Time-dependent approach to bidimensional quantum tunneling: application to the proton emission from deformed nuclei

The time-dependent two-dimensional Schroedinger equation is solved numerically for initial quasi-stationary states which tunnel through an anisotropic, non-separable potential barrier. The time dependence of the decay rate, of the tunneling probability and of its angular distribution are calculated. Applied to the proton emission from deformed nuclei, this approach shows that the escape path chosen by the metastable state depends on the quantum numbers of the initial state (i.e. on its spatial distribution) rather than on the features of the potential. For this reason, there are in general more than one main direction of emission. It is therefore impossible to reduce the problem to one dimension. The importance of the distribution of the angular momentum and its variation in time for the determination of the decay rate is also pointed out. In a couple of cases, no exponential decay was found during the calculated time evolution (2 x 10-21 s) although more than half of the wavefunction escaped