In order to determine the cross section for neutron capture,...

In order to determine the cross section for neutron capture, you are irradiating a thin gold foil, in the form of a circular disk of diameter $3.0 \mathrm{mm}$ and thickness $1.81 \mu \mathrm{m}$ with neutrons to produce the reaction $n+{ }^{197} \mathrm{Au} \rightarrow$ 198 Au $+\gamma$. By observing the outgoing gamma-ray pho- tons in a detector, you determine that the gold decays at a rate of $5.37 \times 10^{6}$ per second. From an independent measurement, you have determined the neutron flux to be $7.25 \times 10^{10}$ neutrons $/ \mathrm{cm}^{2} / \mathrm{s} .$ What value do you deduce for the cross section for this reaction?

Key Concepts

Neutron Flux

Neutron flux is defined as the number of neutrons passing through a unit area per unit time. It is a critical parameter in nuclear experiments because it quantifies the intensity of the neutron beam, which directly influences the rate at which nuclear reactions occur within the target material.

Nuclear Reaction Cross Section

The nuclear reaction cross section represents the effective area that quantifies the probability of a nuclear reaction between an incident particle (such as a neutron) and a target nucleus. It is typically expressed in barns and is a fundamental quantity in nuclear physics that directly relates the measured reaction rate to the available flux and number of target nuclei.

Reaction Rate

The reaction rate is the number of reactions occurring per unit time. In the context of neutron capture experiments, it is measured by counting the number of decay events or emitted gamma rays. The rate is directly linked to both the neutron flux and the effective cross section of the reaction as well as the number of target nuclei present.

Target Characteristics and Geometry

Understanding the physical dimensions and composition of the target is crucial, as these factors determine the number of nuclei available to interact with the incoming neutrons. Thin targets, for example, allow for approximations where the entire target is uniformly irradiated, simplifying the analysis of the reaction rate in relation to the cross section.

Dimensional Analysis and Unit Conversion

Dimensional analysis and proper unit conversion are essential in calculations involving physical quantities such as flux, target area, and reaction rate. They ensure that all measurements are consistent and that the computed cross section has the correct physical units, facilitating accurate interpretation of experimental results.

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