Accurate evaluation of pionium wave functions

Abstract

A suitable numerical approach based on Sturmian functions is employed to solve the pionium problem for both local and nonlocal potentials. The approach accounts for both the short-ranged strong interaction and the long-ranged Coulomb force and provides accurately the wave function and binding energy of pionium. It is found that the ground-state pionium wave function in realistic pion-pion strong interactions might be considerably different from the hydrogen-like one at a small distance.