RESONANCE NEUTRON METHODS FOR DETERMINING STATISTICAL PROPERTIES OF PHONON-SPECTRA

The quantal expression for Doppler broadening of neutron resonances by creation and annihilation of phonons in a crystal is developed into e xpansions in terms of moments of the phonon frequency spectrum, one in corporating the recoilless line, the other explicitly excluding this t erm. Such expressions are useful for calculating the details of resona nce line-shapes when some knowledge of the phonon spectrum is availabl e, or, conversely, if it is wished to use measurements of resonance Do ppler broadening to extract information on the phonon spectrum of the target material (specifically, that portion of the spectrum centred on the atomic species in which the resonance occurs). The possible sensi tivity of the method is tested by simulating sets of neutron transmiss ion data for low energy resonances in the cross sections of a number o f different nuclides and doing a least-squares analysis on these to de termine resonance parameters simultaneously with phonon moments. It is found that phonon moments can be determined independently of the reso nance parameters and with very useful precision for at least the first three moments.