The Wave-Particle Dualism || Neutron Wave Optics Studied with Ultracold Neutrons

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    A. Steyerl

    Technische Universitat MUnchen, D-8046 Garching, Germany

    The paper discusses experiments demonstrating or utilizing the wave properties of neutrons with wavelengths of about 100 nm.


    The preparation of the present paper was difficult for me mainly because I tried at first to relate our experimental data on ultracold-neutron optics, which are simple, to that difficult subject: "non-linear wave mechanics", which has been created by de Broglie over 50 years ago (see /1/) and which seems to be re-sumed nowadays at a time of rapidly growing interest in non-linear phenomena (e.g. /2/). I must confess that for a simple-minded ex-perimental physicist like me it turned out that this programme was too difficult. Therefore, I finally decided not to annoy you with, perhaps, unsound interpretations but present the plain data. I should add that this restraint was facilitated by the fact that, within experimental precision, we did not observe any deviation in the behaviour of ultracold-neutron waves from the predictions made within the framework of standard, linear, quantum mechanics, and therefore an urgent need of possible nonlinearities has not arisen.


    The designation "ultracold" is commonly used for extremely slow neutr"Ons with ~elocitie~ below "'10 m/s. Their energies are of the order of 10- eV (10- K) or below and their d~ ~roglie \'Iavelengths reach nearly macroscopic demensions, ,v 10 A. Ultra-cold neutrons (UCNs) cannot penetrate matter as easily as faster


    S. Diner et al. (eds.). The WaveParticle Dualism, 85-99. is) 1984 by D. Reidel Publishing Company.

  • 86 A.STEYERL

    neutrons, and they suffer total reflection at the walls of suit-able substances, at any angle of incidence. This unique property makes them suited for storage in closed cavities, the so-called "neutron bottles". The neutrons are contained in carefully pre-pared vessels for hundreds of seconds, travelling to and fro be-tween the walls from which they rebound many thousands of times before loss processes due to reactions with the wall nuclei and the finite lifetime for beta-decay become significant /3 - 6/. Storage lifetimes reaching the limit of the fl-decay lifetime have been obtained in a "magnetic storage ring" /7/, and an improve-ment on the lifetime value seems to be possible.

    The main applications of UCNs envisaged until now are high-precision investigations of the properties of the neutron itself, like its lifetime for fl-decay and searches for a possible elec-tric charge and dipole moment. The low energy of UCNs seems to make them suitable for high-resolution spectroscopy, and a third branch of attractive physics with UCNs seems to be neutron optics which is the subject of the present paper.


    Dealing with neutrons of extremely low energy we must take into account a number of interactions which are usually negli-gible in thermal or fast neutron research because of their weak-ness, but play an important role at very low energies. These in-teractions include the gravitational potential (mg ~ 10-7 eV per m of height), the interaction of the neutron magnetic dipole mo-ment ~ with a magnetic field B (~ ~ 6 x 10-8 eV/tesla) , and the interaction with the "scattering potential" U which arises as an effect of multiple coherent scattering in the forward direction and gives rise to refraction and total reflection, as in light optics. For most substances, U is of the order of 10-7 eV. These various interactions may be incorporated in a spatially variable index of refraction, n{r) = [1 - (U(r) + ~B(r) + mgz)/E ]1/2. The sign of the magnetic term + ~B is negative for neutPon spin antiparallel to B and positive for ~ liB. (The magnetic inter-action can be inCluded in this sjmpTe Torm whenever the "adiabat-ic condition" is satisfied, i.e., changes of magnetic field direction "sensed" by the neutron along its trajectory occur slowly compared with the frequency of Larmor precession in the local magnetic field.)

    As a consequence of the gravitational interaction even empty space in the absence of magnetic fields may be considered as a refracting medium with a spatially variable index of refraction. Therefore, the optics of ultracold neutrons deals with curvilin-ear rays, and this introduces new features into the usual frame-work of optics.


    UCN Source (From "Neutron Turbile")

    Fi g. 1:


    Ruled Grating or Mirror


    Scheme of the "gravity diffractometer" for ultracold neutrons. The entrance slit is imaged onto the exit slit.



    The gravitational interaction has been utilized for UCN beam focusing in high-resolution experiments studying interference, diffraction and inelastic scattering phenomena.

    Fig. 1 shows the scheme of the "UCN gravity diffractometer" /8,9/ installed at the Research Reactor at Garching near Munich. In this instrument, the vertical component of neutron velocity is precisely determined by the height of fall from the entrance slit to the horizontal mirror which may be replaced by a reflection sample or a combination of transmission sample and mirror. The beam spreading associated with the free fall from the entrance slit to the sample is undone in the phase of ascent from the sample to the exit slit. Thus the entrance slit is imaged onto the exit slit. The instrument admits of a resolution of 2 neV for the energy corresponding to the vertical neutron motion.

    Before proceeding to the neutron-optical studies made possi-ble with this high resolution, let me mention another scheme of

  • 88 A.S1EYElU.

    UCN focusing which we applied in a "gravity spectrometer" /10/. With this instrument quasi-elastic neutron scattering can be in-vestigated with a resolution of a few neV in energy transfer. This resolution which is much higher than in conventional neutron scattering spectrometers, is achieved by exploiting the simple fact that the maximum reach of the flight parabola described by a very slow neutron in the earth's gravitational field at a launching angle of 45, is a very sensitive measure of its ini-tial kinetic energy. An instrument working according to this prin-ciple has been installed at Garching and a scheme of its design is shown on Fig. 2. It seems worth mentioning that this scheme admits of focusing both in energy and in space. In the monochro-mator, the neutron source is line-to-line focused on the sample, and in the analyser the sample is point-to-point focused onto the detector, using the focusing properties of the slightly ellipti-cal, cylindrical analyser mirrors which divide the analyser flight path into five segments. Energy scanning is accomplished by displacement of the monochromator mirror, thus effectively changing the reach of the monochromator flight path.

    Fig. 2: Scheme of the "gravity spectrometer" NESSIE (for "NEutronen-Schwerkraft-SpektrometrIE"), in whiCh the maxTmum reach oT the flighr-para-bola described by the ultracold neutrons is used for precise energy selection


    The spectrometer is being used for measuring quasi-elastic line broadening (by only a few neV) in polymer solutions. Fig. 3 shows. as a first example. the quasi-elastic scattering from a polydimethylsiloxane (0.05 g/cm3 ) solution in deuterated benzene (C6D6) at 50 C (above the critical "8"-point). and this data is compared to the resolution curve measured with a purely elastic scattering line (electro-graphite). The reason for showing this - preliminary - data in a talk on neutron optics is that it seems to demonstrate the precise functioning of the spectrometer in the way it was designed. The calculations for the fairly complicated neutron paths had all been based on classical mechanics and (curved-) ray optics. assuming an ideal geometry.



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    with an elastically scattering graphite sample is compared to the slightly broadened scattering curve for a polydimethylsiloxane solution in deuterated benzene. The curves are plotted vs the incident neutron energy and are centred on the analyser energy of 412 neV.

  • 90 A. STEYERL


    The experiments on UCN diffraction and interference to be discussed now. had been initiated at a time when the early UCN storage experiments had yielded surprisingly short containment lifetimes and a number of suggestions and speculations had been put forward to account for the apparent anomaly. The most drastic idea was that the observed imperfection of neutron reflection from the bottle wall was perhaps an indication of a fundamental fault in the simple analysis in terms of standard wave mechanics (Ignatovich /11.12/). 5.1 Diffraction from a Ruled Grating

    In a first direct experiment testing the interference pro-perties of ultracold-neutron waves. we measured the diffraction from a ruled reflection grating /8.9/ with the high resolution provided by the "gravity diffractometer". The grating had 1200 mechanically ruled grooves per mm and the groove profile was appropriate for the "blazing" condition in first-order reflection. The grating was coated with nickel (a good neutron reflector) and arranged vertically in the "gravity diffractometer" at the posi-tion indicated on Fig. 1. Since the action of the grating can be understood as the transfer of momentum. hn/d. parallel to the sur-face (d: groove spacing. n: diffraction order). the neutron re-ceives a well-defined push up or down. for n F O. This momentum transfer changes the height of the ascending flight parabola, and this can be sensitively analysed by a vertical displacement of the scanning exit slit. Fig. 4 shows intensity profiles measured in this way. The observed orders of diffraction are clearly sepa-rated. and the linewidths may be fully explained by the instru-mental resolution.

    We have, very tentatively. interpreted the absence of a detectable line broadening in terms of a lower limit for an "in-trinsic coherence length for the neutron wave train". Such a hypo-thetical limit - beyond those determined by the instrumental re-solution and by the finite neutron lifetime - does not exist in ordinary wave mechanics. and I don't have any idea what kind of theoretical modifications would be required to account for a speculative finite "coherence length". Nonlinearities, as proposed by de Broglie /1/ or Bialynicki-Birula and Mycielski /2/ would certainly require drastic revisions in our present view of quantuM phenomena. Thus, in the absence of a clear model even our inter-pretation of the absence of line broadening in terms of a lower limit for the "coherence length" seems doubtful, because even this interpretation may depend on the model. Therefore, the value of NO.1 mm derived from the minimum number of coherently illumina-ted grooves necessary for the observed linewidth, on the basis of the linear theory, should be taken only as a guide number.


    (For the specific, logarithmic, non-linearity, -bf~ al~12, proposed by Bialynicki-Birula and Mycielski /2/ this would corre-spond to a limit for the constant b of 10-15 eV, similar to the limiting value recently reported by Gahler, Klein and Zeilinger /13/ and 100 times lower than the limit given by Shull et ale /14/. However, the proposed modification of theoSchrodinger equation must be understood to be on the classical level, since this equation has, e.g., non-quantized oscillatory "breather" mode solutions, and it would, therefore, seem to require quanti-zation. In the given form for the non-linear term,~(lvI2) (logarithmic or other), the diffraction process, o/partial reflection or any scattering from fixed objects, would require energy for wave dispersion in space, which poses problems regard-ing the proposed probabilistic interpretation of the wave function. At any rate, a non-stationary solution of the non-linear equation for reflection from a potential wall, nothing to say about diffraction from a ruled grating, has apparently not yet been found. For all these reasons, I would rather hesitate to interpret our simple experiments in terms of something as complicated as non-linearitiesl)

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    Fig. 4: Several orders of diffraction from a ruled grating (1200 grooves per mm), measured by vertical scanning of the exit slit in the "gravity diffractometer". Resolution curves are included for comparison.


  • 92 A. STEYERL

    5.2 Mirror Reflection

    The main reason for mentioning the next, even simpler, experiment is that it seems to have provided one of the first direct clues as to the reason for the short UCN containment life-times in "bottles". We placed a float glass plate at the horizon-tal sample position in the "gravity diffractometer" (exchanging the grating by a vertical mirror). The reflection curve measured as a function of the neutrons' height of fall to the sample is shown in Fig. 5 /8/. It exhibits the typical steep edge at the critical height of fall which is determined by the limit for total reflection. However, the measured slope is considerably steeper than that calculated for reflection from a potential step function, i.e., a sharp transition from the vacuum to the bulk glass. The most plausible interpretation seems to be in terms of surface contamination.




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    d= 73' J& b) +'i.t.. rL '~j

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    90 94 98 102 106 110 "eight of fall (mJ

    Fig. 5: Reflectivity vs neutron fall height in the "gravity diffractometer" for a float glass sample. The data points are compared to calcu-lations for a) a step-function potential distribution, and, b) a potential distribution smoothed due to a hydrogenous surface contamin-ation with a gradual change in composition.


    Hydrogenous substances had for a long time been considered a prime candidate for UCN losses at the bottle walls, because of the extraordinarily high cross section for inelastic neutron scattering from protons, but some authors were reluctant to accept the large quantities of hydrogen necessary to explain the data (...


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