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Correlated Basis Function perturbation theory is used to evaluate the zerotemperature response $S(q,\omega)$ of $^3$He-$^4$He mixtures for inelasticneutron scattering, at momentum transfers $q$ ranging from $1.1$ to $1.7\AA^{-1}$. We adopt a Jastrow correlated ground state and a basis of correlatedparticle-hole and phonon states. We insert correlated one particle-one hole andone-phonon states to compute the second order response. The decay of theone-phonon states into two-phonon states is accounted for in boson-bosonapproximation. The full response is splitted into three partial components$S_{\alpha \beta}(q,\omega)$, each of them showing a particle-hole bump and aone phonon, delta shaped peak, which stays separated from the multiphononbackground. The cross term $S_{34}(q,\omega)$ results to be of comparableimportance to $S_{33}(q,\omega)$ in the particle-hole sector and to$S_{44}(q,\omega)$ in the phonon one. Once the one-phonon peak has beenconvoluted with the experimental broadening, the computed scattering functionis in semiquantitative agreement with recent experimental measurements.

physical review. b, condensed matter

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Microscopic approach to the response of−43He mixtures