Perturbation theory of anharmonicity effects in slow neutron inelastic scattering by crystals
Perturbation theory of anharmonicity effects in slow neutron inelastic scattering by crystals
PERTURBATION THEORY OF ANHARMONIC!TY EFFECTS IN SLOW NEUTRON INELASTIC SCATTERING BY CRYSTALS. An earlier perturbation treannent of the corresponding X-ray scattering problem is generalized into a ca!culation of the effect of vibrational anharmonicity on the scattering of slow neutrons by crystals....
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Personal Name(s): | Hahn, H. (Corresponding author) |
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Contributing Institute: |
Publikationen vor 2000; PRE-2000; Retrocat |
Imprint: |
Jülich
Kernforschungsanlage Jülich, Verlag
1963
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Physical Description: |
p. 37-48 |
Document Type: |
Report Book |
Research Program: |
Addenda |
Series Title: |
Berichte der Kernforschungsanlage Jülich
138 |
Link: |
OpenAccess OpenAccess |
Publikationsportal JuSER |
PERTURBATION THEORY OF ANHARMONIC!TY EFFECTS IN SLOW NEUTRON INELASTIC SCATTERING BY CRYSTALS. An earlier perturbation treannent of the corresponding X-ray scattering problem is generalized into a ca!culation of the effect of vibrational anharmonicity on the scattering of slow neutrons by crystals. Of an expansion of the lattice potential in powers of the deviations from the thermally averaged sites, the cubic terms are taken into account up to second order; only first order terms are kept in the quartic anharmonicities. All higher terms are neglected. In particular, formulae for the shifts and broadenings of the one-phonon peaks in coherent scattering are derived in terms of the third and fourth order coupling coefficients. As in X-ray scattering, a simple quadratic relation exists between the shifted "effective frequencies" of the lang wavelength lattice vibrations and the $\underline{isothermal}$ elastic constants of the crystal. The lattice frequencies of the harmonic approximation may be obtained by extrapolating to absolute zero the linear dependence ·on temperature shown by the shifted frequencies above the Debye temperature.of the lang wavelength lattice vibrations and the isothermal elastic constants of the crystal. The lattice frequenciesof the harmonic approximation may be obtained by extrapolating to absolute zero the linear dependence·on temperature shown by the shifted frequencies above the Debye temperature. |