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Ultracold Neutrons: Their Role in Studies of Condensed Matter

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Ultracold Neutrons: Their Role in Studies of Condensed Matter Ultracold neutrons: Their role in studies of condensed matter R. Golub Hahn Meitner Institut, 14109 Berlin, Germany Ultracold neutrons, that is, neutrons whose energy is so low that they can be contained for long periods of time in material and magnetic bottles, provide the basis for the currently most sensitive experiments seeking to detect the neutron electric dipole moment and to measure the neutron lifetime. The goal of this article is to review the work that has been done to date in applying ultracold neutrons to the study of condensed matter and to discuss the future prospects for this type of research. [S0034-6861(96)00202-4] CONTENTS decay lifetime. Pendlebury (1993) gives a review of the current situation with detailed references. I. Introduction 329 In the present article we should like to address the A. Short history of ultracold neutron research 329 issue of the application of ultracold neutrons to studies B. Ultracold neutrons and condensed matter 331 of condensed matter. In comparison with the applica- II. Reflection and Tunneling from Surfaces and More tions mentioned above, the use of UCN scattering as a Complex Structures 331 tool to study condensed matter is still in its infancy. We A. UCN reflectometry 333 shall review what has already been done in this field and III. Elastic Scattering 334 give a few pointers to possible future developments. A. Scattering from homogeneous substances 334 In order to be totally reflected at all angles of inci- B. Scattering from static inhomogeneities 335 dence from an appropriate surface, and hence to have IV. Inelastic Scattering 336 the ability to be stored for long periods of time, neutrons V. Quasielastic Scattering 340 must have a velocity of the order of 5 m/s. Although this VI. Upscattering 341 is very small in comparison to typical velocities of neu- VII. The Future of Ultracold Neutron Scattering 343 trons thermalized at room temperature (v;2200 m/s), A. Future instrumentation 343 or even at the temperature of a liquid hydrogen or deu- B. Future ultracold neutron sources 344 terium cold source (v;700 m/s) all UCN sources to date VIII. Conclusion 345 have operated by extracting neutrons from the low en- Acknowledgments 345 ergy tail of the distribution in the source. The strongest Appendix: Phase Space Limitations existing source is the source installed at the Institut to Inelastic Scattering Experiments: Laue-Langevin (ILL) in Grenoble (Steyerl et al., 1986; The Advantage of Longer Wavelengths 345 Steyerl and Malik, 1989). Other sources currently in op- References 346 eration and the prospects for improved sources have been discussed by Golub et al. (1991). (See also Sec. et al. I. INTRODUCTION VII.B and Serebrov , 1994.) The phenomenon of total reflection of neutrons at Until the early seventies free neutrons could be stud- grazing incidence, first demonstrated experimentally by Fermi and Zinn (1946) and by Fermi and Marshall ied only under conditions in which they spent no more (1947), has found extensive application in the construc- than a brief moment within the experimental apparatus. tion of neutron guide tubes (Maier-Leibnitz and Even ‘‘long-wavelength’’ neutrons with l;10 Å, Springer, 1963) at many installations around the world. v;400 m/s take only 2.5 ms to travel 1 m. When diffus- ing through matter, neutrons have average lifetimes of, A. Short history of ultracold neutron research for example, 0.2 ms (H 2O) or 130 ms (D 2O). However, the development, since the midseventies, of ultracold It is customary to denote as ultracold neutrons those neutron (UCN) technology has now reached the point neutrons having total energies where neutrons can be stored in material and magnetic 2p\2 bottles, for times that are essentially limited by the neu- E,V5 Niai6mW BW , (1) m (i • tron’s b-decay lifetime (tb;900 s) (Mampe et al. 1989a, 1989b). This has opened up the possibility of a wide where Ni is the number density of nuclei of species i in range of new applications, some of which have reached a the material, ai is the coherent scattering length of a comparatively advanced stage of development while species i nucleus, and V is the effective potential for the others are only taking their first tentative steps. neutrons in the medium. In practical units The UCN applications that have shown the greatest V5157r 3a /A66.03B ~neV!, (2) success to date are those relating to the fundamental g/cm fermis kilogauss 3 properties of the neutron: the search for the time- where rg/cm3 denotes the density, measured in g/cm , reversal violating electric dipole moment of the neutron and A the atomic mass of the element in the medium; and the most accurate measurement of the neutron b a is measured in fm and B in kG. Reviews of Modern Physics, Vol. 68, No. 2, April 1996 0034-6861/96/68(2)/329(19)/$12.85 © 1996 The American Physical Society 329 330 R. Golub: Ultracold neutrons The idea that these neutrons will be totally reflected trons so far from the peak of the Maxwell distribution for any angle of incidence and, as a result, could be did indeed exist inside the reactor, and that they could stored in closed containers has been attributed by many be extracted without crippling losses of intensity. That people to Fermi himself. However, the first person to both groups, at Dubna and Munich, were successful al- take the idea seriously enough to put it into print was most simultaneously is one of those coincidences which Zeldovitch (1959) who discussed the possibility of UCN seem to be so common in the history of physics. As was storage in a graphite bottle and estimated the storage already noted, the motivations of the two groups were time due to absorption in the walls as well as the UCN somewhat different, the Dubna group following the lead densities to be expected. Zeldovich estimated that a of Shapiro’s article on electric dipole moments, while thermal neutron flux of 1012 n/cm 2/s cooled to3Kin the Munich group seems to have been more interested liquid helium would produce a UCN density of 50 in pioneering the sorts of UCN applications to 23 cm . It is interesting to note that such densities have condensed-matter studies that will be the main subject now been achieved at the Institut Laue-Langevin, of this review. 15 Grenoble, using a reactor with a thermal flux of 10 The Dubna group under Shapiro (Luschikov et al., 2 n/cm /s cooled to 20 K in a deuterium-filled cold source. 1968, 1969) extracted ultracold neutrons from a very Zeldovich suggested it would be interesting to study the low-power pulsed reactor by means of a curved horizon- interactions of the stored ultracold neutrons with sub- tal channel 9.4 cm inner diameter and 10.5 m long. stances introduced into the cavity, such as (n,g) absorb- Counting rates of 0.8 counts per 102 s (background ers. ;0.4 counts per 102 s) were obtained. By admitting a gas This work was followed by several other proposals. of 4He to the extraction pipe the authors attempted to Vladimirskii (1961) suggested the use of inhomogeneous estimate the storage time in the pipe. The idea is that magnetic field gradients for confining ultracold neutrons. He also suggested extraction of ultracold neutrons from when the average lifetime of a neutron for collisions a reactor core by means of a vertical channel and with the helium 21 pointed out the widening in solid angle as the neutrons tHe5@NHesHev¯ He# (3) travel up the guide. He noted that the effects of the moderator potential on the energy distribution of the is equal to the average lifetime for wall losses the count- ultracold neutrons leaving the moderator could be elimi- ing rate should be reduced by 1/2 with respect to that in nated by vertical extraction. the absence of helium. This first attempt to measure Doroshkevich (1962) suggested beryllium as a storage storage times gave a result of 200 s, which is to be com- material and discussed the temperature dependence of pared to 12 s obtained later from more detailed mea- the loss rate. surements (Groshev et al., 1971), the discrepancy being Foldy (1966) suggested the use of liquid helium attributable to possible impurities in the helium. (V51.131028 eV) as a wall-coating material for a UCN Working at Munich, Steyerl (1969) obtained ultracold bottle. However, this potential is rather low compared neutrons by vertical extraction from a steady-state reac- to those achieved with other materials (V*1027 eV). tor. The beam was pulsed by a rotating chopper con- In 1966 Maier-Leibnitz published some remarks con- structed out of 13 boron silicate glass plates located deep cerning the utility of slow neutrons for measuring neu- within the reactor swimming pool two meters above the tron scattering at low values of v and Q (see the appen- core, allowing time-of-flight measurements of neutron dix). Shortly afterwards, in 1968, Shapiro published a spectra. The counting rate showed a steep drop below 10 review article on the electric dipole moment of elemen- m/s, probably due to absorption in the aluminum win- tary particles. In this article he pointed out the advan- dows, to reflection losses, and to the limited acceptance tages of ultracold neutrons in the search for a neutron angle of the detector. However, total cross sections were electric dipole moment, in particular the greatly in- measured for neutron velocities down to 7 m/s for gold creased observation time and the reduction of the and 5 m/s for aluminum.
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