The Influence of Strong Interaction on the Pionium Wave Functions at Small Distances

The influence of strong π+π− interaction of the behaviour of pionium nS-state wave functions at small distance are investigated both analytically (perturbatively) and so numerically. It is shown that in the whole the accounting of strong interaction results in multiplying of pure Coulomb pionium wave functions by some function practically independent on value of principal quantum number n. Due to this reason the n-independence of probability of π+π− atom production in nS-state remains the same as in case of pure Coulomb π+π− interaction. The method of the measurement of pionium (ππ atom) lifetime, proposed in the ref.[1], is essentially based on the assumption that the n-dependence of probability wn of creation of ππ atom in nS-state or is well known or, at least, may be calculated with high degree of accuracy. The first consideration of this problem have been done in the L. Nemenov’s paper[2], where the following relation wn ∼ n (1) have been derived from more general result of author[2] wn ∼ ∣