Nuclear Optical Model and Wave Properties: Barrier Penetration, Reflection, Absorption, and Resonance

Abstract

A detailed study of the wave properties of the nuclear optical model is presented to elucidate the problem of barrier penetration by charged particles and to remove some of the mystique of optical-model calculations. The wave properties and the concomitant penetration are most straightforward for square wells, for which the resonance, reflection, and penetration are easily ascribed to separate factors. We show that the wave properties of more general diffuse-edge optical potentials achieve a similar simplicity by the construction of an equivalent square well (ESW) which has the same resonance, penetration, and absorption factors as the optical potential, but which differs in its reflection factor. A general construction of the ESW is given, and we apply it to the following problems: (1) the very narrow single-particle resonances of real optical potentials that occur at energies far below the Coulomb barrier, (2) the nuclear absorption cross sections in the presence of barriers, (3) the calculation of absorption cross sections at astrophysical energies (extreme barrier penetration) employing optical models fitted to data at higher energies, and (4) the value of the nuclear radius and sum-rule limits appropriate to the analysis of nuclear reactions. In some cases of extreme barrier penetration, the ESW fails to yield all the properties. For example, cases are described where the bulk of the absorption may attain in the distant "tail" of the imaginary term in the optical potential: The corresponding reaction rates can yield information about the behavior of the nucleus at distances much beyond the normal nuclear radius.