A fractional approach to cluster radioactivity

Abstract

The cluster radioactivity of [Formula: see text]Ra, [Formula: see text]Ac, [Formula: see text]U, [Formula: see text]Pu, [Formula: see text]U, [Formula: see text]U and [Formula: see text]Th isotopes which emitted [Formula: see text]C, [Formula: see text]Ne, [Formula: see text]Mg, [Formula: see text]Ne, [Formula: see text]Mg, [Formula: see text]Ne, respectively, has been analyzed with the help of fractional calculus for investigating the connection between order of the fractional derivative and nuclear structure. When the neutron number of daughter nuclei is equal to magic number, order of the fractional derivative shows a maximum. It is shown that there is a relationship between the order of fractional derivative and shell effect. This order has a similar role to the preformation factor in cluster radioactivity.