The angular momentum dependence of nuclear optical potentials

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.