Investigation of the nonrelativistic singularities of a “square with diagonal” graph

Nonrelativistic singularities of the Feynman graph “square with a diagonal” with respect to the variable $z=\cos\theta$ ($\theta$ being the scattering angle) have been investigated. The determination of the location of these singularities is reduced to the solution of algebraic equation of the seventh degree. In some particular cases, including the practically important case of elastic scattering by a deuteron, the singularities can be found analytically. Considered as examples are the singularities on the physical sheet of $z$-plane for the graphs corresponding to the elastic $Nd$-, $\pi d$-, $N\alpha$- and $\pi\alpha$-scattering.