IMPORTANCE OF CREEPING WAVES IN SCHWINGER VARIATIONAL-PRINCIPLE CALCULATIONS OF BACKSCATTERING FROM CYLINDERS WITH NEUMANN BOUNDARY-CONDITION

The Schwinger variational principle for the scattering amplitude produ ces accurate results when the trial function is selected to contain th e essential physics of the problem. Very simple trial functions that a re capable of satisfying the boundary condition and of approximating t he lit and unlit aspects of shadowing give excellent results for Diric hlet scatterers but not for Neumann scatterers. Physics suggests that creeping waves are the missing ingredient in the latter case. The curr ent study verifies the validity of this suggestion for the test proble m of plane-wave scattering from an infinite cylinder. The validation i s based on a hybrid solution that consists of the variational backscat tering amplitude supplemented by the creeping-wave contribution that i s available from the exact solution. Good accuracy is obtained for the entire frequency range, thereby suggesting that incorporating the cre eping-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 bounda ry condition.