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

TL;DR

This paper explores Riesz fractional integrals as a versatile extension of Coulomb and Yukawa potentials in cluster physics, offering a smooth transition between these models based on a fractional parameter.

Contribution

It introduces Riesz potentials as a novel, unified approach to model nuclear interactions, bridging Coulomb and Yukawa potentials through fractional calculus.

Findings

Riesz potentials can interpolate between Coulomb and Yukawa potentials.

They provide a generalized framework for shell- and pairing-energy contributions.

Riesz potentials offer a promising extension for microscopic energy calculations.

Abstract

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 of the fractional parameter $\alpha$. 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 $\alpha$ values.