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Journal of Surface Investigation X-ray Synchrotron and Neutron Techniques

Interaction of Ultracold Neutrons with a Neutron Interference Filter Oscillating in Space

М. А. Захаров, Aleksandr I Frank, G. V. Kulin, S. V. Goryunov

Published Jan 1, 2020• 6 citations
Publisher

Abstract

Abstract The problem of the interaction of ultracold neutrons with a neutron interference filter oscillating in space is investigated. In the problem, the evolution of the wave packet is considered by means of numerically solving the non-stationary Schrödinger equation by splitting the evolution operator. The filter oscillating in space acts as a quantum modulator of the ultracold neutron flux. The resulting spectra of the transmitted and reflected states are obtained depending on the motion parameters of the interferometer.

DOI
10.1134/s1027451020010218

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Abstract The problem of the interaction of ultracold neutrons with a neutron interference filter oscillating in space is investigated. In the problem, the evolution of the wave packet is considered by means of numerically solving the non-stationary Schrödinger equation by splitting the evolution operator. The filter oscillating in space acts as a quantum modulator of the ultracold neutron flux. The resulting spectra of the transmitted and reflected states are obtained depending on the motion parameters of the interferometer.
The motion of ultracold neutrons in a magnetic field featuring a quadratic inhomogeneity is considered. A partial solution to the stationary Schrödinger equation is found, which leads to a harmonic oscillator equation for the X coordinate. It is demonstrated that, under certain conditions, it is basically possible to provide for a spatial focusing of neutrons with the formation of either a single point focus or two side foci. Dependence of the focusing on the degree of monochromaticity of the neutron beam is considered.
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The interference effect between the neutron spinor components is investigated. It is shown that the diffusion of the neutron wave-packet under an unhomogeneous magnetic field is related to the phase shift angle between the two spinor components. We propose that this effect could be used to detect the phase-shift of a coherent neutron beam having passed through some medium. In the interference experiment based upon this principle one will not need to use Bragg reflection from crystal planes for splitting and recombining the beam, and the dimension of the phase shift region will be much longer than that of the usual Bonse-Kart type neutron interferometer.
The coherence length of a neutron wave packet depends on the spectral width of the distribution of wave vectors that make up the packet. The coherent overlap of the wave packets traversing the two beam paths in a perfect-silicon-crystal neutron interferometer (NI) is altered by placing a material with a neutron-nuclear optical potential in one of the beam paths in the NI. If the optical potential is positive, it causes a delay of the wave packet and a loss of fringe visibility. By use of an analyzer crystal, we narrow the spectral distribution after the mixing and interference has occurred in the last crystal slab of the NI. This increases the coherence length and restores some of the fringe visibility.