Neutron Activation Analysis Calculator
Calculate the induced radioactivity (activation) of a target material irradiated by a neutron flux, accounting for saturation effects. Used in neutron activation analysis (NAA) to determine trace element concentrations in samples.
About this calculator
When a target is irradiated by neutrons, radioactive nuclides are produced at a rate governed by: A = φ × σ × 10⁻²⁴ × N × (1 − e^(−λt)), where φ is the neutron flux (n/cm²/s), σ is the activation cross-section in barns (1 barn = 10⁻²⁴ cm²), N is the target nuclei density (nuclei/cm³), λ is the decay constant of the product nuclide (s⁻¹), and t is the irradiation time (s). The factor 10⁻²⁴ converts barns to cm². The saturation term (1 − e^(−λt)) captures the competition between production and decay: at short irradiation times A grows nearly linearly, but as t → ∞ activity saturates at A_sat = φ σ N × 10⁻²⁴, the saturation activity. Irradiation for one half-life reaches 50% saturation; five half-lives reaches ~97%. This formula is the foundation of NAA, a non-destructive analytical technique used in geochemistry, archaeology, and nuclear forensics.
How to use
A gold (Au-197) foil with N = 5.9 × 10²² nuclei/cm³ is irradiated in a flux φ = 1 × 10¹³ n/cm²/s. The activation cross-section σ = 98.65 barns and the decay constant of Au-198 is λ = 2.975 × 10⁻⁶ s⁻¹. Irradiation time t = 3,600 s (1 hour). Calculation: saturation term = 1 − e^(−2.975×10⁻⁶ × 3600) = 1 − e^(−0.01071) ≈ 0.01065; A = 10¹³ × 98.65 × 10⁻²⁴ × 5.9×10²² × 0.01065 = 10¹³ × 98.65 × 10⁻²⁴ × 5.9×10²² ≈ 5.82×10¹²; × 0.01065 ≈ 6.2 × 10¹⁰ disintegrations/s (62 GBq) at end of irradiation.
Frequently asked questions
How does irradiation time affect the activity produced in neutron activation analysis?
Activity builds up following the saturation curve A(t) = A_sat × (1 − e^(−λt)), so it never exceeds the saturation activity A_sat = φ σ N × 10⁻²⁴. After one half-life of irradiation, 50% of saturation activity is reached; after two half-lives, 75%; after five half-lives, ~97%. For nuclides with very long half-lives, the saturation activity is approached very slowly and short irradiations produce proportionally less activity, making detection of trace elements harder. Analysts therefore choose irradiation times of one to several half-lives of the target nuclide for optimal sensitivity.
What is the activation cross-section and how does it vary between elements?
The activation cross-section σ quantifies how likely a target nucleus is to absorb a neutron and become radioactive; it is measured in barns (1 barn = 10⁻²⁴ cm²). Cross-sections vary enormously: gold-197 has σ ≈ 99 barns, making it an excellent flux monitor, while oxygen-16 has σ < 0.0002 barns, making it essentially transparent to thermal neutrons. Elements with large cross-sections can be detected at part-per-billion concentrations by NAA. The cross-section also depends on neutron energy — thermal neutrons (low energy) typically have much larger cross-sections than fast neutrons due to the 1/v law governing many nuclear reactions.
Why is neutron activation analysis considered a non-destructive analytical technique?
In NAA, the sample is not chemically dissolved or altered — it is simply placed in a neutron field and then measured by gamma-ray spectroscopy after irradiation. Because each activated nuclide emits characteristic gamma-ray energies, the elemental composition can be read out without consuming the sample, which is critical for irreplaceable materials like archaeological artifacts, lunar samples, or forensic evidence. The sample does become temporarily radioactive, so a decay (cooling) period is required before safe handling, but the physical and chemical structure of the sample remains intact.