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 expansions in terms of moments of the phonon frequency spectrum, one incorporating the recoilles line, the other explicity excluding this term. Such expressions are useful for calculating the details of resonance line-shapes when some knowledge of the phonon spectrum is available or, conversely if it is wished to use measurements of resonance Doppler 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 sensitivity of the method is tested by simulating sets of neutron transmission data for low energy resonances in the cross sections of a number of different nuclides and doing a least-squares analysis on these to determine resonance parameters simultaneously with phonon moments. It is found that phonon moments can be determined independently of the resonance parameters and with very useful precision for at least the first three moments.