Experimental determination of the He3 -quasiparticle excitation spectrum for dilute solutions of He3 in superfluid He4

High-precision measurements of the second-sound velocity in $^{3}\mathrm{He}$-$^{4}\mathrm{He}$ solutions with $^{3}\mathrm{He}$ molar concentrations, $X$, of up to 0.01 were made in the temperature range from 40 mK to ${T}_{\ensuremath{\lambda}}(X)$. From the data obtained below 1 K, values of the $^{3}\mathrm{He}$ contribution, ${\ensuremath{\rho}}_{n3}$, to the normal-fluid density were extracted. A quasiparticle spectrum was found, using a computer fitting routine, which is consistent with both these ${\ensuremath{\rho}}_{n3}$ data and with previously reported specific-heat results. This spectrum shows significant deviations from quadratic behavior only for wave numbers greater than about 0.6 ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ and is not in quantitative agreement with any of the previously proposed $^{3}\mathrm{He}$ excitation spectra. The effective mass of the quasiparticles determined from the ${\ensuremath{\rho}}_{n3}$ data ($X,T\ensuremath{\rightarrow}0$) is $2.34{m}_{3}$, which is in good agreement with other experiments. However, the effective mass associated with the normal-fluid density ($T\ensuremath{\rightarrow}0$) is found to increase with increasing $X$. This is contrary to the expected result.