Scattering off an oscillating target: Basic mechanisms and their impact on cross sections

TL;DR

This paper studies classical scattering from an oscillating target in two dimensions, revealing complex cross section structures driven by the phase of initial collisions, despite the absence of periodic orbits.

Contribution

It demonstrates how rich scattering patterns emerge from a non-periodic, convex oscillating target, linking them to the phase of initial collisions and manifolds of parabolic orbits.

Findings

Cross sections show rich structures when particle velocity matches the target's maximum velocity.

The scattering pattern is determined by the phase of the first collision.

Universal profile of the scattering pattern is governed by manifolds of parabolic orbits.

Abstract

We investigate classical scattering off a harmonically oscillating target in two spatial dimensions. The shape of the scatterer is assumed to have a boundary which is locally convex at any point and does not support the presence of any periodic orbits in the corresponding dynamics. As a simple example we consider the scattering of a beam of non-interacting particles off a circular hard scatterer. The performed analysis is focused on experimentally accessible quantities, characterizing the system, like the differential cross sections in the outgoing angle and velocity. Despite the absence of periodic orbits and their manifolds in the dynamics, we show that the cross sections acquire rich and multiple structure when the velocity of the particles in the beam becomes of the same order of magnitude as the maximum velocity of the oscillating target. The underlying dynamical pattern is uniquely determined by the phase of the first collision between the beam particles and the scatterer and possesses a universal profile, dictated by the manifolds of the parabolic orbits, which can be understood both qualitatively as well as quantitatively in terms of scattering off a hard wall. We discuss also the inverse problem concerning the possibility to extract properties of the oscillating target from the differential cross sections.