Principle of NAA:

The technique of NAA involves two steps; irradiation of a sample with neutrons and subsequent measurement of the induced radioactivity. The radionuclides are characterized by their characteristic γ-ray energy and half-life as illustrated in Figure.

Figure: Basic principle of Neutron Activation Analysis

In this process, the rate of formation of the product atoms (N_p) is represented as;

dN_p/dt = N σ φ - λ Np = N σ φ - λ N₁                                   

here N is the number of the target atoms of an element in the sample [ iw N_A /M]

i denotes the isotopic abundance; w is the concentration of element; M is the mass of the target   atom; NA is the Avogadro number;

σ denotes the thermal neutron absorption cross section in barns (b = 10-24 cm²);

φ is the  neutron flux (n cm^-2 s^-1), and

λ is the decay constant (s^-1) = (0.693/ t_{1 / 2}) and t_1/2 = half life of the product nucleus.

On integration, Eq. (13.6) yields

λ N1 = A = N σ φ (1 - e^{- λti} )

where t_i is the irradiation time. Since the sample is delayed for time t_d before counting using a counter along with effectiveness ε, and gamma-ray abundance γ, the complete equation can be written as;

A = (   wiN_A/M) σ φ (1 - e ^{- λti} ) e ^{- λtd} ε γ =(wiN_A/M) σ φ S D C ε γ

where S = (1 - e ^{- λti}  ) is saturation factor, D = (e ^{- λtd} ) is delay factor, and

C = (1 - e ^{- λt c} )/ λ is the correction factor for decay during counting time t_c.