Pressure dependence of the low-momentum phonon dispersion relation in liquid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

The pressure dependence of the low-momentum phonon dispersion relation in liquid $^{4}\mathrm{He}$ has been determined from an analysis of experiments on the interactions between sound waves and thermal phonons. Specifically, changes $\frac{\ensuremath{\Delta}C}{C}$ in sound velocity were studied in the frequency range 1-15 MHz for pressures $0\ensuremath{\lesssim}P\ensuremath{\lesssim}20$ atm, at temperatures $0.1\ensuremath{\le}T\ensuremath{\le}0.45$ K. The results were found to be in agreement with phonon dispersion, for small momenta, of the form $\ensuremath{\epsilon}=Cp(1+\ensuremath{\gamma}{p}^{2}\ensuremath{\cdots})$, with $\ensuremath{\gamma}$ positive at low pressures. At saturated vapor pressure, the present study yields a value $\ensuremath{\gamma}=(16\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{37}$ cgs; $\ensuremath{\gamma}$ decreases linearly with increasing density and reaches zero at a density corresponding to a pressure of \ensuremath{\sim} 18 atm.

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