Eikonal Approximation for Floquet Scattering

TL;DR

This paper extends the eikonal approximation to Floquet scattering problems with periodic Hamiltonians, enabling better analysis of high-energy scattering under external periodic fields, demonstrated through a spherical well example.

Contribution

We generalize the eikonal approximation to handle Floquet scattering problems with periodic Hamiltonians, broadening its applicability in high-energy scattering research.

Findings

The generalized EA matches exact results in a spherical well scattering example.

It provides a useful tool for analyzing high-energy scattering with external periodic fields.

Applicable to manipulation of atomic, molecular, and nuclear collisions using strong laser fields.

Abstract

The eikonal approximation (EA) is widely used in various high-energy scattering problems. In this work we generalize this approximation from the scattering problems with time-independent Hamiltonian to the ones with periodical Hamiltonians, {\it i.e.}, the Floquet scattering problems. We further illustrate the applicability of our generalized EA via the scattering problem with respect to a shaking spherical square-well potential, by comparing the results given by this approximation and the exact ones. The generalized EA we developed is helpful for the research of manipulation of high-energy scattering processes with external field, {\it e.g.}, the manipulation of atom, molecule or nuclear collisions or reactions via strong laser fields.