Cluster radioactivity around shell closures: correlation of half-lives with the energy levels of daughter nuclei

The emission of Be, C, O, and Ne clusters from seven parent nuclei with neutron numbers around the neutron magicities N = 82 and 126 are considered. The universal decay law (UDL) formula, as well as the double-folding model derived from the Michigan three-range Yukawa-Paris NN interaction with zero- and finite-range exchange components, are utilized to compute the half-life time for 23 cluster decay processes. The calculations utilizing the UDL formula show satisfactory agreement with the experimental data. The reliable UDL formula is used to calculate log T (c) for more than 1500 cluster emitters and its variation with the neutron number, N (d), of the daughter nuclei is presented. The behavior of log T (c) with neutron number variation is studied and correlated to the energy levels of the daughter nuclei. For a neutron number N (d) larger than the neutron magic number, log T (c) increases almost linearly with increasing N (d), leaving the daughter nuclei in most cases with the same nuclear spin value. This linear behavior of log T (c) results from equal nuclear spin values of the daughter nuclei. At the magic neutron number, the nuclear spin changes strongly and as a result log T (c) increases as N (d) decreases. Log T (c) reaches to a maximum value when all the neutrons in the cluster are emitted from levels below the neutron gap. Leaving the daughter nuclei in the same spin produces almost linear variation of log T (c). For protons in various clusters emitted from the same level or the same group of levels, log T (c) has almost the same value and the same behavior of variation with N (d). Also, the values of log T (c) for specific types of cluster depend on the N to Z ratio for different isotopes of this cluster. From the available nuclear spin values, the neutron energy levels around the magic numbers are presented.