The influence of the hadronic pi pi interaction on the wave functions of pionium (the Coulomb bound pi (+)pi (-) system) at distances less than or equal to 10 fm is calculated for s-states with principal quantum numbers n less than or equal to 4. Hadronic pi pi potentials are used that reproduce the scattering phase shifts of two-loop chiral perturbation theory. The pionium wave functions psi (n) (r) are obtained by integrating the coupled Schrodinger equations for the (n(+)pi (-), pi (0)pi (0)) system. We find that, for r less than or equal to 10 fm, n(3)/(2) psi (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. (C) 2001 Elsevier Science B.V. All rights reserved. References: 13
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