Physik der kondensierten Materie

, Volume 14, Issue 4, pp 336–352 | Cite as

Neutron scattering from quantum crystals

  • H. Beck
  • P. F. Meier


The cross-section for neutron scattering from an arbitrarily anharmonic crystal is split up in the usual way into the Debye-Waller factor, the multiphonon background and the one-phonon peakS(1). The latter is shown to be built up by the expectation valueD of the displacement operator under the influence of a special mechanical force. The method of functional derivation applied to non-equilibrium Green's functions is used to find non-linear equations of motion forD. The renormalized force constants involved are also defined for singular interparticle potentials. The interference terms inS(1), which are expected to be important for a quantum crystal with large particle fluctuations, are related to the difference betweenD and its linear response value. Finally, the known sum-rules are derived in this formalism and prescriptions to determine the Debye-Waller factor fromD are given.


Neural Network Complex System Nonlinear Dynamics Large Particle Force Constant 
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  1. 1.
    De Wette, F. W., Nijboer, B. R. A.: Phys. Letters18, 19 (1965).CrossRefADSGoogle Scholar
  2. 2.
    Minkiewicz, V. J., Kitchens, T. A., Lipschultz, F. P., Nathans, R., Shirane, G.: Phys. Rev.174, 267 (1968).CrossRefADSGoogle Scholar
  3. 3.
    Reese, R. A., Sinha, S. K., Brun, T. O., Tilford, C. R.: Phys. Rev. A3, 1688 (1971).CrossRefADSGoogle Scholar
  4. 4.
    Osgood, E. B., Minkiewicz, V. J., Kitchens, T. A., Shirane, G.: Preprint.Google Scholar
  5. 5.
    Glyde, H. R.: Canad. J. Phys.49, 701 (1971).Google Scholar
  6. 6.
    ——: J. Low Temp. Phys.3, 559 (1970).CrossRefGoogle Scholar
  7. 7.
    — Khanna, F. C.: Canad. J. Phys. to be published.Google Scholar
  8. 8.
    Horner, H.: Phys. Rev. A1, 1722 (1970) and unpublished calculations.CrossRefADSGoogle Scholar
  9. 9.
    Koehler, T. R., Werthamer, N. R.: Phys. Rev. A3, 2074 (1971).CrossRefADSGoogle Scholar
  10. 10.
    Ambegaokar, V., Convay, J. M., Baym, G. in Lattice Dynamics ed. by R. F. Wallis (Pergamon Press, London, 1965) p. 261.Google Scholar
  11. 11.
    See the excellent review article by N. R. Werthamer in Amer. J. Phys.37, 763 (1969) and the references quoted therein, as well as our Refs [5–8].CrossRefGoogle Scholar
  12. 12.
    Werthamer, N. R.: Phys. Rev. A2, 2050 (1970).CrossRefADSGoogle Scholar
  13. 13.
    Maradudin, A. A., Ambegaokar, V.: Phys. Rev.135, A 1071 (1964).CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    ——, Flinn, P. A.: Phys. Rev.129, 2529 (1963).CrossRefADSGoogle Scholar
  15. 15.
    Cowley, R. A., Buyers, W. J. L.: J. Phys. C2, 2262 (1969).CrossRefADSGoogle Scholar
  16. 16.
    ——, Swensson, E. C., Buyers, W. J. L.: Phys. Rev. Letters23, 525 (1969).CrossRefADSGoogle Scholar
  17. 17.
    Werthamer, N. R.: Phys. Rev. B1, 572 (1970).CrossRefADSGoogle Scholar
  18. 18.
    Beck, H., Meier, P. F.: Z. Phys.247, 189 (1971).CrossRefGoogle Scholar
  19. 19.
    van Hove, L.: Phys. Rev.95, 249 (1954).CrossRefADSMATHGoogle Scholar
  20. 20.
    Craig, R. A.: J. math. Phys.9, 605 (1968).CrossRefGoogle Scholar
  21. 21.
    Beck, H., Meier, P. F.: Phys. kondens. Materie12, 16 (1970).Google Scholar
  22. 22.
    ——: Phys. kondens. Materie12, 330 (1971).Google Scholar
  23. 23.
    Placzek, G.: Phys. Rev.86, 377 (1952).CrossRefADSMATHGoogle Scholar
  24. 24.
    Gillessen, P., Biem, W.: Z. Phys.216, 499 (1968).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • H. Beck
    • 1
  • P. F. Meier
    • 1
  1. 1.Institut für Theoretische PhysikUniversität ZürichZürichSwitzerland

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