Neutron Slowing Down and Thermalization

  • Robert E. MacFarlane
Reference work entry


The theory behind the generation of thermal cross sections is presented, concentrating on the phonon expansion method. Examples are given for graphite, water, heavy water, and zirconium hydride. The graphite example demonstrates incoherent inelastic scattering and coherent elastic scattering for crystalline solids. The water example demonstrates incoherent inelastic scattering for liquids with diffusive translations. Heavy water adds a treatment for intermolecular coherence. Zirconium hydride shows the effects of the “Einstein oscillations” of the hydrogen atoms in a cage of zirconium atoms, and it also demonstrates incoherent elastic scattering. Neutron thermalization is introduced using Monte Carlo simulations of several systems, followed by multigroup discrete-ordinates and collision-probability methods. Size effects in thermalization are demonstrated. Steady-state slowing down is discussed by illustrating typical cross-section data, and showing slowing down by elastic scattering, inelastic scattering, and resonance cross sections in the narrow resonance approximation. Intermediate resonance self-shielding effects are introduced using the NJOY flux calculator and the WIMS implementation. The effects of time and space on slowing down are demonstrated using Monte Carlo simulations, and the theoretical basis is summarized.


Elastic Scattering Spin Group Fission Neutron Zirconium Hydride Background Cross Section 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Alcouffe RE, Baker RS, Dahl JA, Turner SA, Ward RC (Rev. May 2005) PARTISN: a time-dependent, parallel neutron particle transport code system, Los Alamos National Laboratory report LA-UR-05-3925.Google Scholar
  2. Askew JR, Fayers FJ, Kemshell PB (1966) A general description of the lattice code WIMS. J Brit Nucl Energy Soc 5:564.Google Scholar
  3. Bell GI, Glasstone S (1970) Nuclear reactor theory. Van Nostrand Reinhold Company, New YorkGoogle Scholar
  4. Bondarenko II (ed) (1964) Group constants for nuclear reactor calculations. Consultants Bureau, New York.Google Scholar
  5. Briggs JB et al (2004) International handbook of evaluated criticality safety benchmark experiments. Tech. Rep. NEA/NSC/DOC(95)04/I, Nuclear Energy Agency, ParisGoogle Scholar
  6. Butland AT (1973) LEAP and ADDELT, a users guide to two complementary codes on the ICL-470 for calculating the scattering law from a phonon frequency function. Atomic Energy Establishment Winfrith report AEEW-M-1200Google Scholar
  7. Cullen DE (November 2005) TART 2005: a coupled neutron-photon 3-D, time dependent, combinatorial geometry monte carlo transport code. Lawrence Livermore National Laboratory report UCRL-SM-218009Google Scholar
  8. Cullen DE (2007) PREPRO 2007: 2007 ENDF/B pre-processing codes. IAEA-NDS-39, Rev. 13. Nuclear Data Section, International Atomic Energy Agency, ViennaGoogle Scholar
  9. Herman M, (ed) (2005) Data Formats and Procedures for the Evaluated Nuclear Data File ENDF/B-VI and ENDF/B-VII, Brookhaven National Laboratory report BNL-NCS-44945-05-Rev (ENDF-102)Google Scholar
  10. Henryson H II, Toppel BJ, Stenberg CG (1976) MC2-2: a code to calculate fast neutron spectra and multigroup cross sections. Argonne National Laboratory report ANL-8144 (ENDF-239)Google Scholar
  11. Honek H (1961) THERMOS, a thermalization transport theory code for reactor lattice calculations. Brookhaven National Laboratory report 5826Google Scholar
  12. Koppel JU, Houston DH (July 1978) Reference manual for ENDF thermal neutron scattering data. General Atomic report GA-8774 revised and reissued as ENDF-269 by the National Nuclear Data Center at the Brookhaven National LaboratoryGoogle Scholar
  13. Koppel JU, Triplett JR, Naliboff YD (March 1967) GASKET: a unified code for thermal neutron scattering. General Atomics report GA-7417 (Rev.)Google Scholar
  14. Larson NM (October 2008) Updated Users’ guide for SAMMY: multilevel R-matrix fits to neutron data using Bayes’ equations. Oak Ridge National Laboratory report ORNL/TM-9179/R8Google Scholar
  15. Lathrop, KD (November 1965) DTF-IV, a FORTRAN program for solving the multigroup transport equation with anisotropic scattering. Los Alamos Scientific Laboratory report LA-3373Google Scholar
  16. MacFarlane RE (September 1980) ENDF/B-IV and -V Cross sections for thermal power reactor analysis. In: Proceedings international conference of nuclear cross sections for technology, Knoxville, October 22–26, 1979, National Bureau of Standards Publication 594Google Scholar
  17. MacFarlane RE (July 1992) TRANSX2: a code for interfacing MATXS cross-section libraries to nuclear transport codes. Los Alamos National Laboratory report LA-12312-MSGoogle Scholar
  18. MacFarlane RE (March 1994) New thermal neutron scattering files for ENDF/B-VI release 2. Los Alamos National Laboratory report LA-12639-MSGoogle Scholar
  19. MacFarlane RE, Muir DW (1994) The NJOY nuclear data processing system, version 91, Los Alamos National Laboratory report LA-12740-MGoogle Scholar
  20. Mattes M, Keinert J (2005) Thermal neutron scattering data for the moderator materials H2O, D2O and ZrHx in ENDF-6 format and as ACE library for MCNP(X) codes. International Nuclear Data Committee report INDC(NDS)-0470, April 2005.Google Scholar
  21. X-5 Monte Carlo Team (2003) MCNP—A General Monte Carlo N-Particle Transport Code, Version 5, Los Alamos National Laboratory report LA-UR-03-1987 (April 2003)Google Scholar
  22. Skold K (1967) Small energy transfer scattering of cold neutrons from liquid argon. Phys Rev Lett 19:1023CrossRefGoogle Scholar
  23. Sublet J-Ch, Ribon P, Coste-Delcalaux M (2006) CALENDF-2005: user manual. CEA report CEA-R-6131Google Scholar
  24. Tuli JK, Oblizinsky P, Herman M (eds) (December 2006) Special issue on evaluated nuclear data file ENDF/B-VII.0. Nucl Dat Sheets 107(12):2931–3060Google Scholar
  25. Williams MMR (1966) The slowing down and thermalization of neutrons. North-Holland Publishing Company/Wiley, Amsterdam/New YorkGoogle Scholar
  26. Wycoff RWG (1963) Crystal Structures. Wiley, New York/LondonGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Robert E. MacFarlane
    • 1
  1. 1.Nuclear and Particle Physics, Astrophysics and CosmologyTheoretical Division, Los Alamos National LaboratoryLos AlamosUSA

Personalised recommendations