Neutron Activation Analysis

How it works: capture, decay, detect

Neutron activation analysis runs on a beautifully simple three-step idea — irradiate, decay, count — yet it ends up being one of the most sensitive elemental techniques ever built. The trick is to turn the elements you want to find into temporary radioactive beacons, then listen for the light they broadcast as they fade back to stability.

The first step is neutron capture. A sample is placed in a flux of neutrons — typically inside a research reactor where the thermal neutron flux is between 10¹² and 10¹⁴ neutrons per square centimeter per second. A nucleus in the sample absorbs one of these slow (thermal, ~0.025 eV) neutrons and forms a compound nucleus in a highly excited state. This is the radiative capture, or (n,γ), reaction. The newly formed isotope has one extra neutron and the same atomic number, so it is the same element but a heavier, usually unstable, isotope:

²³Na + n → ²⁴Na* → ²⁴Na + prompt γ

That prompt gamma, emitted within ~10⁻¹⁴ seconds of capture, is what prompt-gamma NAA (PGNAA) measures. But the workhorse method, instrumental NAA (INAA), waits for the second step: radioactive decay. The activated isotope is unstable and decays — usually by beta-minus emission — to a daughter nucleus, frequently leaving that daughter in an excited state that relaxes by emitting one or more delayed gamma rays at sharply defined energies. ²⁴Na, for instance, has a 14.96-hour half-life and decays to ²⁴Mg, emitting gammas at 1368.6 keV and 2754.0 keV. Those two energies are a fingerprint: no other isotope produces exactly that pair.

The third step is gamma-ray spectroscopy. The irradiated sample is moved (after a chosen decay time) to a high-purity germanium (HPGe) detector, which records the energy of every gamma it absorbs. The result is a spectrum — a histogram of counts versus energy — covered in sharp peaks. Where a peak sits identifies the element; the area under the peak, corrected for half-life, detector efficiency, and the known irradiation conditions, gives the quantity. Because HPGe detectors resolve energies to roughly 0.1–0.2% (a few keV at 1 MeV), dozens of elements can be untangled from a single spectrum at once.

The numbers that govern sensitivity

How much radioactivity you induce — and therefore how little of an element you can detect — is set by the activation equation. The number of radioactive nuclei present at the end of an irradiation of time t_i is:

A = N · σ · φ · (1 − e^−λt_i)

where A is the activity (decays per second) at end of irradiation, N is the number of target atoms, σ is the neutron-capture cross section (in barns; 1 barn = 10⁻²⁴ cm²), φ is the neutron flux, and λ = ln2/t_½ is the decay constant of the product. The term in parentheses is the saturation factor: irradiating much longer than a few half-lives gives diminishing returns because new nuclei are being created as fast as old ones decay. After the sample is removed, the activity decays as e^−λt_d during the decay (cooling) time t_d.

The cross section σ is the single biggest lever on sensitivity, and it varies over more than six orders of magnitude across the periodic table. Gold's ¹⁹⁷Au has σ ≈ 98.7 barns; dysprosium's ¹⁶⁴Dy has an enormous ~2650 barns; while carbon and oxygen sit below 0.001 barn. This is why NAA is spectacular for gold, the rare earths, arsenic, antimony, and mercury, but nearly blind to the light organic elements. The table below shows how a handful of analytically important isotopes behave.

Target isotope	Product	Half-life	Key gamma (keV)	Thermal σ (barns)	Typical use
¹⁹⁷Au	¹⁹⁸Au	2.70 d	411.8	98.7	Trace gold, jewelry, forensics
²³Na	²⁴Na	14.96 h	1368.6 / 2754.0	0.53	Glass, biological tissue
⁵⁵Mn	⁵⁶Mn	2.58 h	846.8	13.3	Steel, geology, water
⁵⁸Fe	⁵⁹Fe	44.5 d	1099.3 / 1291.6	1.28	Alloys, minerals
⁷⁵As	⁷⁶As	26.3 h	559.1	4.3	Arsenic poisoning, environment
¹⁶⁴Dy	¹⁶⁵Dy	2.33 h	94.7	~2650	Ultra-trace rare earths

The half-life of the product dictates the timing strategy. Short-lived activities (²⁸Al, t_½ = 2.2 min; ²⁰F, 11 s) are counted within minutes of irradiation. Medium-lived isotopes (²⁴Na, ⁵⁶Mn) are counted after hours. Long-lived isotopes (⁶⁰Co at 5.27 years, ⁵⁹Fe at 44.5 days, ⁵¹Cr at 27.7 days) require letting the short-lived "noise" decay away first, so they may be counted days or weeks later when their peaks stand clear above a quieter background. A single sample is often counted several times at different decay intervals to harvest the full element list.

INAA, RNAA, and prompt-gamma variants

The same physics supports several flavors tuned to different problems:

• INAA (instrumental NAA). Irradiate, decay, count — no chemistry. This is the truly nondestructive form and the most widely used. Its limit is that strong matrix activities (²⁴Na, ⁵⁶Mn, ³²P) can bury weak peaks under Compton continuum.
• RNAA (radiochemical NAA). After irradiation, a chemical separation isolates the radioisotope of interest from the interfering matrix. Destructive, but it strips away the background and pushes detection limits down to femtograms for some elements. Because the radioactivity is induced before any chemistry, reagent contamination cannot create a false signal — a key advantage over wet-chemical methods.
• PGNAA (prompt-gamma NAA). The detector watches the sample during irradiation, catching the prompt gammas emitted at the instant of capture. This reaches elements that delayed-gamma NAA cannot — hydrogen, boron, cadmium, gadolinium, nitrogen — and is used for in-line bulk analysis of coal and cement.
• ENAA / FNAA. Epithermal NAA uses a cadmium or boron filter to remove thermal neutrons and exploit large resonance cross sections, improving certain element-to-matrix ratios; fast-neutron NAA uses MeV neutrons to drive (n,p) and (n,α) reactions that reach light elements like oxygen.

Where NAA earns its keep

Archaeometry and art authentication. Because INAA is nondestructive and reads bulk composition, museums use it to fingerprint pottery, obsidian, and glass by their rare-earth and trace-metal patterns, sourcing artifacts to specific clay beds or quarries. NAA famously analyzed Napoleon's hair, finding arsenic levels far above normal, and has been used to test paintings for anachronistic pigments.

Forensics and toxicology. The 559 keV gamma of ⁷⁶As makes arsenic poisoning detectable in a single hair from a few centimeters of growth, letting investigators reconstruct a timeline of exposure. Gunshot-residue work has used NAA to find barium and antimony from primer.

Environmental and geological trace metals. NAA quantifies mercury, selenium, arsenic, chromium, and the rare earths in soils, sediments, coal, and water at sub-ppm levels, with very low blanks because no reagents touch the sample before activation.

Semiconductor and high-purity materials. Silicon wafers and reactor-grade graphite are checked for ppb-level metallic contaminants that would ruin device yield. The cosmochemistry community uses NAA on meteorites — the iridium anomaly at the Cretaceous–Paleogene boundary, evidence for the dinosaur-killing impact, was measured by NAA.

Certifying reference materials. Standards laboratories such as NIST use NAA as a definitive method to assign the "true" concentrations in certified reference materials, against which faster routine methods like ICP-MS and XRF are then calibrated.

NAA versus other elemental techniques

No single technique covers everything; NAA's strengths and gaps are complementary to the optical and mass-spectrometric methods chemists reach for first.

Property	NAA (INAA)	ICP-MS	XRF	AAS
Sample prep	None (nondestructive)	Dissolution required	Minimal	Dissolution required
Detection limit	ppb–pg (element-dependent)	ppt–ppb	ppm	ppb–ppm
Multi-element	Yes, 30–40 at once	Yes, broad	Yes	One at a time (mostly)
Reagent blanks	Essentially none	Significant	None	Significant
Best for	Au, As, rare earths, Sb, Hg	Wide periodic table	Major/minor elements	Single metals, routine
Main limitation	Needs reactor; slow for long-lived	Spectral/matrix interferences	Surface only, low sensitivity	Low throughput

Limitations and safety

NAA's headline drawback is access: a steady, high neutron flux usually means a research reactor, though some labs use ²⁵²Cf isotopic sources or accelerator-driven neutron generators at lower flux. Turnaround can be slow when long-lived isotopes must be counted days later. Light elements — H, C, N, O, and notoriously Pb — are poor or impossible targets because their activation products are stable, short of useful gammas, or have negligible cross sections.

There are interference traps to manage. Spectral interferences arise when two isotopes emit gammas at nearly the same energy; nuclear interferences occur when a different reaction makes the same product (e.g. fast-neutron ²⁷Al(n,α) producing ²⁴Na, mimicking sodium). Self-shielding inside strongly absorbing samples and neutron-flux gradients across the irradiation position must be corrected, often by co-irradiating a flux monitor. Handling is governed by radiation-safety rules: after irradiation, samples are radioactive and are stored to cool before counting and disposal, but in INAA the induced activity is transient and decays away.

Despite these constraints, the core appeal endures. By converting elements into self-reporting radioactive tracers, neutron activation analysis reads composition through solid matter, with almost no blank, at sensitivities that let chemists count single picograms of gold in a coin they never have to scratch.