Transient behaviour in quantum tunneling: time-dependent approach to alpha decay

The alpha decay of quasi-stationary states in 212Po was calculated by solving numerically the time-dependent Schroedinger equation. The decay rate λ was found to be time dependent. In particular there is a transient time of the order of 10-21 s before the asymptotic limit (exponential regime) is reached. The tunneling time can be defined by the delay in attaining this limit at the outer side of the barrier as compared with the inner side. The method of preparing the initial quasi-stationary state influences neither the transient behaviour of λ nor its asymptotic value while the energy of this state influences both the transient and the asymptotic regimes. Finally, the asymptotic values were used to test the Gamow formula. A relatively good agreement was found and a deeper understanding of this formula was achieved. (orig.)