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In cluster physics a single particle potential to determine the microscopicpart of the total energy of a collective configuration is necessary tocalculate the shell- and pairing effects. In this paper we investigate theproperties of the Riesz fractional integrals and compare their properties withthe standard Coulomb and Yukawa potentials commonly used. It is demonstrated,that Riesz potentials may serve as a promising extension of standard potentialsand may be reckoned as a smooth transition from Coulomb to Yukawa likepotentials, depending of the fractional parameter $\alpha$. For the macroscopicpart of the total energy the Riesz potentials treat the Coulomb-, symmetry- andpairing-contributions from a generalized point of view, since they turn out tobe similar realizations of the same fractional integral at distinct $\alpha$values.

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