Absence of a Quadratic Term in theHe4Excitation Spectrum

Abstract

By directly measuring the difference in velocity of 30 and 90 MHz sound waves in liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ below 100 mK, we have determined that the elementary excitation spectrum cannot be described by an expression $\epsilon \mathrm{}\left(k\right)=c\hslash k(1+{\alpha }_{1}k+{\alpha }_2{k}^2+\cdots )$ which has a value for ${\alpha }_1$ that is greater than 0.01 Å.