PHYSICAL REVIEW A VOLUME 39, NUMBER 3 FEBRUARY 1, 1989 Observation of a motion-induced phase shift of neutron de Broglie waves passing through matter near a nuclear resonance M. Arif, ' H. Kaiser, R. Clothier, and S. A. Werner Department of Physics and Research Reactor, University of Missouri C— olumbia, Columbia, Missouri 65211 W. A. Hamilton, A. Cimmino, and A. G. Klein School of Physics, University of Melbourne, Parkville, Victoria 3052, Australia (Received 1 August 1988) We report the results of a neutron interferometry experiment where for the first time (to our knowledge) a phase shift of a neutron de Broglie wave induced by moving matter has been success- fully measured. This experiment is the quantum-mechanical analog of the optical Fizeau effect. The observed phase shift is caused by the motion of matter itself, and not by the motion of its boun- daries. The experimental results are found to be in good agreement with the theoretical predictions. Some unexpected and previously unreported neutron wave interference effects observed during the experiment are also reported. I. INTRODUCTION In recent years a number of theoretical and experimen- tal investigations have been carried out to study the effect of the motion of matter on the phase of a neutron de Bro- glie wave through which it is propagating. ' These studies have brought into focus important, but not so clearly obvious, differences in the interaction properties of photon and neutron waves with moving matter. In an excellent article, Horne et al. showed that for most ma- terials the phase of a neutron wave can be affected only by the motion of the boundary of the moving matter and not by the motion of the bulk of the matter itself. ' This is true when the neutron-nuclear interaction potential is ve- locity independent, which is the case for most materials in the thermal energy range. By contrast, the phase of the photon wave is influenced by motion of bulk material itself. This was first demonstrated by Fizeau in 1859 with the use of a Rayleigh-type optical interferometer. With the advent of neutron interferometers within the last few years, a number of Fizeau-type experiments have been designed and successfully carried out. These experi- ments have validated the theoretical prediction of no Fizeau-type phase shift for neutron waves interacting with materials having an energy-independent scattering length. The results of these experiments have also demonstrated the validity of Galilean transformation properties of (co, k) four vectors for massive particles (neutrons) and have established an upper limit for the en- ergy dependence of a neutron-nuclear Fermi pseudopo- tential. ' Success of these experiments has led us to at- tempt an important experiment where the neutron passes through moving matter at a nuclear resonance. The neu- trons then experience an energy-dependent potential and, as the theory suggests, a neutron wave phase shift truly analogous to the light-wave case should be observable. This represents a fundamentally different situation from earlier experiments in the sense that the observed phase shift results from the motion of the bulk of material and not from the motion of the boundaries of the moving matter. We have carried out a neutron interferometric experi- ment where thermal neutrons pass through natural samarium with 13. 9% isotopic abundance of ' Sm, which has a nuclear resonance at 97.3 meV. In this paper the experiment is described in detail. An account of a preliminary version of this experiment has been given in the proceedings of a workshop. II. THEORY where N~zD and +~&D are the neutron phases accumu- lated on paths ABD and ACD, respectively, and k~ and k~ are the incident wave vectors at points B and C in that frame. The magnitudes of k~ and k& depend direct- ly on the incident angle O and slab velocity W. Accord- ing to Fig. 1 the components of these wave vectors paral- lel and perpendicular to the slab sides are given by m8 key kpsinO —, k~ = kpcosO m8' key kpsinO — kc = kpcosO (3) A diagram of our perfect silicon crystal, Bonse-Hart in- terferometer is shown in Fig. 1. An incident neutron beam is coherently split into two separate beams at point A. These two beams are simultaneously intercepted by a moving material slab with parallel sides of thickness T. If the motion of the slab induces any phase difference in the neutron waves travelling on path ABD relative to path ACD, then this would be made manifest in the phase of the recombined beams at point D. In the rest frame of the moving slab, the phase difference of the neu- tron waves traveling in these two paths is given by bC =4 wa D(k t) t4'sett(k— c) ~ 39 931 1989 The American Physical Society