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

Figure 15. Partial Neutron Scattering Cross Sections for Solid Deuterium at Temperature of 17K
3.5.2 Cross-section data for o-D2 and p-H2 (theory model 2)
Compared to the assumptions for the scattering dynamics model 1 for the solid
moderator, following it is implemented :
• the degrees of freedom for rotation and oscillation can be excited, program SCATHD for
S(α,β) (with S(κ)=1, NDAM=1 and S(α,β=0)=0.0) inelastic Intra-scattering handled
exactly, no incoherent approximation
• frequency distribution for the acoustical modes normalised to 0.5
• coherent elastic scattering by HEXSCAT/IKE, modified Debye-Waller integral for o-D2
• no incoherent elastic scattering from the acoustic modes for p-H2 up to ω rot, modified
Debye-Waller integral for o-D2 and p-H2
In Fig. 15 the partial scattering cross-sections for model 2 are compared to those generated
with model 1 for solid deuterium. As it is clearly seen, the main difference is from the
modification of the Debye-Waller integrals caused by the altered frequency distributions used
for coherent and incoherent elastic neutron scattering. Looking for the inelastic neutron
scattering, the excitation of the rotator for model 2 is obvious.
3.5.3 Verification of the models, comparison with experimental data
For the solid moderators only few experimental data correlated with the frequency
spectra ρ(ω) or the neutron scattering dynamics are known. Hill, Lounasmaa [36] measured
the specific heat Cv for solid deuterium. Cv/3R is simply correlated to ρ(ω), especially for the
acoustical branch, according to:
Cv ⁄ 3 R = ∫ ρ ( ω ) • ( ω / T ) 2 • exp ( ω / T ) ⁄ ( exp ( ω / T ) - 1 ) 2 d ω
In Fig. 16 a comparison is shown for the theoretical models and the experiment. It
seems, that model 2 gives the best agreement to the experimental values.
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