Fractional calculus within the optical model used in nuclear and particle physics

Abstract

The optical model is a fundamental tool to describe scattering processes in nuclear physics. The basic input is an optical model potential, which describes the refraction and absorption processes more or less schematically. Of special interest is the form of the absorption potential. With increasing energy of the incident projectile, a derivation of this potential must take into account the observed energy dependent transition from surface to volume type. The classic approach has weaknesses in this regard. We will discuss these deficiencies and will propose an alternative method based on concepts developed within the framework of fractional calculus, which allows to describe a smooth transition from surface to volume absorption in an appropriate way. Of special interest is the form of the absorption potential. With increasing energy of the incident projectile, a derivation of this potential must take into account energy dependent transition from imaginary surface to volume terms. We discuss the deficiencies of the classical approach and propose an alternative method based on concepts developed within the framework of fractional calculus, which allows to describe a smooth transition from surface to volume absorption in a natural way.