@article {Kothari293,
author = { and },
title = {Thermal inelastic scattering of cold neutrons in polycrystalline solids},
volume = {231},
number = {1186},
pages = {293--307},
year = {1955},
doi = {10.1098/rspa.1955.0175},
publisher = {The Royal Society},
abstract = {A general theory of the influence of thermal motion on the scattering of slow neutrons in polycrystals is discussed. Unlike Weinstock{\textquoteright}s earlier treatment of the same problem, we express temperature displacements of the lattice points as a sum of emission and absorption operators. This alternative approach simplifies the calculation of the transition probability to a considerable extent and provides a simple proof of the Debye-Waller factor. The theory is also generalized to the case of multi-phonon processes. General expressions for both the incoherent and coherent cross-sections, corresponding to an {\textquoteright}l{\textquoteright} phonon process, are derived. The latter, hitherto not treated rigorously, is examined in detail. It is shown that it can be expressed as a sum of two terms, of which the main term, apart from a constant, is identical with the expression for the incoherent part and the other is a correction term. Both terms are put in {\textquoteright}Placzek{\textquoteright} form, and for cold neutrons explicit expressions are obtained for the cases: (i) M \> 1 and T/0 \> 1, and (ii) M ~ 10 and T/0 \> 0.5. Numerical results for magnesium, aluminium, iron, lead and beryllium are discussed and compared with experiment. The agreement is found to be satisfactory.},
issn = {0080-4630},
URL = {http://rspa.royalsocietypublishing.org/content/231/1186/293},
eprint = {http://rspa.royalsocietypublishing.org/content/231/1186/293.full.pdf},
journal = {Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences}
}