Dynamic corrections for neutron scattering of water in the free molecule approximation

We develop a quantum mechanical theory for the inelasticity or Placzek correction for an asymmetric top rigid rotator, and give a formula to compute this correction for neutron scattering. We have, however, used a sphericalized model which satisfies Mecke’s sum rule to compute the correction for H2O and D2O. Since this rigid rotor model fails to satisfy the exact first sum rule, we introduce a form that does satisfy this condition. Good agreement with the large momentum exchange (k) behavior in the case of D2O is obtained. However, for the H2O this is not so and adjustable parameters have to be introduced to obtain the correction asymptotic behavior.