A shadow of the repulsive Rutherford scattering and Hamilton vector

TL;DR

This paper explores the connection between the paraboloidal shadow in repulsive Rutherford scattering and the Hamilton vector, providing a novel explanation that enhances understanding in introductory mechanics.

Contribution

It demonstrates how the Hamilton vector can be used to explain the paraboloidal shadow in repulsive Rutherford scattering, a rarely exploited insight in physics education.

Findings

Hamilton vector explains the paraboloidal shadow

Provides new pedagogical perspective in mechanics

Clarifies geometric aspects of scattering phenomena

Abstract

The fact that repulsive Rutherford scattering casts a paraboloidal shadow is rarely exploited in introductory mechanics textbooks. Another rarely used construction in such textbooks is the Hamilton vector, a cousin of the more famous Laplace-Runge-Lenz vector. We will show how the latter (Hamilton's vector) can be used to explain and clarify the former (paraboloidal shadow).