Calculators / Reactor and fuel cycle
Neutron activation calculator
Activity induced in a sample by a neutron flux, at the end of irradiation and after cooling. Thermal cross sections and resonance integrals are cited per target; the rate follows the Høgdahl convention used in k0 neutron activation analysis.
Free · no account · works offline · iOS, Android and web
The formula
R = N · (φ_th·σ₀ + φₑ·I₀) reactions per second N = m · N_A · θ / M target atoms A(t) = R · (1 − e^(−λ·t_irr)) · e^(−λ·t_cool) φₑ = epithermal flux per unit lethargy (= φ_th / f)
Worked examples
Gold foil. 50 mg of gold in a TRIGA rotary rack (φth = 1.00 × 1012, φe = 5.00 × 1010 n/cm²/s) for 1 h, counted after 1 h:
- SATURATION
- 26.9 GBq
- END OF IRRADIATION
- 287 MBq
- AFTER 1 h
- 284 MBq · 7.68 mCi
Cobalt. 1 g of cobalt for 30 days in a materials test reactor core (φth = 1.00 × 1014): 449 GBq (12.1 Ci) of Co-60 — only 1.1 % of saturation, because Co-60’s half-life is 5.27 years.
Cross sections used
| REACTION | σ0 (b) | I0 (b) | PRODUCT T½ |
|---|---|---|---|
| Na-23 (n,γ) Na-24 | 0.528 | 0.311 | 14.956 h |
| Mn-55 (n,γ) Mn-56 | 13.3 | 14 | 2.579 h |
| Co-59 (n,γ) Co-60 | 37.18 | 74 | 5.271 y |
| Cu-63 (n,γ) Cu-64 | 4.5 | 4.97 | 12.701 h |
| Ag-109 (n,γ) Ag-110m | 4.7 | 76.6 | 249.8 d |
| In-115 (n,γ) In-116m | 162.3 | 2,640 | 54.29 m |
| Au-197 (n,γ) Au-198 | 98.65 | 1,550 | 2.694 d |
Fast-neutron (threshold) reactions
A threshold reaction needs a fast neutron, so its cross section depends on the source’s spectrum. The app averages the IAEA IRDFF-II evaluations over the spectrum of the source you choose; these are the averages, in millibarns per unit total flux:
| REACTION | U-235 FISSION | Am-Be | D-D 2.45 MeV | D-T 14.1 MeV |
|---|---|---|---|---|
| O-16(n,p)N-16 | 0.0303 | n/a | 0 | 42.7 |
| Al-27(n,α)Na-24 | 0.687 | n/a | 0 | 121 |
| Fe-54(n,p)Mn-54 | 76.6 | 255 | 59 | 339 |
| Ni-58(n,p)Co-58 | 105 | 322 | 98.6 | 353 |
| Ti-46(n,p)Sc-46 | 11.1 | 64 | 0.0239 | 256 |
| S-32(n,p)P-32 | 66.8 | 191 | 83.6 | 247 |
| Cu-63(n,α)Co-60 | 0.514 | n/a | 8.95 × 10-4 | 45.5 |
Zero means the source’s neutrons are below the reaction’s threshold. n/a means no value is given: the published Am-Be spectrum is too coarse above 10 MeV for the three highest-energy reactions. Nickel as a fast-flux monitor: 1 g of nickel for 30 days in a TRIGA core (5.00 × 1010 n/cm²/s above 0.5 MeV) holds 10.8 MBq of Co-58 at the end of irradiation.
Assumptions
- Thin sample: no neutron self-shielding and no burn-up of target or product. Both matter for strong absorbers and long irradiations.
- Constant flux. Partial cross sections are to the named product (Ag-110m, In-116m), not total absorption.
- Fast flux means flux above 0.5 MeV. A reactor’s fast flux is taken to have the U-235 fission shape; a moderated D-D generator’s is taken at 2.45 MeV, an upper bound.
Sources
- Thermal cross sections: Mughabghab, Atlas of Neutron Resonances (2006); IAEA PGAA database.
- Fast cross sections: IRDFF-II, Trkov et al., Nucl. Data Sheets 163 (2020); O-16 from ENDF/B-VIII.0. Spectra: ENDF/B-VIII.0 U-235 fission; ISO 8529-1 Am-Be (IAEA TRS-403).
- Rate convention: Høgdahl (1962); De Corte, k0 NAA.
- Half-lives: IAEA NUBASE2020.
Numbers on this page computed by the physics code of Nuclear Toolkit 1.4.1, the same code as the app. How it is checked.