Three-Body Coulomb Functions in the Hyperspherical Adiabatic Expansion Method

Three-Body Wave Functions in the Continuum: Application to the Repulsive Coulomb Case

“…Note that the most important contribution in each Ψ i component in Eq. 1is given by the diagonal f ii function [2]. As seen in the figure, a variation in the box size not bigger than 2 fm is enough to fine tune the energy to the desired value.…”

“…This problem can be solved as shown in Ref. [2] by simply solving the coupled set of radial equations by imposing a box boundary condition. When done, the different discrete states appear en groups of states with a very similar energy, and in such a way that each group of states contains n 0 terms, which is the number of open channels.…”

“…Obviously, this method can be applied for the particular case in which only the Coulomb interaction between the pairs of particles is considered. In this way, one can immediately obtain the regular threebody continuum wave functions just as solutions of the corresponding hamiltonian [2]. From the regular solutions the irregular partners are obtained after diagonalization of the regular radial function, and replacing the regular Coulomb functions in the diagonal by their corresponding irregular counterparts.…”

“…As shown in [2], four different tests were found to be successfully fulfilled by the regular and irregular Coulomb functions: i) The irregular functions are solution of the coupled set of radial equations, ii) the sum of the squares of the regular and irregular functions goes asymptotically to the identity matrix, iii) the Wronskian relation is satisfactorily fulfilled, and iv) the computed S-matrix satisfies the unitarity condition.…”