Experimental and theoretical investigation of absorption by aluminum materials for beta particles

In this study, the half-values thickness of the aluminum absorbers has been investigated experimentally and theoretically. The 99Tc, 36Cl, 14C, 210Pb, 147Pm, 90Sr/90Y, 137Cs and 204Tl radio-isotopes have been used as beta sources. There is an inconsistency between the experimental measurements and standard theoretical calculations. Standard attenuation equation has been resolved with using fractional calculus. In this context, the Caputo fractional derivative operator has been performed instead of the first order derivative operator in attenuation equation. The solution of this new equation has been obtained in terms of the Mittag – Leffler function. Fractional derivative order has been calculated to make experimental measurements be coherent with theoretical calculations. Even if different beta sources are used, the equivalent experimental and theoretical half-value thickness have been found for fractional derivative order =0.31. It is concluded that, for different beta sources, the half-value thicknesses of aluminum foils can be calculated by using simple fractional differential equation of order 0.31.