Inverse classical scattering using fractional derivative

TL;DR

This paper introduces a fractional calculus-based method to invert potential energy functions from classical scattering data, demonstrating its effectiveness on Rutherford and Lennard-Jones scattering cases.

Contribution

It presents a novel fractional calculus approach for inverse scattering problems, providing proofs of existence and high-precision retrieval of potential functions.

Findings

Potential functions retrieved with high accuracy

Method applied successfully to Rutherford and Lennard-Jones scattering

Provides theoretical proofs of solution existence

Abstract

The fractional calculus framework will be used to invert the potential energy function from the classical scattering angle, which will be related to Riemann-Liouville fractional integral. Numerical solution of this fractional order problem will be applied to the inverse Rutherford scattering and to the inverse scattering of Xe--Rn atoms, in which the potential is given by Lennard-Jones function. Proofs of existence will be presented for more clarity and completness of the present work. In the two cases considered, the potential energy function can be retrieved with a desired precision. The present method gives a clear understanding of the inverse fractional problem framework.