NAA Quantification

The measured count rate (*R*) of the gamma rays from the decay of a specific isotope
(^{110}Ag) in the irradiated sample can be related to the amount (*n*) of the original,
stable isotope (^{109}Ag) in the sample through the following equation (1):

*R = ε I*_{γ} A = ε I_{γ} n φ σ
(1-e^{-λ ti}) e^{-λd}

Equation 1

where:

*R* = measured gamma-ray count rate (counts per second)
*A* = absolute activity of isotope ^{A+1}Z in sample
*ε* = absolute detector efficiency
*I*_{γ} = absolute gamma-ray abundance
*n* = number of atoms of isotope ^{A}Z in sample

*φ* = neutron flux (neutrons·cm^{-2}·sec^{-1})
*σ* = neutron capture cross section (cm^{2}) for isotope ^{A}Z
*λ* = radioactive decay constant (s^{-1}) for isotope ^{A+1}Z
*t*_{i} = irradiation time (s)
*t*_{d} = decay time (s)
If the neutron flux φ, neutron capture cross section σ, absolute detector efficiency ε, and absolute gamma-ray abundance Ι

_{γ} are known, the number of atoms

*n* of isotope

^{A}Z in the sample can be calculated directly. In most cases, however, a standard is irradiated and counted under similar conditions as the sample, and the mass of the element in the sample (W

_{sam}) is found by comparing the measured count rates (R) for the sample and standard through the following equation (2):

Equation 2

where:

W_{sam} = mass of element in sample (g)

W_{std} = mass of element in standard (g)

R_{sam} = gamma-ray count rate from the sample (counts per second)

R_{std} = gamma-ray count rate from the standard (counts per second)