Theory of inelastic neutron scattering from molecular fluids

Slow-neutron scattering by molecules

“…The first term in (4.14) is the classical result and was also given by De Gennes [11] and more recently by Eglestaff et al [12] (EGGM) but only for a homonuclear .17) is not exact to order t 2, but allows an estimate of the importance of the non-classical: term. The ratio of the prefactors of the two terms is 88 a,~ so that the classical result is again valid for a m ~ 1.…”

“…The ratio of the prefactors of the two terms is 88 a,~ so that the classical result is again valid for a m ~ 1. EGGM suggest [12] that the value of d may be determined from the measured second moment (they actually consider only a homonuctear molecule) M2(Q ) = bA2M2A(Q ) + bB2M2B(Q ) + 2/~,/~BM2AB(Q), using the fact that the first bracket in (4.14) has a minimum at Qd ~ Err and hence so does M2(Q)/Q 2, if the classical approximation is valid. In fact the second bracket in (4.14) has a minimum at Qd ~ ~Tr, so that unless ~m < 1 in the appropriate region of Q the more complete results (4.14) and (4.12) should be used.…”

The scattering of slow neutrons by diatomic molecular fluids

“…Thus the lowest order terms of interest are of order (molecular mass) -2. In the single molecule case the coefficient of this term involves the mean square torque and force, and quantities [2] of similar magnitude are expected to appear in the intermolecular term. Similar remarks would apply to the higher terms also, and therefore if the experimental conditions are, such that the single molecule term is density independent the intermolecular term should be also.…”

“…Wick [2] followed the same procedure but expanded about the momentum transfer for single particle recoil. Thus Placzek's expansion may be used for the majority of cases while Wick's expansion will be useful for low effective mass self terms where recoil is important.…”