Theoretical Studies of Rare-Earth Nuclei leading to ${}_{50}$Sn-Daughter Products and the Associated Shell Effects

Abstract

Cluster decays of rare-earth nuclei are studied with a view to look for neutron magic shells for the ${}_{50}$Sn nucleus as the daughter product always. The ${}^{100}$Sn and ${}^{132}$Sn radioactivities are studied to find the most probable cluster decays and the possibility, if any, of new neutron shells. For a wide range of parent nuclei considered here (from Ba to Pt) ${}^{12}$C from ${}^{112}$Ba and ${}^{78}$Ni from ${}^{210}$Pt parent are predicted to be the most probable clusters (minimum decay half-life) referring to ${}^{100}$Sn and ${}^{132}$Sn daughters, respectively. Also, ${}^{22}$Mg decay of ${}^{122}$Sm is indicated at the second best possibilty for ${}^{100}$Sn-daughter decay. In addition to these well known magic shells (Z=50, N=50 and 82), a new magic shell at Z=50, N=66 (${}^{116}$Sn daughter) is indicated for the ${}^{64}$Ni decay from ${}^{180}$Pt parent.

7 pages