Splitting of the phonon spectrum in3He-4He solutions
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The dynamic structure function for 4 He- 4 He density correlationsS44(k, ω) is calculated as a function of the wave vectork and frequency ω for a simple model of a 3 He- 4 He solution at various temperatures and small 3 He molar concentrationx. The inputs to the model include the measured 4 He phonon spectrum and the zero-concentration 3 He quasiparticle energy (above thek=0 value), which is taken to be quadratic ink and to intersect the phonon spectrum atk c near the roton minimum. Taking into account the decay of a phonon into a quasiparticle-hole pair, which is effected in the model by a quantum hydrodynamic interaction, we find that the phonon spectrum is split into two distinct branches. Atk c the splitting of the phonon branches depends on a coupling constant γ and the crossover parameter ε(k c )/k c . If in 3 He- 4 He solutions γ is large enough and ε(k c )/k c is small enough, then the phonon spectrum is split into two branches.
KeywordsSimple Model Magnetic Material Structure Function Dynamic Structure Phonon Spectrum
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