Three-Body Coulomb Functions in the Hyperspherical Adiabatic Expansion Method

Abstract

In this work we describe a numerical method devised to compute continuum three-body wave functions. The method is implemented using the hyperspherical adiabatic expansion for the three-body wave function imposing a box boundary condition. The continuum energy spectrum results discretized and, for specific quantum number values, all the possible incoming and outgoing channels are simultaneously computed. For a given energy, the hyperradial continuum functions form a matrix whose ij-term refers to specific incoming and outgoing channels. When applied to three-body systems interacting only through the Coulomb potential, this method provides the adiabatic representation of the regular three-body Coulomb wave function. The computation of the irregular Coulomb wave function representation is also discussed. These regular and irregular Coulomb functions can be used to extract the \({\mathcal {S}}\)-matrix for those reactions where, together with some short-range potential, the Coulomb interaction is also present. The method is illustrated in the case of the \(3\rightarrow 3\) process of three alpha particles.