Specific Heat of Dilute Solutions ofHe3inHe4and theHe3-Quasiparticle Excitation Spectrum

High-precision measurements of the constant-volume specific heat of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ solutions with up to 1% ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are presented for the temperature range $70 \mathrm{mK}<T<\mathrm{}1\mathrm{} \mathrm{K}$. The data are inconsistent with three previously proposed ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-quasiparticle excitation spectra: (1) a spectrum which is purely quadratic in wave number $\mathcal{k}$, (2) a spectrum which is quadratic for small $\mathcal{k}$ and possesses a "roton" minimum at larger $\mathcal{k}$, and (3) a spectrum which as a ${\mathcal{k}}^4$ term in addition to the ${\mathcal{k}}^2$ term at all values of $\mathcal{k}$.