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

TL;DR

This theoretical study investigates cluster decays of rare-earth nuclei to identify neutron magic shells in daughter nuclei, predicting probable decay modes and suggesting a new magic shell at Z=50, N=66.

Contribution

The paper introduces a theoretical framework for analyzing cluster decays leading to $_{50}$Sn daughters, predicting new potential decay modes and identifying a novel magic neutron shell at N=66.

Findings

$^{12}$C is the most probable cluster for $_{50}$Sn daughters from Ba to Pt.

$^{22}$Mg decay is a significant second possibility for $_{50}$Sn-daughter decay.

A new magic shell at Z=50, N=66 is suggested for $_{116}$Sn daughter.

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.