The ratio of pionium formation probabilities in ns-states stays at (n2/n1)^3 to O(10^-3) under first-order strong-interaction corrections, and the Deser level shift is rewritten in terms of the strong-interaction radius and the wave-function correction at the origin.
A method for research on behaviour of a dimesoatomic wave function at small distances
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abstract
The Schr\"odinger equation discribing the local potential model of a strong $\pi^+\pi^-$-interaction was studied. The influence of the strong $\pi^+\pi^-$-interaction of the behaviour of pionium nS-state wave functions at small distances is studied both analytically (perturbatively) and numerically. It is shown that in the whole the accounting of strong interaction results in multiplying pure Coulomb pionium wave functions by some function is practically independent of the value of the principal quantum number n. Due to this reason, the n-independence of probability of $\pi^+\pi^-$-atom production in nS-state remains the same as in the case of a pure Coulomb $\pi^+\pi^-$-interaction.
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Formulation of the Deser formula for the shift of energy levels of hadronic atoms in terms of the effective radius of the strong interaction with the Coulomb wave function of hadronic atoms at the origin
The ratio of pionium formation probabilities in ns-states stays at (n2/n1)^3 to O(10^-3) under first-order strong-interaction corrections, and the Deser level shift is rewritten in terms of the strong-interaction radius and the wave-function correction at the origin.