The liquid-solid phase transition of helium at low temperatures is shown to result from the instability of the roton mode. In a simple model of the roton-roton interactions, the instability arises at a finite value of the roton energy as a result of the hybridization of a single roton with a bound roton pair. Thus our model exhibits a discontinuous jump of the soft-mode energy at the phase transition in agreement with neutron scattering experiments.
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Celli et al. (1972) studied this question.
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