We have explored the decay mechanisms, both ground state (GS) and excited state (ES), of Xe, Ba and Nd nuclei using energy density functional theory. Within this study, the preformed cluster model is employed to examine GS decay, while the analysis of ES phenomena utilises the dynamical cluster decay model. The comprehensive investigation includes an analysis of the spin-density-dependent potential \(V_{J}\) , addressing its role in both decay processes. Furthermore, the study explicitly explores the impact of deformations and orientations by comparing outcomes with spherical fragmentation. The dynamics of ground-state decay is analysed by calculating the half-lives of clusters emitted from the even isotopes of \(^{108-116}\) Xe, \(^{112-120}\) Ba and \(^{120-130}\) Nd parent nuclei. Apart from cluster decay, other possible mechanisms such as 2 \(\alpha \) emission and sequential decay of \(\alpha \) -particle are also investigated. In the context of the excited-state decay, we estimate the evaporation residue (ER) cross-sections for the \(^{112}\) Xe \(^{*}\) , \(^{118}\) Ba \(^{*}\) and \(^{130}\) Nd \(^{*}\) compound nuclei and compared them with the experimental data for the validation purpose.
