Neutron energy loss

In an INS experiment we observe how the strength of neutron scattering varies with the energy transfer and momentum transfer. The spectrum is typically in neutron energy loss, where energy is transferred from the incident neutrons to the scattering atoms. 

The delta function can be omitted since the expression is only evaluated at specific transitions, where its value is unity. This is the basis of Eq. (2.32), in Chapter 2, where the significance of 5 is explained. The spectrum consists of transitions, appearing as a sequence of sharp bands at neutron energy loss values corresponding to the energies of all the internal excitations of the molecule. 

The temperature dependences of the integrated intensities of the 6.4 meV and 1.6 meV peaks are well described in terms of the Boltzmann thermal population factors of the split ground-state levels, both for the neutron-energy gain and neutron-energy loss. On the other hand, the observed temperature dependences of the peak intensities differ qualitatively from those expected for phonons or harmonic oscillators [124]. 

Fig. 2. Neutron energy loss spectrum for -palladium deuteride containing 3.7 at- JH. The spectrum measured for the deuteride before introducing the H defects is also shown as a dashed line. The position of the dominant density-of-states peaks for 3-PUHq is indicated by the arrow.

Fig. 3. Neutron energy loss spectra at 80K for a saturation coverage of H on Pt black (dashed line) and of 90%D and 10 H (experimental points and solid line).

Moore,W.E., Kirouac,G.J., Trevino,S.F. Neutron energy-loss scattering fr n stretch oriented polyethylene, (private communication) (1969). 

An important feature is that the neutron energy loss depends on the atomic mass of the scattering atom and hence different masses occur at different times-of-flight. In the harmonic approximation, the peak width depends on the Gaussian average of the vibrational frequencies. The peak intensity depends only on the number of scatterers and their cross section. Thus NCS functions as a neutron mass spectrometer , albeit with poor mass resolution. Hydrogen is usually well separated from other elements and allows its quantification, even in the presence of deuterium. 

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