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 μ 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 μ values which are closed to one, where time becomes homogenous and continuous, the shell closure effects are predominant and that the fractional derivative order μ (i.e., fractality of time) and nuclear structure are closely related to each other.
In this work, the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix has been investigated by studying the eleven well-known superallowed Fermi Beta decays; their parent nuclei are 10 C, 14 O, 26 Al, 34 Cl, 38 K, 42 Sc, 46 V, 50 Mn, 54 Co, 62 Ga, and 74 Rb. The numerical value of the V ud element of the CKM mixing matrix has been calculated following the standart procedure. Using a different method from those of the previous studies, the effect of the isospin breaking due to the Coulomb forces has been evaluated more accurately. Here, the shell model has been modified by Pyatov's restoration because of the isospin breaking and the transition matrix elements have been found by means of the random phase approximation (RPA).
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