Application Of The Transition Matrix To A Ribbon Shaped Scatterer

The transition matrix for scalar waves scattered by a ribbon shaped obstacle with Neumann boundary conditions is derived using a basis set for the surface field expansion chosen to facilitate convergence. An analytic expression for the scattering amplitude in arbitrary directions exact to order (ak)is derived from the transition matrix. Comparisons with the results based on the geometrical theory of diffraction and solutions for the integral equation at low frequencies indicate that valid numerical results are obtained throughout the range of frequencies considered (0<ak < 10).