Functional medium-dependence of the nonrelativistic optical model potential

TL;DR

This paper analytically separates the optical potential into medium-independent and medium-dependent parts, highlighting the role of density derivatives and their impact on surface phenomena in nuclear interactions.

Contribution

It provides an exact analytical decomposition of the optical potential into distinct medium-dependent and independent contributions based on the structure of two-body interactions.

Findings

Medium-dependent term is proportional to the radial derivative of the reduced matrix element.

Surface effects are enhanced by density derivatives, while volume effects are suppressed.

The separation is general and applicable to surface-sensitive phenomena.

Abstract

By examining the structure in momentum and coordinate space of a two-body interaction spherically symmetric in its local coordinate, we demonstrate that it can be disentangled into two distinctive contributions. One of them is a medium-independent and momentum-conserving term, whereas the other is functionally --and exclusively-- proportional to the radial derivative of the reduced matrix element. As example, this exact result was applied to the unabridged optical potential in momentum space, leading to an explicit separation between the medium-free and medium-dependent contributions. The latter does not depend on the strength of the reduced effective interaction but only on its variations with respect to the density. The modulation of radial derivatives of the density enhances the effect in the surface and suppresses it in the saturated volume. The generality of this result may prove to be useful for the study of surface-sensitive phenomena.