EXCITATION OF PHONONS IN LIQUIDS AND CRYSTALS THROUGH GAMMA-RAY SCATTERING
Gamma-ray scattering is considered as a means of obtaining information about collective excitations in simple crystals, liquid helium II, and certain nearly classical fluids. The energy transfer dependent differential cross section for the almost elastic scattering of gamma rays from an assembly of atoms (assumed for simplicity to be of the same kind) is derived from first principles and is found to be proportional to the Fourier transform of the correlation kernel obtained by Zemach and Glauber and Van Hove in connection with similar studies for the case of cold neutron scattering. Through a straightforward quantization of the classical velocity potential, a plausible expression is obtained for the differential cross section in the case of liquid helium II. This result indicates the general form of the energy transfer dependent scattering cross section and enables one to estimate the intensity of the scattering at the energy transfer values corresponding to the creation or annihilation of collective excitations. A similar result is obtained for simple crystals, using the quantized harmonic oscillator representation for the timedependent atomic position vectors. A convenient and fairly general expression is given for the contribution to the coherent scattering cross section corresponding to singlephonon interactions, and the background produced by multiple-phonon interactions and umklapp effects is considered in detail. Incoherent scattering from nearly classical fluids is investigated using the dispersion relations obtained by Schofield together with Vineyard's assumption of a Gaussian form for the self-correlation function governing the single-atom scattering processes. Approximation techniques for obtaining quantum-mechanical corrections to the classical representations for the selfcorrelation function are considered, and an approach is found which appears somewhat better than other proposals which have been advanced. Other results of interest include a derivation of criteria for the goodness of Vineyard's Gaussian approximation for the self-correlation function together with an extremely simple expression for its most general form, and a discussion of the Bloch Theorem conceining the expectation values of exponentials of quantities having a Gaussian distribution function. (Dissertation Abstr. XXIII, No. 8)
- Research Organization:
- Originating Research Org. not identified
- NSA Number:
- NSA-17-020946
- OSTI ID:
- 4719680
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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Related Subjects
ATOMS
BACKGROUND
BLOCH THEORY
CIRCUITS
CROSS SECTIONS
CRYSTALS
DISPERSION THEORY
ELECTRONS
ENERGY
EXCITATION
FLUIDS
FOURIER ANALYSIS
GAMMA RADIATION
GAUSSIAN PROCESSES
HELIUM
INTERACTIONS
LATTICES
LIQUIDS
MATHEMATICS
MOTION
OSCILLATIONS
OSCILLATORS
PHONONS
PHYSICS
QUANTUM MECHANICS
SCATTERING
STATISTICS
THERMAL NEUTRONS
THERMAL RADIATION
UMKLAPP PROCESSES
VECTORS
VELOCITY