Semiclassical propagator approach for emission processes from deformed nuclei

Abstract

We describe a more rigorous formulation of the 3D semiclassical approach, corresponding to deformed potentials, which leads to the exact results and we also compare them with the much simpler expressions given by the angular Wentzel–Krames–Brillouin (WKB) and linearized WKB with its approximation, known as Fröman WKB method. We define the semiclassical fundamental matrix of solutions, describing the effect of the deformed field. Its inverse, proportional to the so-called propagator matrix, connects the solution in two points. A comparison between the coupled channels fundamental matrix of solutions to various semiclassical counterparts evidences close results in the barrier region. We express the scattering amplitudes in terms of the propagator matrix multiplied by the ratio between internal wave function components and irregular Coulomb waves. The relative influence of nuclear and Coulomb action terms together with nuclear and Coulomb centrifugal barriers upon the penetration process reveals the dominance of the Coulombian parts. An analysis of alpha-emission processes between ground states and to excited states of even–even nuclei in terms of the propagator matrix evidenced the important role played by deformation of the Coulomb field and the shape of the nuclear interaction.