Application of generalized classical trajectories in nuclear physics

Abstract

A new semi-classical method, the so-called uniform semiclassical approximation, is described briefly and then applied to two nuclear physics problems. The basic features of this method are that the dynamics of the problem is treated completely classically (that is, one solves classical equations of motion), but the quantum mechanical superposition principle is retained by evaluating a phase along the classical trajectory and adding probability amplitudes for indistinguishable processes rather than probabilities themselves. The first problem considered is the backscattering from a deformed nucleus and the excitation of rotational states in the target at energies up to the Coulomb barrier. The multiple Coulomb excitation calculations are in quantitative agreement with a very different method (the de Boer-Winther code). A nuclear optical potential is also considered and the nuclear-Coulomb interference for heavy ions is studied. The second problem considered is the tunneling through a two-dimensional barrier. This problem (which is supposed to simulate the penetration through a two-dimensional fission barrier) is investigated by a fully quantum-mechanical coupled-channel calculation and by the uniform semiclassical approximation. A quantitative agreement is found. (auth)