Critical view of WKB decay widths

Abstract

A detailed comparison of the expressions for the decay widths obtained within the semiclassical WKB approximation using different approaches to the tunneling problem is performed. The differences between the available improved formulae for tunneling near the top and the bottom of the barrier are investigated. Though the simple WKB method gives the right order of magnitude of the decay widths, a small number of parameters are often fitted. The need to perform the fitting procedure remaining consistently within the WKB framework is emphasized in the context of the fission model based calculations. Calculations for the decay widths of some recently found super heavy nuclei using microscopic alpha-nucleus potentials are presented to demonstrate the importance of a consistent WKB calculation. The half-lives are found to be sensitive to the density dependence of the nucleon-nucleon interaction and the implementation of the Bohr-Sommerfeld quantization condition inherent in the WKB approach.Comment: 18 pages, Late

Signature of theN= 126 shell closure in dwell times of alpha-particle tunneling

“…As shown in [11], different semiclassical approaches lead to one and the same expression for the decay width, given by,…”

“…P α = t and Coulomb (C) potentials [11]. The α is restricted within the classical turning points r 1 , r 2 and r 3 defined by V (r) and the Q values [11]. The factor in square brackets appearing before the penetration probability P in (1) arises due to the normalization of the bound state wave function in the region from r 1 to r 2 .…”

“…The tunneling probability, cluster preformation factor, assault frequency of the alpha at the barrier and the dwell time are calculated using a nuclear potential which is based on a double folding model with realistic nucleon-nucleon interactions [10]. The potential is fitted to scattering data and has also been tested in the α decay of several nuclei [9,11]. In the next section we discuss the theoretical approach used for evaluating the decay width and the different tunneling time concepts used.…”

“…P α is the preformation probability of the α in the parent nucleus and is often chosen as a free parameter to fit the theoretical half lives to the experimental ones, i.e. P α = t and Coulomb (C) potentials [11]. The α is restricted within the classical turning points r 1 , r 2 and r 3 defined by V (r) and the Q values [11].…”

“…where the strength λ of the nuclear part V N is fixed by the Bohr Sommerfeld quantization condition [11]:…”