Three-Body Coulomb Functions in the Hyperspherical Adiabatic Expansion Method

15 pags., 9 figs., 1 tab. ; This article belongs to the special issue “30th anniversary of Few-Body Systems”.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 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 → 3 process of three alpha particles. © Springer-Verlag Wien 2016This work was supported by funds provided by DGI of MINECO (Spain) under contract No. FIS2014-51971-P.Peer Reviewe