Study of Alpha Decay of Super Heavy Elements Using S-Matrix and WKB Methods

Abstract

A comparative study of the S-matrix and the WKB methods for the calculation of the half widths of alpha decay of super heavy elements is presented. The extent of the reliability of the WKB methods is demonstrated through simple illustrative examples. Detailed calculations have been carried out using the microscopic alpha-daughter potentials generated in the framework of the double-folding model using densities obtained in the relativistic mean field theories. We consider alpha-nucleus systems appearing in the decay chains of super heavy parent elements having A = 277, Z = 112 and A = 269, Z = 110. For negative and small positive log τ 1/2 values the results from both methods are similar even though the S-matrix results should be considered to be more accurate. However, when log τ 1/2 values are large and positive, the width associated with such state is infinitesimally small and hence calculation of such width by the S-matrix pole search method becomes a numerically difficult problem. We find that overall, the WKB method is reliable for the calculation of half lives of alpha decay from heavy nuclei.

Quasi-bound states, resonance tunnelling, and tunnelling times generated by twin symmetric barriers

“…(28) with energy E at the above-barrier energies for the potential given by eq. (15). The potential parameters are V0 = 8, a = 3, b = 3.5.…”

“…Evaluations of such states are very important in areas like nuclear scattering and decay of unstable nuclei via alpha decay, proton emission etc. as evident from refs [14][15][16][17][18][19]. A detailed procedure exists for the study of such states in 3D scattering theory.…”

“…The non-relativistic quantal theory of 3D potential scattering provides a unified analysis of bound states below the threshold energy E = 0 and continuum above the threshold [9][10][11][12][13][14][15]. The bound states are fully normalizable negative energy states; however, above the threshold the regular radial wave functions for positive energy behave like sin(kr − lπ/2 + δ l ) for large r, where δ l is the partial wave phase shift.…”

“…Hence it is appropriate to use the term quasi-bound (QB) states for these sharp resonances. Analytic S-matrix (SM) theory of potential scattering [9][10][11][12][13][14][15] provides a unified picture of bound states and resonances in terms of the pole structure of partial wave SM. Evaluations of such states are very important in areas like nuclear scattering and decay of unstable nuclei via alpha decay, proton emission etc.…”

Alpha radioactivity for proton-rich even Pb isotopes

“…Thirdly, exact expression for transmission coefficient through the barrier has been used to calculate the half-lives whereas in the earlier studies transmission probabilities through the barrier have been calculated using WKB approximation method. In a recent study, it has been shown that the transmission probabilities calculated using WKB method are insensitive to the tail region of the barrier potential especially for large half-life values [10]. In order to test the accuracy of WKB method we have calculated T WKB and T Exact for Eckart barrier of different ranges.…”