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Physical Review

Single-Slit Diffraction of Neutrons

C. G. Shull

Published Mar 15, 1969• 111 citations
Publisher

Abstract

Observations are reported on single-slit diffraction of monochromatic slow neutrons (wavelength 4.43 \AA{}) upon passage through fine slits of width between 21 and 4.1 \ensuremath{\mu}. Gadolinium-edged slits were used because of the high-absorption cross section for this material, and the angular broadening effects in the range up to 20\ensuremath{''} of arc were studied on a high-resolution double-crystal spectrometer utilizing perfect crystals of silicon. The observed broadening agrees well with that calculated, and this supplies evidence on the width of the coherent wavefront of a neutron wave packet.

DOI
10.1103/physrev.179.752

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his was one of the conclusions that emerged from the Vienna Symposium on the Foundations of Modern Physics held in June this year.Organised by Anton Zeilinger, ably assisted by Markus Aspelmeyer and the staff of the Institute of Quantum Optics and Quantum Information (IQOQI) this Symposium, the 2 nd in the series, also served as a Fest-schri for Helmut Rauch and Danny Greenberger, noted experimental and theoretical luminaries in the field.In particular,it was Helmut Rauch who,together withWolfgang Treimer and Ulrich Bonse, was first to demonstrate the first Single Crystal Neutron Interferometer in 1974 [1].Closely analogous to a Mach-Zehnder Interferometer in classical optics, these wonderful devices are carved out of a monolithic piece of highly perfect single crystal of silicon,of the kind used in the semiconductor electronics industry.A photograph and a schematic are shown in fig 1. ree parallel slabs of silicon,connected by a base,contain perfectly aligned planes of atoms,which,by virtue of Bragg Diffraction, coherently split a beam of monochromatic neutrons, whose wavelengths are comparable in magnitude to the lattice spacing of the silicon crystal.Furthermore, the silicon is almost completely transparent to neutrons -so that absorption is essentially negligible.us, the first slab acts as a beam splitter, with a transmitted and a diffracted beam emerging from it.Both these beams continue to the second slab at which Bragg diffraction occurs once again.Ignoring the transmitted beams (which escape from the system), the two diffracted beams continue on their way to the third, equidistant slab, where they recombine in a way similar to the first beam splitter.

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Observations are reported on single-slit diffraction of monochromatic slow neutrons (wavelength 4.43 \AA{}) upon passage through fine slits of width between 21 and 4.1 \ensuremath{\mu}. Gadolinium-edged slits were used because of the high-absorption cross section for this material, and the angular broadening effects in the range up to 20\ensuremath{''} of arc were studied on a high-resolution double-crystal spectrometer utilizing perfect crystals of silicon. The observed broadening agrees well with that calculated, and this supplies evidence on the width of the coherent wavefront of a neutron wave packet.
Up to the present time, perfect crystal interferometers of both two‐crystal and three‐crystal Laue‐case variety have been used to explore the optical characteristics of neutrons of diffracting wavelength. In addition, very recently the classical optical experiments on the diffraction by an absorbing edge, by an absorbing wire and by single and double slit assemblies have been performed for cold neutrons. These experiments show with high precision the validity for matter waves of the standard Fresnel‐Kirchhoff approach to diffraction.
The authors report detailed experiments and comparison with first-principle theoretical calculation of the diffraction of cold neutrons ($\ensuremath{\lambda}\ensuremath{\approx}2$ nm) at single- and double-slit assemblies of dimensions in the 20-100 \ensuremath{\mu}m range. Their experimental results show all predicted features of the diffraction patterns in great detail. Particularly, their double-slit diffraction experiment is its most precise realization hitherto for matter waves.
A series of experiments is reviewed on precision measurements of the diffraction of slow neutrons paralleling those with light: diffraction at an absorbing edge, at an absorbing wire, and at single- and double-slit assemblies. Besides their educational value, the experimental results also provide precise confirmations of the theoretical predictions as calculated via a Fresnel–Kirchhoff approach. The intensity in all these experiments was so low that the formation of the interference patterns individual neutron by individual neutron could easily be observed. The experiments are presented and analyzed in a way suitable for undergraduate teaching.
Phenomena of electron, neutron, atomic and molecular diffraction have been studied in many experiments, and these experiments are explained by many theoretical works. We study neutron single-slit diffraction with a quantum mechanical approach. It is found that the obvious diffraction patterns can be obtained when the single-slit width a is in the range of 3λ~60λ. We also find a new quantum effect of the thickness of single-slit which can make a large impact on the diffraction pattern. The new quantum effect predicted in our work can be tested by the neutron single-slit diffraction experiment.
his was one of the conclusions that emerged from the Vienna Symposium on the Foundations of Modern Physics held in June this year.Organised by Anton Zeilinger, ably assisted by Markus Aspelmeyer and the staff of the Institute of Quantum Optics and Quantum Information (IQOQI) this Symposium, the 2 nd in the series, also served as a Fest-schri for Helmut Rauch and Danny Greenberger, noted experimental and theoretical luminaries in the field.In particular,it was Helmut Rauch who,together withWolfgang Treimer and Ulrich Bonse, was first to demonstrate the first Single Crystal Neutron Interferometer in 1974 [1].Closely analogous to a Mach-Zehnder Interferometer in classical optics, these wonderful devices are carved out of a monolithic piece of highly perfect single crystal of silicon,of the kind used in the semiconductor electronics industry.A photograph and a schematic are shown in fig 1. ree parallel slabs of silicon,connected by a base,contain perfectly aligned planes of atoms,which,by virtue of Bragg Diffraction, coherently split a beam of monochromatic neutrons, whose wavelengths are comparable in magnitude to the lattice spacing of the silicon crystal.Furthermore, the silicon is almost completely transparent to neutrons -so that absorption is essentially negligible.us, the first slab acts as a beam splitter, with a transmitted and a diffracted beam emerging from it.Both these beams continue to the second slab at which Bragg diffraction occurs once again.Ignoring the transmitted beams (which escape from the system), the two diffracted beams continue on their way to the third, equidistant slab, where they recombine in a way similar to the first beam splitter.