Spline-Galerkin Solution of Integral Equations for Three-Body Scattering above Break-Up
Abstract
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.
- Publication:
-
Journal of Computational Physics
- Pub Date:
- February 1986
- DOI:
- 10.1016/0021-9991(86)90135-X
- Bibcode:
- 1986JCoPh..62..383A
- Keywords:
-
- Galerkin Method;
- Integral Equations;
- Scattering Functions;
- Three Body Problem;
- Cauchy Problem;
- Linear Equations;
- Pade Approximation;
- Singularity (Mathematics);
- Spline Functions;
- Physics (General)