\begin{document}$ \beta_2 $\end{document}) and hexadecapole (\begin{document}$ \beta_4 $\end{document}) deformed target nuclei. The study analyzes the influence of higher-order deformations and corresponding orientation criteria adopted for the exploration of the dynamics of the considered nuclei. The influence of these parameters has been studied in terms of capture cross-section (\begin{document}$\sigma_{\rm cap}$\end{document}), compound nucleus (CN) formation probability (\begin{document}$P_{\rm CN}$\end{document}), survival probability (\begin{document}$W_{\rm sur}$\end{document}), and the fusion-ER cross-sections across center of mass energies (\begin{document}$E_{\rm c.m.}$\end{document}). The study recognizes the importance of the fission barrier in determining the survival probability (\begin{document}$W_{\rm sur}$\end{document}) of the compound nucleus and subsequently the ER cross-sections. A discrepancy among the calculated and experimental ER cross-sections is observed, particularly in reactions with lower fission barriers. In reactions with a lower fission barrier of formed CN, the level density parameter ratio (\begin{document}$ a_f/a_n $\end{document}) of the fission and neutron-evaporation channels assists in the study of experimental data."> Impact of quadrupole and hexadecapole deformations and associated orientations on a variety of asymmetric nuclear reactions -
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