Excitation spectrum of aHe3atom moving in He II at zero temperature

The recoil spectrum $S(q,\omega )$ for a single ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ moving in He II at zero temperature is calculated within a mode-coupling approximation. The effective mass of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ particle is found to be $m^{*}=2.35\mathrm{}{m}_3$. The dispersion curve for elementary excitations is shown to deviate considerably from a parabolic one yielding a higher density of states for energies near the He II roton gap. The undamped quasiparticle excitations cease to exist for a momentum about 2 ${\mathrm{\AA }}^{-1\mathrm{}}$; their excitation strength drops to zero. The dispersion curve continues above 2 ${\mathrm{\AA }}^{-1\mathrm{}}$ as a resonance in the multiple-excitation background.