interactions are customarily $l$
independent in calculations of nuclear elastic scattering and in standard
reaction codes. The evidence for various forms of $l$ dependence of OMPs is
reviewed and the importance of implementing these forms is evaluated. Existing
arguments and evidence for $l$ dependence are reviewed and new arguments and
calculations are introduced. The relationship is examined between (i) $l$
dependence, and, (ii) the undularity (waviness) of $l$-independent potentials
that are $S$-matrix equivalent to $l$-dependent potentials. Such undularity is
a property of the dynamic polarisation potential (DPP) generated by the
coupling to reaction channels, or by coupling to excited states of the target
or projectile nuclei. Various examples, particularly involving weakly bound
projectile nuclei, are presented. Such undularity also occurs in
$l$-independent potentials that have been found in model independent fits to
precise wide angular range elastic scattering angular distributions. Cases of
such phenomenological undularity, for both light and heavy ions, are referenced
and shown to be related to undulatory properties of the dynamic polarisation
potentials (DPPs) arising from channel coupling. Other forms of $l$ dependence,
that could be standard options in direct reaction codes, are noted. Of
particular importance are $l$ dependencies arising from full
antisymmetrization. The case is made that reaction-induced $l$ dependence is a
general property of nucleon-nucleus and nucleus-nucleus interactions and
represents a valid extension of the nuclear optical model.
