Neutrons as Waves

Salvatore Esposito, Ofelia Pisanti

Bertram T. M. Willis, Colin J. Carlile

Abstract Neutron optics refers to phenomena which arise from the interference between the incident and the scattered neutron waves. This is in contrast to the topics in earlier chapters of this book, where we have been concerned with interference between the scattered waves alone. The wave Halban and Preiswerk (1936) and by Mitchell and Powers (1936) using ‘white’ neutrons from a radium–beryllium source, and more convincingly by Zeilinger et al. (1988) using monochromatic neutrons from a reactor source. The subject of neutron optics itself began with the work of Fermi and Zinn (1946), who demonstrated the mirror reflection of a collimated beam of thermal neutrons. Since then nearly all the classical optical phenomena of reflection, refraction and interference have been shown to occur with neutrons.

R.L. Brehm

U. Bonse, Andreas Rumpf

Energies, wave vectors, and amplitudes of waves that are generated when a neutron is incident onto a moving parallel-sided plate are calculated by solving Schr\"odinger's equation. It is shown that the wave entering the plate and those reflected at the plate surfaces suffer energy (frequency) changes due to ``inelastic'' interaction with the moving plate. The motion-induced phase shift caused by such a plate in a neutron interferometer is evaluated, including the contribution which arises in the presence of dispersion of the coherent scattering length, e.g., near a resonance or as a result of local-field effects. With thermal neutrons the amplitudes of reflected waves are about ${10}^{\mathrm{\ensuremath{-}}4}$ of the incident wave amplitude. Energy changes amount to 4\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ (reflected waves) and to less than ${10}^{\mathrm{\ensuremath{-}}6}$ (entering wave) for neutrons with a 4-A\r{} wavelength. Nonlinear contributions to the interferometric phase shift have to be taken into account when the plate and/or the medium velocity exceed 1% of the neutron velocity.

Guenter Nimtz, Paul Bruney

Tunnelling and barrier interaction times of neutrons were previously measured. Here we show that the neutron interaction time with barriers corresponds to the universal tunnelling time of wave mechanics which was formerly observed with elastic, electromagnetic and electron waves. The universal tunnelling time seems to hold for neutrons also. Such an adequate general wave mechanical behaviour was conjectured by Brillouin. Remarkably, wave mechanical effects, and even virtual particles, hold from the microcosm to the macrocosm.

V. K. Ignatovich