2. K0-standardization method in neutron activation analysis

at neutron energy E per one atom of the irradiating sample in a neutron flux distribution ϕ(E),

where σγ (E) is capture cross section. During the irradiation processes, strong resonance reactions deplete the neutron spectrum at the resonance energy due to absorption and scattering. For the energy regions just lower than the resonance energies, the neutron distribution is raised due to multiple scatterings from the resonances. Therefore, the capture reaction rate is affected because of the perturbation in the neutron spectrum. It is assumed that, for a sample or monitor with similar thickness but infinitely diluted, the neutron distribution inside this sample or monitor is a none-perturbed spectrum. The self-shielding correction factors can be estimated

as the ratio of the reaction rate by the none-perturbed to that by the perturbed spectra.

source geometries, and applicable only for single element samples.

Although the research topic on neutron self-shielding has been considered for a long history, the available resources for neutron activation analysis (INAA) applications are still limited in

The problem of calculations for determining the neutron self-shielding correction factors has been considered in neutron capture experiments, but in neutron activation analysis it is still less of information and numerical data. These correction factors are always needed to be taken into account in the data analysis of experiments such as neutron reaction cross sections measurements, neutron flux and spectrum measurements, and neutron activation analysis, and so on. In these experimental studies, the thickness of the irradiated sample or standard monitor is frequently not thin enough for ignoring the variance of neutron flux distribution inside the sample space. Therefore, the correction factors for the self-shielding and multiscattering effects of thermal, epithermal and resonance neutrons should be determined exactly. This research topic had been previously carried out, and reported in case by case, which can be briefly discussed as follows. Lopes et al. [1] calculated the values of epithermal neutron selfshielding factors, including isotopic scattering, for foil of Au-197 and Co-59. Eastwood et al. [2] reported experimental values of resonance neutron self-shielding factors for foils and wires of Co-59, by the activation technique. Brose [3] measured the resonance neutron absorption factors for Gold foils with different thickness. Hisashi Yamamoto and Kazuko Yamamoto [4] reported their calculated values of resonance neutron self-shielding correction factors for foils of Au-197, W-186, Mn-55 and In-115. The effects of Doppler broadening and potential scattering were taken into account, considering only main individual resonances. Senoo et al. [5] introduced a Monte Carlo code, TIME-MULTI, for neutron multiple scattering calculations with time-of-flight spectra. Shcherbakov and Harada [6] proposed a fast analysis method for calculations of epithermal neutron self-shielding factors, which was made used the Padé approximation for Doppler broadening function. Trkov et al. [7] introduced a computer program for self-shielding factors in neutron activation analysis, in which the calculation method is based on the neutron slowing-down equation. The program can be used for calculations with multi-element samples and applicable only for reactor isotropic neutron field. Gongalves et al. [8, 9] performed resonance neutron self-shielding factors for foils and wires of different materials by using the MCNP code and proposed universal curves for a number of neutron

R Eð Þ¼ ϕð Þ E σγð Þ E , (1)

is defined as the following expression:

56 Advanced Technologies and Applications of Neutron Activation Analysis

In the absolute standardization method, the concentration of the nuclide in a given sample can be determined as the following formula [10]:

$$\rho(\mu\text{g/g}) = N\_{\rho} \left[ \Delta\_{k}, \frac{N\_{\mu}W.\theta.\gamma\_{k}}{M} . \varepsilon\_{p}, \Phi\_{v}.\sigma\_{v} \left( G\_{h}, f + G\_{qv}.Q\_{b}(\alpha) \right) \right] 10^{6} \tag{2}$$

In the K0-standardization method, the concentration of the nuclide in a given sample can be determined as the following formula [10]:

$$\rho\_a(\mu g/g) = \left[\frac{\left(\frac{N\_p/t\_m}{w.S.D.\complement \mathcal{E}}\right)\_a}{A\_{sp,Au}}\right] \cdot \frac{1}{k\_{0,Au}(a)} \cdot \frac{\left[G\_{th}.f + G\_{epi}.Q\_0(\alpha)\right]\_{Au}}{\left[G\_{th}.f + G\_{epi}.^{epi}Q\_0(\alpha)\right]\_a} \cdot \frac{\varepsilon\_{p,Au}}{\varepsilon\_{p,a}} \cdot 10^6\tag{3}$$

in which Gth and Gepi are the thermal and epithermal self-shielding correction factors and the k0-factor is defined as [10]:

$$k\_{0,c}(\mathbf{s}) = \frac{M\_c.\theta\_s.\sigma\_{0,s}.\mathcal{V}\_s}{M\_s.\theta\_c.\sigma\_{0,c}.\mathcal{V}\_c} \tag{4}$$
