Alternative implementation of atomic form factors

TL;DR

This paper introduces a novel mathematical approach for calculating atomic form factors in hydrogen-like atoms, leveraging a recent integral result involving special functions, and compares it with existing methods.

Contribution

It presents an alternative calculation method based on a new integral involving Bessel functions and Laguerre polynomials, expanding computational options for atomic physics.

Findings

Provides a new integral-based method for atomic form factors

Includes a comparative overview of existing methods

Enhances computational efficiency for hydrogen-like atoms

Abstract

Using a new result on the integral involving the product of Bessel functions and associated Laguerre polynomials, published in the mathematical literature some time ago, we present an alternative method for calculating discrete-discrete transition form factors for hydrogen-like atoms. For comparison, an overview is also given of two other commonly used methods.