Non-Regge Singularities in a Three-Body Model

We investigate a special model to see if it is possible to extend the three-body scattering amplitude to complex values of the total angular momentum $J$ by an integral equation with completely continuous kernel, or by extending the Fredholm solution of the Faddeev equations from integral $J$ to complex $J$. This model is a helium atom with infinitely heavy nucleus, neglecting the interaction between electrons and replacing the Coulomb potentials by a superposition of finite-range Yukawa potentials. One finds poles in $J$ which depend not only upon the total energy but also upon the subenergies of the electrons. Accordingly, the problems stated above have no solution.