The influence of the hadronic interaction on the pionium wave functions
نویسنده
چکیده
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 ψn(r) are obtained by integrating the coupled Schrödinger equations for the (π+π−, ππ) system. We find that, for r ≤ 10 fm, nψn(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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