Folded potentials in cluster physics - A comparison of Yukawa and Coulomb potentials with Riesz fractional integrals

摘要

In cluster physics, a single-particle potential to determine the microscopic part of the total energy of a collective configuration is necessary to calculate the shell and pairing effects. In this paper, we investigate the properties of the Riesz fractional integrals and compare their properties with the standard Coulomb and Yukawa potentials commonly used. It is demonstrated that Riesz potentials may serve as a promising extension of standard potentials and may be reckoned as a smooth transition from Coulomb- to Yukawa-like potentials, depending on the fractional parameter α. For the macroscopic part of the total energy, the Riesz potentials treat the Coulomb, symmetry and pairing contributions from a generalized point of view, since they turn out to be similar realizations of the same fractional integral at distinct α values.