Abstract
Abstract The influence of the hadronic ππ interaction on the wave functions of pionium (the Coulomb bound π + π − system) at distances ⩽10 fm is calculated for s-states with principal quantum numbers n ⩽4. Hadronic ππ potentials 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 Schrodinger equations for the ( π + π − , π 0 π 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.
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