Proton decay from excited states in spherical nuclei

The recent interest in nuclei beyond the proton drip line prompted the study of proton emission from the ground state of such nuclei. This process consists in the tunneling of the proton across a potential barrier. The centrifugal potential was added to the Coulomb barrier for this kind of radioactivity. The tunneling time is important in decay processes, in fission or in fusion reactions. The Time Dependent Schrodinger Equation (TDSE) was solved including the time evolution of a wave packet propagating in a classical forbidden region. The question of proton-decay from orbitals with l ≠ 0 for the spherical nucleus 208Pb was taken into account. The description of the decaying system is fully contained in the state vector. The time evolution of this vector enables us to determine the decay probability at any moment t. The influence of the potential on the tunneling quantities was studied and the dependence of errors of the WKB method on the energy of the quasi-stationary state and on the angular momentum was determined. The behavior of the proton wave function passing across the barrier was observed. The discrepancy between the time dependent method and the WKB method decreases when the difference between the top of the barrier and the energy of the quasi-stationary state increases. For a fixed set of Woods-Saxon parameters we investigated the dependence of the proton tunneling on time choosing one quasi-stationary state for every angular momentum. The accuracy of the WKB approximation increases with l. For a comparison with the experiment one should fit some of the WS parameters, e.g. the potential depth, to reproduce the observed energy. The future investigations of proton decay using TDSE could eventually answer to some questions related to this phenomenon. (authors)