- Physical Review Journals
All JournalsPhysics Magazine

Physical Review C

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Scattering cross sections of solid ortho-deuterium for ultracold neutrons: Role of defects, phonons, and temperature

Stefan Döge1,2,*, Jürgen Hingerl1,2, and Christoph Morkel1

  • *Contact author: stefan.doege@tum.de
PDF

Phys. Rev. C 113, 044614 – Published 17 April, 2026

DOI: https://doi.org/10.1103/5rx2-j8cq

Abstract

Solid ortho-deuterium is a widely used converter material in ultracold-neutron (UCN) sources. Although it has been studied with neutrons for more than two decades, some of its scattering properties remain poorly understood until this day. We remeasured the total scattering cross section of solid deuterium for ultracold neutrons and—as an improvement over previous experiments—eliminated side effects by employing low-roughness, transparent sample container windows. In this paper, we show the decomposition of the total scattering cross section into its constituents: incoherent elastic scattering, one-phonon up-scattering (using the corrected incoherent approximation), and coherent scattering from crystal defects. Applying both the Guinier approximation and a model using a spherical form factor to describe the defects, we were able to quantify the size and concentration of defects in the deuterium crystal at two different temperatures. Surprisingly, they account for about half of the total scattering cross section. Our work challenges the current picture of ultracold-neutron scattering in solid ortho-deuterium and explains the inability of state-of-the-art simulations to reproduce earlier experimental results. It represents a crucial step toward reliable scattering kernels for the planning of new UCN sources. Ultimately, our measurements allow to deduce the mean free path of UCNs in solid ortho-deuterium, which is 2.5 to 3.5 cm in the relevant temperature range and for a neutron velocity of 10 m/s. The optimal operating temperature for UCN converters is deduced to be between 10 and 12 K, contrary to the 5 K accepted hitherto.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (59)

  1. D. Dubbers and M. G. Schmidt, The neutron and its role in cosmology and particle physics, Rev. Mod. Phys. 83, 1111 (2011).
  2. H. Abele et al., Particle physics at the European spallation source, Phys. Rep. 1023, 1 (2023).
  3. F. M. Gonzalez et al., Improved neutron lifetime measurement with UCNτ, Phys. Rev. Lett. 127, 162501 (2021).
  4. J. M. Pendlebury et al., Revised experimental upper limit on the electric dipole moment of the neutron, Phys. Rev. D 92, 092003 (2015).
  5. A. Crivellin and M. Hoferichter, β Decays as sensitive probes of lepton flavor universality, Phys. Rev. Lett. 125, 111801 (2020).
  6. A. I. Frank, Ultracold neutrons and the interaction of waves with moving matter, Phys. Part. Nuclei 47, 647 (2016).
  7. A. Steyerl, H. Nagel, F.-X. Schreiber, K.-A. Steinhauser, R. Gähler, W. Gläser, P. Ageron, J. M. Astruc, W. Drexel, G. Gervais, and W. Mampe, A new source of cold and ultracold neutrons, Phys. Lett. A 116, 347 (1986).
  8. S. Döge, J. Hingerl, and C. Morkel, Measured velocity spectra and neutron densities of the PF2 ultracold-neutron beam ports at the Institut Laue–Langevin, Nucl. Instrum. Methods Phys. Res. Sect. A 953, 163112 (2020).
  9. F. Atchison, B. Blau, K. Bodek, B. van den Brandt, T. Bryś, M. Daum, P. Fierlinger, A. Frei, P. Geltenbort, P. Hautle, R. Henneck, S. Heule, A. Holley, M. Kasprzak, K. Kirch, A. Knecht, J. A. Konter, M. Kuźniak, C.-Y. Liu, C. L. Morris, et al., Cold neutron energy dependent production of ultracold neutrons in solid deuterium, Phys. Rev. Lett. 99, 262502 (2007).
  10. B. Lauss, Ultracold neutron production at the second spallation target of the Paul Scherrer Institute, Phys. Procedia 51, 98 (2014).
  11. A. Serebrov, V. Mityuklyaev, A. Zakharov, A. Erykalov, M. Onegin, A. Fomin, V. Ilatovskiy, S. Orlov, K. Konoplev, A. Krivshitch, V. Samsonov, V. Ezhov, V. Fedorov, K. Keshyshev, S. Boldarev, and V. Marchenko, Preparation of facilities for fundamental research with ultracold neutrons at pnpi, Nucl. Instrum. Methods Phys. Res. Sect. A 611, 276 (2009), Particle Physics with Slow Neutrons.
  12. E. Korobkina, G. Medlin, B. Wehring, A. Hawari, P. Huffman, A. Young, B. Beaumont, and G. Palmquist, Ultracold neutron source at the pulstar reactor: Engineering design and cryogenic testing, Nucl. Instrum. Methods Phys. Res. Sect. A 767, 169 (2014).
  13. J. Kahlenberg, D. Ries, K. U. Ross, C. Siemensen, M. Beck, C. Geppert, W. Heil, N. Hild, J. Karch, S. Karpuk, F. Kories, M. Kretschmer, B. Lauss, T. Reich, Y. Sobolev, and N. Trautmann, Upgrade of the ultracold neutron source at the pulsed reactor TRIGA Mainz, Eur. Phys. J. A 53, 226 (2017).
  14. T. M. Ito, E. R. Adamek, N. B. Callahan, J. H. Choi, S. M. Clayton, C. Cude-Woods, S. Currie, X. Ding, D. E. Fellers, P. Geltenbort, S. K. Lamoreaux, C.-Y. Liu, S. MacDonald, M. Makela, C. L. Morris, R. W. Pattie, J. C. Ramsey, D. J. Salvat, A. Saunders, E. I. Sharapov, et al., Performance of the upgraded ultracold neutron source at Los Alamos National Laboratory and its implication for a possible neutron electric dipole moment experiment, Phys. Rev. C 97, 012501(R) (2018).
  15. W. Schreyer, C. Davis, S. Kawasaki, T. Kikawa, C. Marshall, K. Mishima, T. Okamura, and R. Picker, Optimizing neutron moderators for a spallation-driven ultracold-neutron source at TRIUMF, Nucl. Instrum. Methods Phys. Res. Sect. A 959, 163525 (2020).
  16. A. Frei, The source for ultra-cold neutrons at the FRM II, J. Neutron Res. 24, 167 (2022).
  17. C. M. Lavelle, C.-Y. Liu, W. Fox, G. Manus, P. M. McChesney, D. J. Salvat, Y. Shin, M. Makela, C. Morris, A. Saunders, A. Couture, and A. R. Young, Ultracold-neutron production in a pulsed-neutron beam line, Phys. Rev. C 82, 015502 (2010).
  18. E. Lychagin, V. Mityukhlyaev, A. Muzychka, G. Nekhaev, V. Nesvizhevsky, M. Onegin, E. Sharapov, and A. Strelkov, UCN sources at external beams of thermal neutrons. An example of PIK reactor, Nucl. Instrum. Methods Phys. Res. Sect. A 823, 47 (2016).
  19. G. Bison, M. Daum, K. Kirch, B. Lauss, D. Ries, P. Schmidt-Wellenburg, G. Zsigmond, T. Brenner, P. Geltenbort, T. Jenke, O. Zimmer, M. Beck, W. Heil, J. Kahlenberg, J. Karch, K. Ross, K. Eberhardt, C. Geppert, S. Karpuk, T. Reich, et al., Comparison of ultracold neutron sources for fundamental physics measurements, Phys. Rev. C 95, 045503 (2017).
  20. W.-D. Seiffert, Messung der Streuquerschnitte von flüssigem und festem Wasserstoff, Deuterium und Deuteriumhydrid für thermische Neutronen, Ph.D. thesis, Technische Universität München, Munich, Germany, 1970, also Euratom Report No. EUR 4455 d.
  21. W. D. Seiffert, B. Weckermann, and R. Misenta, Messung der Streuquerschnitte von flüssigem und festem Wasserstoff, Deuterium und Deuteriumhydrid für thermische Neutronen, Z. Naturforsch. A 25, 967 (1970).
  22. F. Atchison, B. Blau, B. van den Brandt, T. Bryś, M. Daum, P. Fierlinger, P. Hautle, R. Henneck, S. Heule, K. Kirch, J. Kohlbrecher, G. Kühne, J. A. Konter, A. Pichlmaier, A. Wokaun, K. Bodek, M. Kasprzak, M. Kuźniak, P. Geltenbort, and J. Zmeskal, Measured total cross sections of slow neutrons scattered by solid deuterium and implications for ultracold neutron sources, Phys. Rev. Lett. 95, 182502 (2005).
  23. W. Bernnat, J. Keinert, and M. Mattes, Evaluation of scattering laws and cross sections for calculation of production and transport of cold and ultracold neutrons, in Forschungszentrum Jülich Matter and Materials 20, edited by H. Conrad (Jülich Research Center, Forschungszentrum Jülich, 2004), pp. 9–42.
  24. J. R. Granada, Neutron scattering kernel for solid deuterium, Europhys. Lett. 86, 66007 (2009).
  25. A. J. M. Plompen et al., The joint evaluated fission and fusion nuclear data library, JEFF-3.3, Eur. Phys. J. A 56, 181 (2020).
  26. N. Otuka et al., Towards a more complete and accurate experimental nuclear reaction data library (EXFOR): International collaboration between nuclear reaction data centres (NRDC), Nucl. Data Sheets 120, 272 (2014).
  27. Experimental Nuclear Reaction Data (EXFOR): https://www-nds.iaea.org/exfor/.
  28. S. Döge, J. Hingerl, E. V. Lychagin, and C. Morkel, Scattering of ultracold neutrons from rough surfaces of metal foils, Phys. Rev. C 102, 064607 (2020).
  29. G. Placzek, Incoherent neutron scattering by polycrystals, Phys. Rev. 93, 895 (1954).
  30. V. F. Turchin, Slow Neutrons, Israel program for scientific translations (Sivan Press, Jerusalem, 1965), Russian original: Medlennye nejtrony (Gosatomizdat, Moscow, 1963).
  31. S. Döge, C.-Y. Liu, A. Young, and C. Morkel, Incoherent approximation for neutron up-scattering cross sections and its corrections for slow neutrons and low crystal temperatures, Phys. Rev. C 103, 054606 (2021).
  32. I. F. Silvera, The solid molecular hydrogens in the condensed phase: Fundamentals and static properties, Rev. Mod. Phys. 52, 393 (1980).
  33. G. Placzek and L. Van Hove, Interference effects in the total neutron scattering cross-section of crystals, I Nuovo Cim. 1, 233 (1955).
  34. F. Atchison, B. van den Brandt, T. Bryś, M. Daum, P. Fierlinger, P. Hautle, R. Henneck, K. Kirch, J. Kohlbrecher, G. Kühne, J. A. Konter, A. Pichlmaier, A. Wokaun, K. Bodek, M. Kasprzak, M. Kuźniak, P. Geltenbort, M. Giersch, J. Zmeskal, M. Hino, et al., Measured total cross sections of slow neutrons scattered by gaseous and liquid H22, Phys. Rev. Lett. 94, 212502 (2005).
  35. Y. N. Pokotilovski, UCN transport simulation in solid deuterium crystals, Nucl. Instrum. Methods Phys. Res. Sect. A 675, 29 (2012).
  36. M. Hamermesh and J. Schwinger, The scattering of slow neutrons by ortho- and paradeuterium, Phys. Rev. 69, 145 (1946).
  37. I. I. Gurevich and L. V. Tarasov, Low-Energy Neutron Physics (North-Holland Publishing Company, 1968).
  38. A. Guinier and G. Gournet, Small Angle Scattering of X-Rays (John Wiley and Sons, Ltd., 1955).
  39. G. Kostorz, Small-angle scattering and its applications to materials science, in Neutron Scattering, edited by G. Kostorz, Treatise on Materials Science and Technology Vol. 15 (Academic Press, New York, 1979), pp. 227–289.
  40. S. Doege, C. Morkel, J. Hingerl, B. Lauss, and N. Hild, Measurement of the mean free path of ultracold neutrons (UCNs) in liquid and solid hydrogen and deuterium at various temperatures, Institut Laue–Langevin, https://doi.org/10.5291/ill-data.3-14-374.
  41. S. Döge, J. Hingerl, W. Petry, and C. Morkel, Direct measurement of the scattering cross sections of liquid ortho-deuterium for ultracold neutrons and comparison with model calculations, Phys. Rev. B 106, 054102 (2022).
  42. S. Döge, C. Herold, S. Müller, C. Morkel, E. Gutsmiedl, P. Geltenbort, T. Lauer, P. Fierlinger, W. Petry, and P. Böni, Scattering cross sections of liquid deuterium for ultracold neutrons: Experimental results and a calculation model, Phys. Rev. B 91, 214309 (2015).
  43. A. Anghel, T. L. Bailey, G. Bison, B. Blau, L. J. Broussard, S. M. Clayton, C. Cude-Woods, M. Daum, A. Hawari, N. Hild, P. Huffman, T. M. Ito, K. Kirch, E. Korobkina, B. Lauss, K. Leung, E. M. Lutz, M. Makela, G. Medlin, C. L. Morris, et al., Solid deuterium surface degradation at ultracold neutron sources, Eur. Phys. J. A 54, 148 (2018).
  44. S. Döge and J. Hingerl, A hydrogen leak-tight, transparent cryogenic sample container for ultracold-neutron transmission measurements, Rev. Sci. Instrum. 89, 033903 (2018).
  45. S. Döge, Scattering of ultracold neutrons in condensed deuterium and on material surfaces, Ph.D. thesis, Technische Universität München, Munich, Germany, 2019, http://doi.org/10.14459/2019md1464401.
  46. A. Steyerl, A time-of-flight spectrometer for ultracold neutrons, Nucl. Instrum. Methods 101, 295 (1972).
  47. V. F. Sears, Neutron scattering lengths and cross sections, Neutron News 3, 26 (1992).
  48. C.-Y. Liu, A. R. Young, and S. K. Lamoreaux, Ultracold neutron upscattering rates in a molecular deuterium crystal, Phys. Rev. B 62, R3581 (2000).
  49. T. Bryś, Extraction of ultracold neutrons from a solid deuterium source, Ph.D. thesis, ETH Zürich, Zurich, Switzerland, 2007, http://doi.org/10.3929/ethz-a-005540305.
  50. B. Davison and J. B. Sykes, Neutron Transport Theory (Oxford University Press, London, 1958).
  51. C. L. Morris, J. M. Anaya, T. J. Bowles, B. W. Filippone, P. Geltenbort, R. E. Hill, M. Hino, S. Hoedl, G. E. Hogan, T. M. Ito, T. Kawai, K. Kirch, S. K. Lamoreaux, C.-Y. Liu, M. Makela, L. J. Marek, J. W. Martin, R. N. Mortensen, A. Pichlmaier, A. Saunders, et al., Measurements of ultracold-neutron lifetimes in solid deuterium, Phys. Rev. Lett. 89, 272501 (2002).
  52. A. P. Serebrov, V. A. Mityukhlyaev, A. A. Zakharov, T. Bowles, G. Greene, and J. Sromicki, Solid deuterium source of ultracold neutrons based on a pulsed spallation source, JETP Lett. 66, 802 (1997).
  53. K. K. H. Leung, S. Ivanov, F. M. Piegsa, M. Simson, and O. Zimmer, Ultracold-neutron production and up-scattering in superfluid helium between 1.1 K and 2.4 K, Phys. Rev. C 93, 025501 (2016).
  54. R. Golub and K. Böning, New type of low temperature source of ultra-cold neutrons and production of continous beams of UCN, Z. Phys. B 51, 95 (1983).
  55. Z.-C. Yu, S. S. Malik, and R. Golub, A thin film source of ultra-cold neutrons, Z. Phys. B 62, 137 (1986).
  56. A. Frei, Produktion von ultrakalten Neutronen mit einem festen Deuteriumkonverter, Ph.D. thesis, Technische Universität München, Munich, Germany, 2008.
  57. F. Atchison, B. van den Brandt, T. Bryś, M. Daum, P. Fierlinger, P. Hautle, R. Henneck, S. Heule, M. Kasprzak, K. Kirch, J. A. Konter, A. Michels, A. Pichlmaier, M. Wohlmuther, A. Wokaun, K. Bodek, U. Szerer, P. Geltenbort, J. Zmeskal, and Y. Pokotilovskiy, Production of ultracold neutrons from a cold neutron beam on a H22 target, Phys. Rev. C 71, 054601 (2005).
  58. A. P. Serebrov, V. A. Mityukhlyaev, A. A. Zakharov, V. V. Nesvizhevsky, and A. G. Kharitonov, Is it possible to produce next generation of UCN sources with density 103–104cm−3, Pis'ma Zh. Eksp. Teor. Fiz. 59, 728 (1994) [JETP Lett. 59, 757 (1994)].
  59. S. Döge and C. Morkel, Implications for the design of ultracold-neutron sources based on solid deuterium: A review of the literature and recent experiments (unpublished).

Outline

Information

Phys. Rev. C 113, 044614– Published 17 April, 2026
  • Received 9 September 2024
  • Revised 1 November 2025
  • Accepted 11 March 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation