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An improved semi-analytic approach to the barrier penetration probability is developed in the frame work of the Wentzel-Kramers-Brillouin (WKB) approximation. It is used to calculate decay half-lives and preformation probabilities for a set of 304 cluster emitters in the range 87 ≤ Z ≤ 96 and a set of 390 α-emitters in the range 52 ≤ Z ≤ 120. For cluster decay, the validity of our approach is tested against Coulomb and proximity potential model (CPPM) by comparing decay half-lives and barrier penetration probabilities. Our results are found to be in a good agreement with CPPM calculations and with the available experimental data. In case of α-decay, our calculations are tested against the experimental data and also a very good agreement is achieved. In both cases, results are also compared with calculations of some other well known universal decay laws that are used in many recent studies. Our approach shows a better agreement with experimental data than most of the other models. Our study is extended to calculate the assault frequency and preformation probability of the cluster inside the parent nucleus. A strong correlation is obtained for all these parameters with each other. Neutron shell closures are found to be more important in the cluster decay process than proton shell closure. It is also noted that the odd–even staggering behavior dominates the decay processes involving the emission of clusters with odd neutron number.

An improved semi-analytic approach for the barrier penetration probability is developed in the framework of the Wentzel–Kramers–Brillouin approximation. It is used to calculate the α-decay half-life, assault frequency and α-preformation probability for many radioactive nuclei in the range Z = 52–99. Calculations are also extended to the super heavy region with Z = 100–120. Results are compared with the experimental data and some other recent studies. This approach achieves a better agreement with the experimental data than many other models. A strong correlation is found between the experimental decay half-life and the calculated penetration probability, assault frequency and preformation probability. Therefore, this approach achieves both reasonable accuracy and good consistency with the expected nuclear physical observations.

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The properties of nonlinear dust-acoustic rogue waves in an unmagnetized, collisionless, four-component dusty plasma system consisting of electrons, nonthermal ions, hot and cold dust species have been investigated. The basic set of fluid equations is reduced to a nonlinear Schrodinger equation. The dependence of the rogue wave properties on the ion energetic population parameter is discussed. The results of the present investigation could be applicable in Saturn F-ring.