Inelastic scattering of phonons by quadrupole defects with internal degrees of freedom |
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Authors: | T N Antsygina V A Slyusarev K A Chishko |
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Institution: | (1) B. I. Verkin Low-Temperature Physicotechnical Institute, National Academy of Sciences, 310164 Kharkov, Ukraine |
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Abstract: | We solve the quantum mechanical problem of the inelastic scattering of phonons by a quadrupole defect in a crystal lattice
for the case of solid parahydrogen whose matrix contains pair complexes of H2 orthomolecules. By employing the pseudospin approximation for the operator of the energy of quadrupole-quadrupole interaction
of the molecules in an orthopair we derive an effective Hamiltonian that describes the interaction of phonons with a pair
quadrupole orthodefect in the lattice. We set up the scattering matrix and calculate the effective phonon relaxation time
τ(ω, T) as a function of the frequency ω and the crystal temperature T. We also find that a pair quadrupole defect, which has a complicated system of levels, can be replaced by an effective two-level
system with temperature-dependent parameters. The fact that a pair quadrupole orthocluster has internal degrees of freedom
results in a resonant scattering peak near a certain critical temperature T
0. Our estimates for H2 yield T
0≃ 6–7 K. Finally, we discuss the contribution of this mechanism to the low-temperature thermal conductivity of solid hydrogen.
Zh. éksp. Teor. Fiz. 114, 555–569 (August 1998) |
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