Prog. Theor. Phys. Vol. 28 No. 5 (1962) pp. 784-802
Ultrasonic Attenuation in Liquid Helium
Research Institute for Fundamental Physics, Kyoto University, Kyoto
(Received May 18, 1962)
The attenuation of the first sound in liquid helium II, expressed in terms of the time fluctuation of the force acting on the relevant normal coordinate, is studied from the quantum-hydrodynamical point of view, and is shown to serve for determining the effective interaction between phonons at low temperatures. The attenuation constant calculated is in quantitative agreement with the observed values by Chase and Herlin at a frequency of 12 Mc/sec in the temperature region below about 0.8°K, where Khalatnikov's theory does not work at all. Below 0.4°K, the dependence of the attenuation constant on temperature and frequency is the same as that obtained previously by several authors. The effective interaction here obtained is not quite the same as that obtained with the use of the so-called quantum hydrodynamics. This situation may be analogous to that encountered in determining the effective interaction responsible for the damping of ferromagnetic spin waves.
Since the hydrodynamical treatment of the sound wave cannot be applied in the region of interest and the nature of the sound wave is not yet completely clear, both adiabatic and isothermal cases are investigated, and it is shown that the isothermal desciption is better for treating the sound attenuation below about 0.8°K.
DOI : 10.1143/PTP.28.784
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