Spline-Galerkin solution of integral equations for three-body scattering above break-up

We investigate a Galerkin method for solving the integral equations for three-body scattering at energies above the break-up threshold. The scattering equations that we consider are one-dimensional integral equations that arise from a separable potential model. Cubic spline approximants with multiple knots are used to construct a non-smooth solution function. Numerical results are obtained both for a system of spin-0 (boson) and spin-1/2 (fermion) particles interacting via separable two-body potentials. The results demonstrate that our numerical treatment of this problem is both robust and accurate with a small number of basis functions