Adiabatic Perturbation Theory on Reactions at Higher Incident Energies

Abstract

An adiabatic perturbation theory proposed is an extension of the adiabatic approximation of Johnson and Soper to treat projectile breakup, and as accurate as the method of continuum discretized coupled-channels. An equation for the total wave function is derived in two ways, one based on the adiabatic theorem and the other on the adiabatic approximation. A quantity first discussed by Berry on its geometrical properties appears in all orders of the perturbation, but it never becomes a geometrical quantity such as Berry's phase because of no diabolic point in parameter space. Discussions are made on whether a kernel of the equation is of L^2 type. The resultant expansion of the total wave function has wrong asymptotic forms, so a new expansion is derived from the old one. An approximate but practical way of calculating the new expansion is proposed for deuteron induced reactions.