# The Breakdown of Superfluidity in Liquid $^{4}$He: An Experimental Test of Landau's Theory

D. R. Allum, P. V. E. McClintock, A. Phillips

## Abstract

A single pulse time of flight technique has been used to determine the drift velocity $\overline{v}$ of the negative ions injected into liquid $^{4}$He from a field emission source. Measurements of $\overline{v}$ as a function of temperature T, pressure P and electric field E are presented within the range: 0.29 $\leq$ T $\leq$ 0.5 K; 21 $\times$ 10$^{5}\leq$ P $\leq$ 25 $\times$ 10$^{5}$ Pa; 1 $\leq$ E $\leq$ 300 kV m$^{-1}$. The experimental results are in good agreement with Landau's theory of superfluidity. The data are used to demonstrate the inapplicability of two theories of supercritical dissipation: by Takken, based on an assumption of coherent roton emission; and by Bowley & Sheard, based on the assumption of incoherent single-roton emission. The results are, however, shown to be in excellent agreement with Bowley & Sheard's incoherent two-roton theory, and the data are used to derive a numerical value of the matrix element characterizing two-roton emission. The surprising absence of the single-roton emission process is discussed, and an upper bound is placed on the relevant matrix element.