Bootcamp for Science

9.1: Notation and Introduction

Scattering experiments with electrons showed that the radius of a nuclear with A nucleons is roughly given by:

(1)   \begin{equation*}R=r_0A^{1/3}\end{equation*}

where r_0=1.2fm

Consider a beam of neutrons of intensity I incident on a slab of matter of thickness dx, cross-sectional area S, and volume density n (the number of atoms per volume). Then nSdx is the total number of nuclei, and \sigma nSdx is the effective area covered by all nuclei in the slab. The fraction of neutrons that get scattered is:

(2)   \begin{equation*}\frac{dI}{I}=-\frac{\sigma nSdx}{S}=\sigma n dx\end{equation*}

There is a negative sign in front because intensity decreases.

Integrating, we get:

(3)   \begin{equation*}\boxed{I(x)=I(x)e^{-\sigma nx}}\end{equation*}