few-body problem in nuclear reactions: beyond the horizon of the three-body faddeev equations

Recent progress in few-body problem physics based on the three-body Faddeev equations is reviewed for three-related fields. The first field involves the description of light nuclear reactions in terms of multi-channel three-body Faddeev equations. The second field is the investigation of the two- and three-body threshold behaviors for the NNπ system using the three-body Faddeev equations, where the πD and the NN′ or N-(Nπ) scattering lengths are calculated, and also we show that the NN′ potential has a long range term of 1/r2 form. The third is a new Coulomb treatment in terms of a generalized screening range to describe on-shell Coulomb amplitudes which is useful in the threebody Faddeev equations. This procedure reproduces both of the Coulomb phase shift and the wave function from the electron-electron to the heavy-ion-heavy-ion systems.