INELASTIC SCATTERING OF NEUTRONS BY ANHARMONIC CRYSTALS.
Abstract
A theoretical framework is provided within which to determine the phonon frequencies and lifetimes from inelastic scattering of neutrons by crystals. When a crystal has anharmonicities interference effects can occur between in which the neutron creates only one phonon and processes in which it creates several phonons; these coherences are due to the fact that when a phonon can decay into several phonons, the final state in which the neutron has created one phonon is not orthogonal to final states in which the neutron has created several phonons. The one-phonon cross-section has a resonance at the phonon frequency, with a width proportional to the inverse of the phonon lifetime. The interference terms have the effect of shifting the center of this resonance, as observed, from the one-phonon frequency, and also changing the shape from an expected Lorentzian form. A very crude estimate of the effect is made which indicates that under favorable conditions in lead interference effects may lead to an asymmetry in the line shape of the order of a few per cent. It would appear that the anharmonicities in a crystal place an upper limit on the accuracy with which one can directly determine the phonon frequencies and lifetimes from the one-phonon resonances in neutron scattering data. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1964
- Accession Number
- AD0623339
Entities
People
- Gordon Baym
- John M. Conway
- Vinay Ambegaokar
Organizations
- Cornell Laboratory of Atomic and Solid State Physics