  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.
