THERMODYNAMIC GREEN'S FUNCTION METHODS IN NEUTRON SCATTERING BY CRYSTALS
Journal Article
·
· Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D
Formulas were derived for the transition probabilities per unit time for both inelastic coherent scattering of neutrons by crystals and resonant emission of photons and neutrons by nuclei bound in crystals, without making the assumption that the crystal is hamnonic. In deriving these transition probabilities, the analytic structure of thermodynamic correlation or Green's functions, considered as functions of complex temperatures and times, was developed and used. In particu1ar a spectral form was found for the phonon Green's function. Only one assumption was made about the crystal, namely that the displacement of the nuclei due to the forces exerted by the neutron in scattering are linear functions of these forces. This led to an evaluation of the transition probabilities in terms of the exact thermodynamic displacement autocorrelation function. This evaluation obeyed the detailed balancing condition, and Placzek's sum rule. A consequence of this evaluation is that the widths of the "one-phonon" peaks in the neutron scattering are exactly equal to the widths of the corresponding phonon states of the crystal. (auth)
- Research Organization:
- Harvard Univ., Cambridge, Mass.
- NSA Number:
- NSA-15-009528
- OSTI ID:
- 4100390
- Journal Information:
- Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 121; ISSN PHRVA
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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