Contribution of Absorption-Reemission Process to the Complex Level Shift in the Pionic Atom

Abstract

Calling attention to the pion-nucleon interaction at low energy, we derive an absorptive interaction including a rescattering process on the basis of the dispersion relation. The cross section for the reaction π⁺+d →p+p is calculated for the s-wave pion at low energy in order to verify our approach, and the value is in good agreement with the recent experimental result. Then it is shown that the real part of the two-nucleon amplitude associated with the absorption is attractive and about twice as large as the imaginary amplitude. From this consideration the pionic complex level shift is predicted for the deuteron.