Experimental determination of theHe3-quasiparticle excitation spectrum for dilute solutions ofHe3in superfluidHe4

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 $T_{\lambda }\mathrm{}\left(X\right)\mathrm{}$. From the data obtained below 1 K, values of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ contribution, ${\rho }_{n3\mathrm{}}$, to the normal-fluid density were extracted. A quasiparticle spectrum was found, using a computer fitting routine, which is consistent with both these ${\rho }_{n3\mathrm{}}$ 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 ${\mathrm{\AA }}^{-1\mathrm{}}$ 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 ${\rho }_{n3\mathrm{}}$ data ($X,T\to 0$) is $2.34m_3$, which is in good agreement with other experiments. However, the effective mass associated with the normal-fluid density ($T\to 0$) is found to increase with increasing $X$. This is contrary to the expected result.