Investigation of the structure and reaction observables of light-heavy nuclei

Identifying the intricate interactions among the large numbers of nucleons within the nucleus remains a challenging task. To address this issue, this study employs a binary clustering model to elucidate the experimental observations associated with both light and heavy nuclei. In the first stage, a comprehensive investigation of the nuclear structure and reaction observables of $^{20}\textrm{Ne}$ and $^{24}\textrm{Mg}$ nuclei has been conducted using different clusture configurations. This includes the systematic evaluation of positive parity excitation energies, $B(E2\downarrow)$ transition strengths, as well as the decay widths pertaining to $^{8}\textrm{Be}$ and $^{12}\textrm{C}$ clusters originating from the $^{24}\textrm{Mg}$ nucleus. The phenomenological Morse potential has been employed to describe the $^{20}\textrm{Ne}$=$\alpha$+$^{16}\textrm{O}$ configuration, while the double folding potential incorporating nucleon-nucleon Michigan 3 Yukawa (M3Y) interaction has been utilized to model the $^{24}\textrm{Mg}$=$\alpha$+$^{20}\textrm{Ne}$, $^{8}\textrm{Be}$+$^{16}\textrm{O}$, and $^{12}\textrm{C}$+$^{12}\textrm{C}$ configurations. The decay widths have been determined through the application of the Wentzel-Kramers-Brillouin (WKB) approximation. Furthermore, the $\alpha$-elastic scattering differential cross sections on the $^{16}\textrm{O}$ and $^{20}\textrm{Ne}$ targets have been calculated. The obtained results are compared with the results of prior similar theoretical studies and the results for the $^{24}\textrm{Mg}$ nucleus are developed. In the second stage, the binary cluster model has been employed to determine the decay half-lives of alpha and heavier clusters for both heavy and superheavy nuclei. Specifically, the decay half-lives of alpha and heavier clusters have been calculated from heavy nuclei with atomic number range of $87\leq Z \leq 96$ using a Geiger-Nuttal like simple half-life formula based on the analytical solution of modified harmonic oscillator and spherical Coulomb potentials. Subsequently, the branching ratios of the heavy cluster decay half-lives with respect to alpha decay have been determined. Then, alpha decay half-lives have been calculated from superheavy nuclei with atomic number in the range $104\leq Z \leq 120$. The obtained results are in excellent agreement with experimental data, and minimum rms deviations have been obtained. Furthermore, estimations of the half-lives have been provided for nuclei lacking available experimental data. Notably, the analysis of nuclei in the $Z=118-120$ region reveals a pronounced shell closure effect at $N=178$ and $N=184$ through the variation of alpha decay half-lives as a function of neutron number.