Neutron Flux Calculator
Calculate the number of radioactive atoms produced when a target material is irradiated in a neutron flux, accounting for activation cross-section and decay during irradiation. Used in reactor isotope production and neutron activation analysis.
Last updated: May 2026
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About this calculator
When a stable target nucleus captures a neutron it becomes radioactive, and the resulting activity builds up over the irradiation period while simultaneously decaying. The saturation activity formula gives the number of activated atoms at time t: A(t) = (φ × σ × 10⁻²⁴ × N) × (1 − e^(−λt)) / λ, where φ is the thermal neutron flux in n/cm²·s, σ is the neutron absorption cross-section in barns (1 barn = 10⁻²⁴ cm²), N is the target nucleus density in nuclei/cm³, λ is the decay constant of the product nuclide in s⁻¹, and t is the irradiation time in seconds (hours × 3600). The production rate R = φ × σ × 10⁻²⁴ × N is constant, but as activated atoms accumulate they begin to decay. At saturation (t ≫ 1/λ) the factor (1 − e^(−λt)) → 1 and activity reaches its maximum value R/λ. This is the basis of neutron activation analysis (NAA) and the production of medical radioisotopes such as Mo-99 and Lu-177 in research reactors.
How to use
A gold foil (Au-197) is irradiated in a reactor with φ = 1×10¹³ n/cm²·s. The foil has N = 5.9×10²² nuclei/cm³, σ = 98.7 barns for Au-197, and the product Au-198 has λ = 2.97×10⁻⁶ s⁻¹ (t½ ≈ 2.69 days). Irradiation time = 24 hours = 86,400 s. Enter all values. Calculation: production rate R = 1×10¹³ × 98.7 × 10⁻²⁴ × 5.9×10²² = 5.82×10¹² activations/s. Saturation factor = 1 − e^(−2.97×10⁻⁶ × 86,400) = 1 − e^(−0.2564) ≈ 0.2264. Activated atoms = 5.82×10¹² × 0.2264 / 2.97×10⁻⁶ ≈ 4.43×10¹⁷ atoms of Au-198 produced.
Frequently asked questions
What is neutron activation and how is it used in isotope production?
Neutron activation occurs when a stable nucleus captures a thermal neutron and becomes a radioactive isotope of the same or a neighbouring element. Reactor-based neutron activation is the primary route for producing medical radioisotopes: Mo-99 (parent of the widely used Tc-99m imaging agent), I-131 for thyroid therapy, and Lu-177 for peptide receptor radionuclide therapy are all made this way. The target material is placed in a high-flux reactor channel for hours to weeks, and the resulting specific activity depends on the flux, cross-section, irradiation time, and decay constant. After irradiation, chemical separation isolates the product from the target matrix.
What does neutron absorption cross-section in barns mean for activation calculations?
The neutron absorption cross-section σ is a measure of how likely a nucleus is to capture a passing neutron, expressed in barns (1 barn = 10⁻²⁴ cm²). A large cross-section means the nucleus is a strong neutron absorber. For context, Au-197 has σ ≈ 99 barns, making it an excellent neutron flux monitor, while Co-59 has σ ≈ 37 barns. Some isotopes like Xe-135 have enormous cross-sections (2.6 million barns) and act as strong neutron poisons in reactors. Cross-section values depend on neutron energy; the values in this calculator apply to thermal (slow) neutrons at approximately 0.025 eV, typical of the thermal column in a research reactor.
How long should I irradiate a target to achieve maximum activation saturation?
Activation approaches saturation exponentially: after one half-life of the product nuclide, 50% of saturation activity is reached; after two half-lives, 75%; after five half-lives, 97%. For practical purposes, irradiating beyond three to five half-lives of the product provides diminishing returns, as the activation and decay rates approach equilibrium. For short-lived isotopes like F-18 (t½ = 110 min), saturation is reached in about 9 hours, while for longer-lived products like Co-60 (t½ = 5.27 years) true saturation would require decades. Reactor time is expensive, so irradiation schedules are optimised by balancing desired activity, irradiation cost, and the fraction of saturation activity acceptable for the application.