Theory of excitations inHe3-He4mixtures

The elementary excitation spectrum of liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixture is calculated from first principles. The boson quasiparticles are treated by a density-variable formalism, and their interaction with the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ excitations is explicitly derived. Using the liquid-structure factor for pure ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, we calculate the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ excitation dispersion over a wide momentum range; renormalization of the phonon-roton (boson) spectrum due to the presence of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$; lifetime of the roton excitations as a function of momentum and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ concentration; and we estimate the possibility of resonances formed by rotons and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ quasiparticles. The results are in contrast to previous speculations regarding the existence of a ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ roton excitation. However, our calculations provide good agreement with available experimental data. The sensitivity of the roton linewidth to the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ quasiparticle interactions indicates that future light and neutron scattering experiments may provide insight into the microscopic nature of the interatomic helium potential.