Functional integral for the scattering amplitude in the presence of a long-range interaction Journal Theoretical and Mathematical Physics

A generalization is obtained of the functional integral for the scattering amplitude (and also for the stationary wave function of the scattering problem) in the case of “moderate” long-range interactions, i.e., in the case of potentials $\mathfrak{b}(r)$ having the behavior $zr^{-\lambda}$, $1/2<\lambda\leqslant1$, for large $r$. The quasiclassieal expansion of the scattering amplitude is considered.