# Prediction of deviations from the Rutherford formula for low-energy Coulomb scattering of wavepackets

## TL;DR

This paper investigates how wavepacket scattering from a Coulomb potential deviates from Rutherford's formula at low energies and angles, revealing measurable effects and theoretical insights into wavepacket behavior in long-range potentials.

## Contribution

It introduces a wavepacket-based approach to Coulomb scattering, enabling finite probability calculations and analysis of deviations from Rutherford's formula at low energies.

## Key findings

- Deviations from Rutherford formula occur at low angles and energies.
- Low-energy scattering shows a measurable shadow zone around the forward direction.
- Wavepacket analysis extends partial wave analysis to infinite-range potentials.

## Abstract

We calculate the nonrelativistic scattering of a wavepacket from a Coulomb potential and find deviations from the Rutherford formula in all cases. These generally occur only at low scattering angles, where they would be obscured by the part of the incident beam that emerges essentially unscattered. For a model experiment, the scattering of helium nuclei from a thin gold foil, we find the deviation region is magnified for low incident energies (in the keV range), so that a large shadow zone of low probability around the forward direction is expected to be measurable. From a theoretical perspective, the use of wavepackets makes partial wave analysis applicable to this infinite-range potential. It allows us to calculate the everywhere finite probability for a wavepacket to wavepacket transition and to relate this to the differential cross section. Time delays and advancements in the detection probabilities can be calculated. We investigate the optical theorem as applied to this special case.