Dynamical study of proton emission from deformed nuclei

The most intuitive and direct way to study proton emission from unbound nuclear states is to start with a proton wave packet localized inside the well of the p-nucleus interacting potential and follow its time evolution by solving numerically the time-dependent Schrödinger equation (TDSE). Then the physical properties of the decaying system can be inferred from its solution. The most important calculable quantities are: the tunneling probability and the decay rate. In the present paper we consider bi-dimensional axially symmetric nuclear shapes, allowing the treatment of both spherical and deformed nuclei. The solution of TDSE is obtained by the Crank-Nicolson method. We discuss also the treatment of numerical boundary conditions, the preparation of the initial wave function as a quasi-stationary state and the calculation of the decay rate using the flux. In application we reveal the influence of the deformation on the decay rate