The Effect of Transverse Wavefront Width on Specular Neutron Reflection

Published

August 1, 2022

Author(s)

Charles Majkrzak, Norman F. Berk, Brian B. Maranville, Joseph Dura, Terrence J. Jach

Abstract

In the analysis of neutron scattering measurements of condensed matter structure, it normally suffices to treat the incident and scattered neutron beams as if composed of incoherent distributions of plane waves with wavevectors of different magnitudes and directions which are taken to define an instrumental resolution. However, despite the wide-ranging applicability of this conventional treatment, there are cases in which the wave function of an individual neutron in the beam must be described more accurately by a spatially localized packet, in particular with respect to its transverse extent normal to its mean direction of propagation. One such case involves the creation of orbital angular momentum (OAM) states in a neutron via interaction with a material device of a given size. It is shown in the work reported here that there exist two distinct measures of coherence of special significance and utility for describing neutron beams in scattering studies of materials in general. One measure corresponds to the coherent superposition of basis functions and their wavevectors which constitute each individual neutron packet state function whereas the other measure can be associated with an incoherent distribution of mean wavevectors of the individual neutron packets in a beam. Both the distribution of the mean wavevectors of individual packets in the beam as well as the wavevector components of the superposition of basis functions within an individual packet can contribute to the conventional notion of instrumental resolution. However, it is the transverse spatial extent of packet wavefronts alone -- over which the phase is sufficiently uniform -- that determines the area within which a coherent scattering process can occur in the first place. This picture is shown to be entirely consistent in principle with the formal tenets of standard quantum theory. It is also demonstrated that these two measures of coherence can be distinguished from one another experimentally in practice.

Citation

Journal of Applied Crystallography

Volume

55

Issue

Part 4

Pub Type

Journals

Keywords

wave packet, wave front, coherence, neutron

Citation

Majkrzak, C. , Berk, N. , Maranville, B. , Dura, J. and Jach, T. (2022), The Effect of Transverse Wavefront Width on Specular Neutron Reflection, Journal of Applied Crystallography (Accessed April 19, 2025)