Analytical s matrix approach for the study of alpha decay of super heavy elements

Abstract

One of the most exciting fields in nuclear physics in recent times is the production, identification and study of super heavy nuclei. It has been possible to synthesize nuclei upto Z =118 in the laboratory. With the discovery of many super heavy elements beyond Z=100 and their decay processes involving, among others, -decay chains have revived interest in the careful analysis of Q-values of -decay and the corresponding decay constant. For the study of -decay one requires a reliable input of -daughter nucleus potential. Using the latest developments in mean field theory methods, many potentials for many pairs of -daughter nuclei systems have become available. For example, using explicitly calculated neutron and proton densities in the double folding model (t approximation) one can generate the alpha-nucleus potentials. The most commonly used simple method to study -decay is to treat it as a tunneling problem and evaluate the decay constant or life time in terms of transmission across the Coulomb barrier and assault frequency at the decay energy. Further, it is also possible to evaluate the decay energy using WKB type approximation for bound states. It should be noted that the WKB formula is semi-classical approximation having its own limitations and essentially takes into account only the barrier felt by the decaying state as far as the determination of the transmission co-e cient (T) is concerned. Input from the potential pocket region is only in terms of assault frequency for which classical expression is often used. The potential beyond the outermost turning point has no role in this approach. On the other hand, one notices that formation and dexii cay of the Quasi bound(QB) state associated with -decay is more accurately described by the full partial wave Schr¨odinger equation and hence the computation of QB state parameters within the frame work of complete solution of Schr¨odinger equation is desirable. ..