Importance of creeping waves in Schwinger variational-principle calculations of backscattering from cylinders with Neumann's boundary condition

The Schwinger variational principle for the scattering amplitude produces accurate results when the trial function is selected to contain the essential physics of the problem. Very simple trial functions that are capable of satisfying the boundary condition and of approximating the lit and unlit aspects of shadowing give excellent results for Dirichlet scatterers but not for Neumann scatterers. Physics suggests that creeping waves are the missing ingredient in the latter case. The current study verifies the validity of this suggestion for the test problem of plane-wave scattering from an infinite cylinder. The validation is based on a hybrid solution that consists of the variational backscattering amplitude supplemented by the creeping-wave contribution that is available from the exact solution. Good accuracy is obtained for the entire frequency range, thereby suggesting that incorporating the creeping-wave effects into the shadowed-boundary-Born trial functions is as much improvement as is needed and desirable in order to obtain good fully variational results for smooth scatterers with Neumann's boundary condition.