Dynamic scaling and ultrasonic attenuation in 4He near the superfluid transition point

Abstract

Attenuation of first sound has been measured in 4He under saturated vapor pressure near the lambda temperature Tλ at frequencies Ω/2π ranging from 10.2 to 271 MHz. The frequency dependence of the critical part of the attenuation is determined and the dynamic scaling hypothesis is examined. Above the lambda point, it is found that the critical attenuation is described by a scaling function α(Ω, ɛ) = γ1+y F(ΩΤ), where Τ = Τ0ɛ−x and ɛ = T/Tλ − 1, with the results x = 1.02±0.05 and y = 0.33±0.03. The characteristic frequency of the order-parameter fluctuation with the wave number k equal to the inverse correlation length is then proportional to ɛ x , which is in an excellent agreement with the prediction of dynamic scaling. Below the lambda point, a characteristic relaxation time or times shorter than previously expected at lower frequencies appears to exist in the present frequency range.