Semiquantum approach for fast atom diffraction: Solving the rainbow divergence

Abstract

In this work we introduce a distorted wave method, based on the Initial Value Representation (IVR) approach of the quantum evolution operator, in order to improve the semiclassical description of rainbow effects in diffraction patterns produced by grazing scattering of fast atoms from crystal surfaces. The proposed theory, named Surface Initial Value Representation (SIVR) approximation, is applied to He atoms colliding with a LiF(001) surface along low indexed crystallographic channels. For this collision system the SIVR approach provides a very good representation of the quantum interference structures of experimental projectile distributions, even in the angular region around classical rainbow angles where common semiclassical methods diverge.

Influence of beam collimation on fast-atom diffraction studied via a semiquantum approach

“…(1), describe the shape of the positionand momentum-wave packet associated with the incident projectile. In a previous paper [17] …”

“…By employing the IVR method [21], the scattering state of the projectile at the time t can be approximated as [17]:…”

“…(1), within the framework of the time-dependent distortedwave formalism [23], the SIVR transition amplitude, per unit of surface area S, can be expressed as [17] …”

“…the extreme deflection angles of the classical projectile distribution. The SIVR approach, instead, provides an appropriate description of FAD patterns along the whole angular range, even around classical rainbow angles, without requiring the use of convolutions to smooth the theoretical curves [17]. Therefore, the SIVR method can be considered as an attractive alternative to quantum wave packet propagations, offering a clear representation of the main mechanisms of the process in terms of classical trajectories through the Feynman path integral formulation of quantum mechanics.…”

“…Motivated by Ref. [1], in this article we investigate the influence of the collimation of the incident beam on FAD patterns making use of a recently developed approach, named Surface-Initial Value Representation (SIVR) approximation [17]. With this goal we explicitly take into account the experimental collimating conditions to determine the surface region that is coherently illuminated by the particle beam, using this information to build the initial wave packet that describes the unperturbed state of the incident particle within the SIVR method.…”