Dispersion relation for phonon second-sound waves in superfluid helium
The velocity and attenuation of phonon second-sound waves in superfluid 4He at saturated vapor pressure have been calculated, as a function of sound-wave frequency ω, over the entire frequency range at a single temperature 0.25 °K. Second sound is obtained as a wavelike normal mode of a model phonon Boltzmann equation containing, in addition to the lifetime τ∥ of a single thermal phonon due to small-angle scattering, a sequence of longer lifetimes characterizing wide-angle scattering of phonons with anomalous dispersion. The calculated second-sound phase velocity shows a dispersion spread out over four orders of magnitude in frequency in the range ωτ∥ approximately-less-than 1. Moreover, there is a wide frequency range satisfying ωτ∥ very-much-greater-than 1 in which a second- sound collective mode still propagates, with the same velocity as a thermal phonon but with an attenuation length much longer than the thermal-phonon mean free path. The existence of a collective mode in the regime ωτ∥ very-much-greater-than 1, due to small-angle scattering, supports Maris's proposed explanation of resonancelike dispersion in the first-sound velocity, and also implies that the transition from collective to ballistic propagation in heat-pulse experiments is more complicated than previously supposed.
- Research Organization:
- Department of Physics, Arizona State University, Tempe, Arizona 85281
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-33-024391
- OSTI ID:
- 4041414
- Journal Information:
- Physical Review, B: Solid State, Vol. 13, Issue 3; Other Information: Orig. Receipt Date: 30-JUN-76; ISSN 0556-2805
- Country of Publication:
- United States
- Language:
- English
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