Range Integration¶

One important aspect of materials science as it relates to nuclear energy is the range or stopping power of a material. This is a straightforward integration determination, however the knowledge of the dependencies will help you determine relative differences in materials. The textbook I learned it from was [Nastasi1996].

The calculation of the range of a particle is defined by the integral from the incident energy to zero of the reciprocal of its energy deposition function.

\[R=\int_{E_{i}}^{0} \frac{dE}{\nicefrac{dE}{dx}}\]

In general, the nuclear energy deposition follows the equation

\[\left.\frac{dE}{dx}\right|_{n}=N_{\Pi} \frac{Z_{1}^{2}Z_{2}^{2}e^{4}M_{1}}{E_{i}M_{2}} \ln \frac{\Lambda E_{i}}{E_{a}}\]

and the electrical energy deposition is

\[\left.\frac{dE}{dx}\right|_{e}=\frac{dE}{k\sqrt{E_{i}}}\]

Range Integration¶

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