Weakly bound systems in the case of complex potentials

We consider weakly bound two-body systems. We study the behavior of the ground state mean square radius as the binding energy tends to zero in the case of complex potentials. We show that the asymptotic law, obtained with real potentials, is modified by the occurrence of a finite width in the case of finite-range potentials. The case of the PT-symmetric potentials is also discussed. We complete our study with few remarks concerning the same problem for three weakly bound particles. (author)