Analytic properties of the scattering amplitude in strong coupling theory

A system of two nonrelativistic particles and a quantized scalar field is considered. Under the assumption that the particles are strongly coupled to the field, the interaction potential between the particles (5) is smooth and a Yukawa one as $r\to\infty$. The analytic properties of the scattering amplitude are studied and the amplitude is estimated for momentum transfers that are small compared with the energy.