The hydrogen vibrational potential

The potential surface on which the hydrogen atom vibrates can be probed in some detail for two different cases single particle dynamics where dispersion is absent and collective dynamics where dispersion is important. 

Single particle dynamics occurs where there are no interactions between hydrogen atoms in the metal so the oscillator mass, p, is close to unity and the INS spectra extend over several harmonics ( 5.2.1.2). 

The observed transitions can be used to parameterise the potential, either according to simple models or, in terms of the symmetry adapted spherical harmonics for the most general potential [51]. The advantage of this approach is that the wavefimctions of the hydrogen in its excited states can be extracted. Further the full form of the Scattering Law (see Fig. 2.4) for any transition can be calculated. These can be compared with those observed on direct geometry spectrometers ( 5.3.2.1) [64]. 

The results of such measurements would be unsurprising to the molecular spectroscopist where the system is, like ZrH2, reasonably harmonic but some systems show significant deviation from harmonicity, like NbHo.3, see Table 6.10 [64]. A spectral characteristic of these systems is the unusually weak transitions at the higher energies. It appears that the high energy wavefimctions are more extended than the 

In systems where inter-hydrogen forces are important, usually because of the close proximity of hydrogen neighbours, dispersion is clearly seen in the one quantum spectrum, as in Fig. 6.22. The higher order transitions from such systems would not then be expected to appear as sharp transitions, since the two phonon spectrum should resemble the self convolution of the one phonon spectrum ( 2.6.3). Occasionally, however, sharp transitions are observed, at E(2 o just below the energy of 2E(i o) If -d is the full width at half height of the (1 —0) transition. Then, provided that 

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