Determination of half-value thickness of aluminum foils for different beta sources by using fractional calculus

Reduction of beta-ray intensity with respect to thickness of absorber material exhibits a non-exponential behavior due to the different types of the energy loss processes and many different fractal-like paths followed by beta particles in material. According to Caputo formalism of fractional calculus, the reduction process of beta-ray intensity is governed by using a simple fractional differential equation of order α ≈ 0.31. The solution is obtained in terms of Mittag–Leffler function which depends on a mass attenuation coefficient μm and a fractional order α that can be considered as a measure of fractality of absorbing material. In the experimental part of the study, 99Tc, 36Cl, 14C, 210Pb and 147Pm radioisotopes have been used as beta sources. In the framework of fractional calculus approach, the experimental and calculated half-value thicknesses of all samples have been obtained in agreement with each other.