Neutron activation

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.

Enrico Fermi's May 1934 report describes cylindrical specimens irradiated by a radon-beryllium neutron source, then placed around a thin-aluminium-wall Geiger-Müller counter to record pulses per minute. The irradiation and counting were successive operations.^[ref]

The October paper by Enrico Fermi, Edoardo Amaldi, Bruno Pontecorvo, Franco Rasetti and Emilio Segrè reports that interposed paraffin wax increased silver activation; surrounding blocks enhanced it further, depending on geometry. Water gave a comparable effect. A preparation without beryllium gave no effect, arguing against gamma rays alone. Oxygen-containing material without hydrogen did not give a comparable enhancement, and not all activated elements responded alike. Repeated collisions with hydrogen were proposed to slow the neutrons.^[ref]

The University of Pisa's account of Bruno Pontecorvo's work with Edoardo Amaldi describes stronger silver activation on wood than on marble. This is a retrospective account; the October paper above directly documents the deliberate paraffin wax and water comparisons.^[ref]

To interpret this readout, compare an irradiated specimen with an unirradiated specimen or empty-counter background, using the same counting geometry. Compare irradiation conditions at matched irradiation durations, delays and counting windows. These are requirements of the measurement model, rather than a claim that every such control is documented in the short October letter. Otherwise ordinary radioactive decay during transfer can imitate a change in activation. A persistent, decaying excess after irradiation supports an unstable product; neither a larger count nor a fitted half-life uniquely identifies an isotope.

In his 1938 Nobel lecture, Enrico Fermi distinguished single and superposed exponential decay curves and described chemical separation to identify their carriers. His slowing interpretation connected elastic collisions with enhanced capture. The lecture also described neutron capture resonances, so its account cannot support a universal rule that slower always means more reactive.^[ref]

The 1934 assignments of some uranium activities to elements beyond uranium were mistaken interpretations, not a discovery of nuclear fission. The published lecture's later footnote explicitly calls for reexamining the transuranic assignments after evidence of splitting. Distinguish that correction from the lecture as delivered.^[ref]

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 $1/v$.

A neutron capture resonance is an energy interval where a matching excited state of the combined atomic nucleus enhances capture. Its collision cross-section can have a peak rather than a monotone dependence on energy. The resonance pole description connects this to quantum scattering. Slowing a neutron through such a region can first increase and then decrease a particular reaction response. The capture probability also competes with other reaction channels.

Let $\overline{N}$ be the expected value of the number of radioactive product atomic nuclei, initially zero, produced at constant rate $R$. Let their nuclear decay constant be $\lambda >0$. Assume one product species, negligible target depletion and negligible capture by the product. During irradiation, production adds $Rdt$ while radioactive decay removes $\lambda \overline{N}dt$ in expectation. Multiplying the resulting ordinary differential equation by $e^{\lambda t}$ givesThe expected radioactive activity $\overline{A}=\lambda \overline{N}$ tends to the production rate $R$. This saturation is a balance of continuing production and radioactive decay, not exhaustion of target atomic nuclei.

If irradiation ends at $t_i$, let $s$ denote elapsed time afterward. Setting the production term to zero givesFor detection efficiency $\epsilon$, constant background count rate $b$, delay $d$ and counting-window duration $\Delta$, integrating the expected count rate givesThis assumes at most one recorded pulse per product transformation and negligible counter losses. Detector response, branching fractions and background must be calibrated independently. Subtracting an estimated background does not remove its counting uncertainty. Several products give a sum of these terms with distinct nuclear decay constants; a single exponential decay fit can then mislead.

For a wholly stipulated example, choose $R=120{\min }^{-1}$, half-life $2\min$ and $t_i=4\min$. Then $\lambda =\log 2/(2\min )$, $\overline{A}(t_i)=90{\min }^{-1}$ and $\overline{N}(t_i)\simeq 259.69$. Choose $\epsilon =0.25$, $b=2{\min }^{-1}$ and $d=\Delta =2\min$. The result isThe background contributes four expected counts. Multiplying the initial net count rate in that window by its duration would give $22.5$ net counts, overestimating the integrated $16.23$ because the product decays appreciably during counting. All these values and the following curves are original examples, not measured historical data or parameters assigned to a particular silver isotope.