Validity of Quasi-classical Approaches to True Three-Body Decays

Abstract

Within the hyperspherical harmonics (HH) method the three-body problem is reduced to a motion of one effective particle in a “strongly deformed” field, which is described in the coupled-channel formalism. This method is well suited to studies of so-called true three-body decays. The reduction of the hyperspherical equations set to a single-channel approximation provides the basis of standard quasi-classical (QC) expression for width evaluation. We demonstrate that by itself the quasi-classical approach is quite precise in application to typical three-body effective potentials. However, the reduction to a single channel leads to a significant overestimation of the width.