An optical potential for nuclei with collective states

Abstract

In first approximat ion the optical potent ia l is s imply related to the target densi ty (x), and the elastic scat ter ing of medium-energy protons (2) and or-particles (8) can be of use in determining the size and shape of closed-shell nuclei. In contrast for nuclei which possess s t rongly excited low-lying states the corrections to the first-order optical potent ia l arising from the vi r tual excitat ion of these collective states may be important , and unless they are explici t ly included in a coupled-channel calculation the parameters of the result ing opt ical potent ia l are no longer s imply re la ted to the ta rge t densi ty and appear to be anomalous (4,~). The contributions from these collective states are reflected as differences in the optical potent ia ls employed in coupled.channel and DWBA calculations, and i t is of interest to systemat ical ly unders tand the connection between them (5). The determinat ion of a local optical potent ia l which reproduces the elastic pa r t of a given mult ichannel scattering problem is quite complicated, and the solution is nonunique (6). In this note we present a simple construction of a local optical potent ia l which uses the high-energy eikonal approximat ion as an in termediary (*). Although our approach is quite general , i t is best i l lus t ra ted in terms of a specific example. Fo r the sake of s implici ty the development is carried out for the generalized optical potent ia l int roduced for v ibra t ional nuclei by BOHR and MOTT~LSON (s):