Theory

1.1 Mass attenuation coefficient (MAC)

Mass attenuation coefficient serves as a measure of absorbing properties of the matter, characterized the interaction y-rays with substance, and depends on its element composition and energy photons. In other worlds MAC is a measurement of how strongly a substance absorbs the radiation. Is a measure of the average number of interactions between incident photons and matter that occur in a given mass-per-unit area thickness of material encountered (Hubbell 1982).

A narrow beam of mono-energetic photons is attenuated to an intensity I from an incident intensity I0 in passing through a layer of material with thickness x according to the exponential absorption law (Hubbell 1982) or Lambert-Beer law:

I(x) = I0e-Mpx (1)

where:

ц – mass attenuation coefficient (MAC), p – density of the material of thickness x Equation (l) can be rewritten as:

Подпись: (2)ln(I(x)/Ip)
-px

For materials composed of multi elements the total MAC-ц is the sum of the ц values of each constituent element by the following mixture rule (Han, Demir et al. 2009):

V = Yfi Vi (3)

where:

ci – is the concentration of individual chemical element in the sample or in other words is the proportion by weight and Д; is mass attenuation coefficient of the i-th element.

Подпись: V = mAu, mA Подпись: PZNA A Подпись: (4)

For materials composed of multi elements, the fraction by weight is given by (Hubbell 1982; Gigante, Pedraza et al. 1985)

where:

a – the total atomic cross section, NA – is the Avogadro’s number, Z – the atomic number and A – the atomic number of element.

Considering three main mechanisms of interaction, mass attenuation coefficient ц of low energy y-radiation in matter is the sum of (Perumallu, Rao et al. 1985; Bhandal and Singh 1993; Manohara and Hanagodimath 2007)

Подпись: (5)V = VPhot + VCoh + VCom

where:

Vphot – mass attenuation coefficient for photo effect;

Vcoh, Vcom – coefficients for coherent and Compton attenuations, respectively.