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


Sen M., Calik A. E. , Ertik H.

NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION B-BEAM INTERACTIONS WITH MATERIALS AND ATOMS, cilt.335, ss.78-84, 2014 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 335
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1016/j.nimb.2014.06.005
  • Dergi Adı: NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION B-BEAM INTERACTIONS WITH MATERIALS AND ATOMS
  • Sayfa Sayıları: ss.78-84

Özet

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 alpha approximate to 0.31. The solution is obtained in terms of Mittag-Leffler function which depends on a mass attenuation coefficient mu(m) and a fractional order a that can be considered as a measure of fractality of absorbing material. In the experimental part of the study, Tc-99, Cl-36, C-14, (210)pb and Pm-147 a Pm 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. (C) 2014 Elsevier B.V. All rights reserved.