Druck-Materie 20b.qxd - JUWEL - Forschungszentrum Jülich

Figure 4. Energy levels of methane in methane hydrate and assignment of the levels
The tentative assignments are as follows. The levels labeled a, b, c and d would be rotational
levels of transitions, J=0 to 1,2,3 and 4, respectively. A and B would correspond J=1 to 2 and
3. Here, J is the quantum number of the rotation level. The rotational energy levels observed
are almost the same as those of the free rotation α and β would be vibration of the methane
molecule in the large and the small cages.
Finally we tried to measure a tunneling level of the rotational mode since there may be
little difference between observed and free rotation. The energy level of the methane rotation
will be split by potential around the methane molecule. The measurements was performed on
LAM-80 at KENS. Fig. 5 shows the scattering data, which shows weak peak around 0.5 meV
and quasi-elastic like tail around the elastic peak. Rise of intensity starting from 0.8 meV is
due to the first rotational level around 1 meV. We found that the peak around 0.5 meV is
spurious one due to the mica analyzer. So, there is no peak due to the splitting of the rotational
levels.
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35.0
30.0
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Figure 5. High resolution inelastic scattering data
We tried to analyze the quasi-elastic part although it may not be real one. The formula
we used is rotational diffusion model.
w
w
R
2
2 ~
S ( Q , ω ) = j ( Q d ) δ ( ω ) + ( 2l
+ 1)
j ( Q d ) F ( ω )
inc
0
∑ ∞
l = 1
~ 1 l ( l + 1)
D r
F l ( ω
) = 2
π ω + { l ( l + 1)
D }
r
2
100
l
l