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Neutron activation is the production of radioactivity by irradiating a material with neutrons. One route is neutron capture producing an unstable isotope; other nuclear reactions can also produce unstable atomic nuclei. A specimen's later radioactive decay provides a way to detect that a transformation occurred during irradiation. It does not by itself identify the product or reconstruct the incoming neutron energy distribution.

This makes neutron activation a useful bridge between an invisible radiation field and a delayed measurement. The neutron flux and collision cross-section determine production; radioactive decay and detection efficiency determine what remains observable later. Neutron activation buildup and decay keeps these stages separate.

Let $n(E)dE$ be the number of neutrons per unit volume in an energy interval. The scalar neutron flux per unit energy is $\varphi (E)=v(E)n(E)$, with $v(E)$ the speed. Its integral has units of inverse area per unit time. It counts path length traversed per volume per time, including all directions; it is not the signed current through an oriented surface.

For a small uniform specimen containing $N_T$ target atomic nuclei, a reaction-specific collision cross-section ${\sigma }_a(E)$ gives the expected production rateAssume the incident field is little changed within the specimen, target depletion is negligible and each counted reaction creates the product of interest. If that product has a production branching fraction below one, include it in ${\sigma }_a$ or as an additional factor. A single neutron activation measurement supplies one weighted integral of an energy distribution, not a unique reconstruction of that distribution.

For an original two-group example, stipulate response collision cross-sections ${\sigma }_s=10{\sigma }_f$. With the same total scalar neutron flux $\Phi$, changing from all fast neutrons to half slow and half fast changes $R/(N_T{\sigma }_f\Phi )$ from $1$ to $5.5$. No additional neutrons need be emitted by the source. The chosen factor ten is not a historical silver measurement.

For some capture reactions over a limited low-energy interval, ${\sigma }_a\propto 1/v$ is a useful approximation. At fixed neutron flux, it gives increasing reaction probability per path length as speed decreases. At fixed neutron number density, ${\sigma }_{a}v$ is constant in this approximation, so the rate per target is unchanged. A real neutron moderator changes the local density, energy distribution, escape and absorption together. Neither all collision cross-sections nor all neutron activation rates vary monotonically as $1/v$.