A FRACTIONAL CALCULUS APPROACH TO INVESTIGATE THE ALPHA DECAY PROCESSES

Calik A. E., Ertik H., Oder B., ŞİRİN H.

INTERNATIONAL JOURNAL OF MODERN PHYSICS E, cilt.22, sa.7, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 7
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1142/s0218301313500493
  • Dergi Adı: INTERNATIONAL JOURNAL OF MODERN PHYSICS E
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Fractional calculus, nuclear decay equation, alpha decay, Mittag-Leffler function, KINETIC-EQUATION, DIFFUSION
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this study, the nuclear decay equation is taken under consideration by making use of fractional calculus. In this context, the first-order time derivative is changed to a Caputo fractional derivative hence, the resulting equation is the time fractional nuclear decay equation. The solution of this equation is obtained in terms of Mittag-Leffler function which plays an important role to study the non-Markovian feature of physical processes. As an application of this time fractional formalism, alpha decay half-life values have been calculated for Pb, Po, Rn, Ra, Th and U isotopes. Consequently, the theoretical half-life values have been obtained in consistent with the experimental data. The dependence of the order of fractional derivative mu being a measure of fractality of time, on the nuclear structure has been established, In the investigations carried out we have arrived to the conclusion that for the p values which are closed to one, where time becomes homogenous and continuous, the shell closure effects are predominant and that the fractional derivative order mu (i.e. fractality of time) and nuclear structure are closely related to each other.