Quantum ray mapping: A geometrical electron optics technique, corrected for the phase shifts induced by ray caustics

Semiclassical quantum scattering analysis utilizes geometrical electron optics to calculate classical-ray-interferences to approximately analyze electron scattering. Previous researchers employing this technique for scattering analysis simply ignore classical-ray-caustics which induce phase-shifts to a classical-ray's nominal phase length. The previous ignoring of caustic-induced-phase-shifts has produced obvious errors in prior semiclassical scattering analyses. However, a few researchers have correctly assessed caustic-induced-phase-shifts to successfully analyze some bound state problems, and this has encouraged this undertaking to utilize caustic-corrections for semiclassical analysis of scattering scenarios.; Where nearest neighboring classical-rays appear to cross they form a ray-caustic, while the wave-normals to the actual scattering wavefronts, do not appear to cross. The crossing classical-rays outgoing from a ray-caustic seem to match up directionally with the primary outgoing actual-wave-normals , except the phases do not match. This initial version of Quantum Ray Mapping simply maps the classical particle trajectories as classical-rays; continues to map them through the anomalous ray-caustic regions in spite of the known discrepancy; assumes that the outgoing classical-rays re-align with the outgoing actual-wave-normals; but then assigns an appropriate phase-shift to the classical-ray for having encountered the classical-ray-caustic; and then calculates the caustic-corrected semiclassical ray-interference.; When semiclassical ray analyses are corrected for the phase-shifts induced by ray-caustics, the ray-interference reasonably predicts the generalized Ramsauer-Townsend minima, thus revealing an intuitively appealing causality for this primary feature in the scattering profile of medium energy electrons elastically scattered by single atoms. Semiclassical ray analyses of higher energy electrons scattered by multiple co-linear atoms also shows how ray-interference produces the many oscillations of scattering amplitude versus scattering angle. With these successes, Quantum Ray Mapping should inspire a new sense for the legitimate applicability for the geometrical electron optics technique.