With the discovery of a large number of superheavy nuclei undergoing decay through 𝛼 emissions, there has been a revival of interest in 𝛼 decay in recent years. In the theoretical study of 𝛼 decay the 𝛼-nucleus potential, which is the basic input in the study of 𝛼-nucleus systems, is also being studied using advanced theoretical methods. In the light of these, theWentzel–Kramers–Brillouin (WKB) approximation method often used for the study of 𝛼 decay is critically examined and its limitations are pointed out. At a given energy, the WKB expression uses barrier penetration formula for the determination of the transmission coefficient. This approach utilizes the 𝛼-nucleus potential only at the barrier region and ignores it elsewhere. In the present era, when one has more precise experimental information on decay parameters and better understanding of 𝛼-nucleus potential, it is desirable to use a more precise method for the calculation of decay parameters. We describe the analytic 𝑆-matrix (SM) method which gives a procedure for the calculation of decay energy and mean life in an integrated way by evaluating the resonance pole of the 𝑆-matrix in the complex momentum or energy plane. We make an illustrative comparative study of WKB and 𝑆-matrix methods for the determination of decay parameters in a number of superheavy nuclei.
Volume 96, 2022
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