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Nuclear Instruments and Methods in Physics Research Section B Beam Interactions with Materials and Atoms

Quantum Theory of Low-Energy Neutron Double-Slit Diffraction

Yi-Qing Guo

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

The phenomena of electron,neutron,atomic and molecular diffraction were researched by many experiments in recent year and these experiments were explained by various theory.In this paper,we study the double-slit diffraction of neutron with an approach of quantum mechanics at frist.We find some new results: When slit width a and slit distance d is the ratio of(a+d)/a=n(n=1,2,3,…),order n,2n,3n,… are missing in diffraction pattern;When the ratio of(a+d)/a≠n(n=1,2,3,…),there isn't missing order in diffraction pattern;The length of slit b only affects the diffraction intensity while the thickness c not only affects the intensity,but also changes the missing order in diffraction patterns.

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The phenomena of electron,neutron,atomic and molecular diffraction were researched by many experiments in recent year and these experiments were explained by various theory.In this paper,we study the double-slit diffraction of neutron with an approach of quantum mechanics at frist.We find some new results: When slit width a and slit distance d is the ratio of(a+d)/a=n(n=1,2,3,…),order n,2n,3n,… are missing in diffraction pattern;When the ratio of(a+d)/a≠n(n=1,2,3,…),there isn't missing order in diffraction pattern;The length of slit b only affects the diffraction intensity while the thickness c not only affects the intensity,but also changes the missing order in diffraction patterns.
We studied electron single-slit,double-slit and three-slit diffraction with a new quantum mechanics approach and obtained the following results.(1) For single-slit diffraction,the thickness of the single-slit can make a large impact on the diffraction intensity and pattern.(2) For double-slit diffraction,when the ratio of(a+d)/a=n(n=1,2,3,…),orders n,2n,3n,… are missing in diffraction pattern,when the ratio of(a+d)/a≠n(n=1,2,3,…),there isn't missing order in diffraction pattern.(3) For double-slit diffraction,it can be found that when the thickness of the double-slit increases,the diffraction intensity and pattern will be changed,and when the thickness of the double-slit increases,the missing order phenomena disappear.(4) For three-slit diffraction,when the thickness of the slit increases,the diffraction intensity and pattern will be changed,and there is one secondary maxima and two minima between the two principle maxima.
Phenomena of electron, neutron, atomic and molecular diffraction have been studied in many experiments, and these experiments have been explained by some theoretical works. We study electronic double-slit diffraction with a quantum mechanical approach and obtain the following results: (1) When the ratio of ( d + a )/ a = n ( n = 1,2,3,…), orders n ,2 n ,3 n ,… are missing in diffraction pattern. (2) When the ratio of ( d + a )/ a ≠ n ( n = 1,2,3,…), there is not missing order in diffraction pattern. (3) The slit thickness c has a large affect on the electronic diffraction pattern, which is a new quantum effect. We believe that all the predictions in our work can be tested by the electronic double slit diffraction experiment.
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.
Phenomena of electron,neutron,atomic and molecular diffraction have been researched by many experiments throughout the last year and these experiments are explained by various theory.In this paper,we study the single-slit diffraction of 4He with a new approach of quantum mechanics at first.We find some new results: Both the shape of single-slit and the energy of neutron have affect the diffraction pattern.The obvious diffraction phenomenon can be obtained when the single-slit width a is in the range of 3a60λ.The length of the single-slit affects the diffraction intensity and the thickness not only affects the intensity,but also changes the diffraction patterns.The energy of 4He only affect the intensity.Those effect predicted in our work can be tested by the 4He single-slit diffraction experiment.
We study electronic multiple-slit diffraction with a quantum mechanical approach. Our theoretical results are in good agreement with classical theoretical calculations and we obtain the following resluts: (1) There are N − 2 secondary maxima and N − 1 minima between the two principle maxima in diffraction pattern. (2) As the slit number N increasing, the diffraction intensity increases and the pattern width becomes narrow. (3) The slit thickness c dose not have any influence on diffraction pattern when slit width a is far greater than the electronic wavelength λ, for example, the ratio of a λ = 10, and at the ratio, the missingorder phenomenon can be observed when d+a a = n (n = 1, 2, 3 . . .), where d is the distance of slit-to-slit. (4) When a is not far greater than λ (the ratio of a λ = 500), the slit thickness c has an effect on diffraction pattern. The missing-order phenomenon can be shown only if the slit thickness c is small enough, and it disappears when the slit thickness c becomes large. In addition, the slit thickness c affects the relative diffraction intensity of the diffraction pattern.