The influence of the hadronic interaction on the pionium wave functions
arXiv:hep-ph/0104059 · doi:10.1016/S0370-2693(01)00753-5
Abstract
The influence of the hadronic ππinteraction on the wave functions of pionium (the Coulomb bound π^+π^- system) at distances less than 10 fm is calculated for s-states with principal quantum numbers n<5. Hadronic ππpotentials are used that reproduce the scattering phase shifts of two-loop chiral perturbation theory. The pionium wave functions ψ_n (r) are obtained by integrating the coupled Schrödinger equations for the (π^+π^-,π^0π^0) system. We find that, for r<10 fm, n^{3/2} ψ_n (r) is practically independent of n. From this we conclude that the production rates of the s-states of pionium are proportional to n^{-3}, a result needed for the interpretation of the DIRAC experiment currently running at CERN.
9 pages including 2 figures