Abstract
The recent successful calculation of the lower collective branch of the excitation spectrum in liquid4He by Sunakawaet al. contains a phenomenological parameter φ(k) whose relation to microscopic theory is obscure. To clarify matters, an exact identity is presented for the absorptive part of the density-density correlation function and is employed to show that Pines' “zero-sound” concept of the phonon in liquid4He is accurate in the limit of infinitely long wavelengths. Since the zero-sound theory can be made to produce an explicit relation between φ(k) and the two-particle potential in the liquid, the foundation has been laid for a microscopic expression for the excitation spectrum in the range of very low wave numbers, where the classic Feynman theory of the phonon is known to be accurate. A numerical calculation of φ(k) using this expression results in a theoretical excitation spectrum which is in excellent agreement with neutron scattering measurements in the regionk≲0.4 Å −1.
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Sposito, G. Collective oscillations at long wavelengths in liquid4He. J Low Temp Phys 12, 85–99 (1973). https://doi.org/10.1007/BF00654727
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DOI: https://doi.org/10.1007/BF00654727