Dimensional analysis and Rutherford Scattering

TL;DR

This paper uses dimensional analysis, specifically Buckingham's Pi theorem, to derive an expression for the impact parameter and compares it with Rutherford's original scattering results.

Contribution

It applies Buckingham's Pi theorem to derive impact parameter expressions and relates them to Rutherford's scattering findings.

Findings

Derived impact parameter expression using dimensional analysis

Compared derived expression with Rutherford's original results

Validated the use of Buckingham's theorem in scattering problems

Abstract

Dimensional analysis, and in particular the Buckingham $\Pi$ theorem is widely used in fluid mechanics. In this article we obtain an expression for the impact parameter from Buckingham's theorem and we compare our result with Rutherford's original discovery found in the early twentieth century.