\begin{document}$Z \geq 102 $\end{document}, remains scarce. Further, concerning the transfermium elements, the nuclear shell structure is key to ensuring nuclear stability. Hence, the shell effects have key implications on such nuclei. Many experimental and theoretical investigations have been conducted to examine the reactions induced by heavy ions and the subsequent decay mechanisms in the superheavy mass region. In addition, the region of transfermium elements is of great interest because of the neutron/proton shell effects. Here, our objective is to analyze the decay mechanisms of nuclides having Z = 102 nuclei, i.e., 248No* and 250No*. An extensive study was conducted using the dynamical cluster-decay model (DCM) based on Quantum Mechanical Fragmentation Theory (QMFT). The focus was to investigate compound nucleus (CN) and non-compound nucleus (nCN) mechanisms, including fusion-fission (ff), quasi-fission (QF), and fast fission (FF). The specific isotopes of interest are 248No* and 250No*, with attention given to the role of the center-of-mass energy \begin{document}$(E_{\rm c.m.})$\end{document} and angular momentum \begin{document}$ (\ell) $\end{document}. The nuclear interaction potential was derived using the Skyrme energy density formalism (SEDF) with the GSkI force parameters. The capture cross-sections were calculated using the \begin{document}$ \ell $\end{document}-summed Wong Model. The determination of the probability of compound nucleus formation (PCN) involved a function that is dependent upon the center-of-mass energy. The lifetimes of the ff and QF channels were also investigated. Here, CN and nCN decay mechanisms for two isotopes of Z = 102 nobelium were analyzed over the range of center-of-mass values \begin{document}$(E_{\rm c.m.})$\end{document} considering the quadrupole deformation \begin{document}$ (\beta_2) $\end{document} and optimum orientations \begin{document}$(\theta_{\rm opt.})$\end{document} of the decaying fragments. The fragmentation potential, preformation probability, neck length parameter, and reaction cross-sections were explored. Further, PCN was calculated to determine the mechanisms of decay of 248No* and 250No* isotopes. The obtained fusion–fission lifetimes and quasi-fission lifetimes are compared with the dinuclear system (DNS) approach. Among the considered isotopes having Z = 102, i.e., the 248No* formed in the 40Ca + 208Pb reaction and 250No* formed via two different entrance channels, 44Ca+206Pb and 64Ni+186W, show asymmetric fragmentation with the effect of \begin{document}$ \beta_2 $\end{document} deformation at the energies beyond the Coulomb barrier. Of note, the nCN (QF and FF) decay mechanisms compete with the CN fission channels. The calculations based on the DCM show a strong correlation with the experimental data. The most probable fragments, such as 122Sn and 128Te, were observed near the magic shell closure at Z = 50 and N = 82. Further, as the excitation energy increased, the fusion–fission and quasi-fission lifetimes decreased."> Investigation of decay mechanisms and associated aspects of exotic nobelium isotopes using the Skyrme energy density formalism -
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