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The dynamic structure factor and the eigenmodes of density fluctuations inthe uniform liquid $^3$He are studied using a novel non-perturbative approach.This new version of the self-consistent method of moments invokes up to ninesum rules and other exact relations involving the spectral density, thetwo-parameter Shannon information entropy maximization procedure, and the abinitio path integral Monte Carlo (PIMC) simulations which provide crucialreliable input information on the system static properties. Detailed analysisof the dispersion relations of collective excitations, the modes decrements andthe static structure factor (SSF) of $^3$He at the saturated vapor pressure isperformed. The results are compared to available experimental data~[1,2]. Thetheory reveals a clear signature of the roton-like feature in the particle-holesegment of the excitation spectrum with a significant reduction of the rotondecrement in the wavenumber range $1.3 A^{-1} \leq q\leq 2.2 A^{-1}$. Theobserved roton mode remains a well defined collective excitation even in theparticle-hole band, where, however, it is strongly damped. Hence, the existenceof the roton-like mode in the bulk liquid $^3$He is confirmed like in otherstrongly interacting quantum fluids~[3]. The phonon branch of the spectrum isalso studied with a reasonable agreement with the same experimental data beingachieved. The presented combined approach permits to produce ab initio data onthe system dynamic characteristics in a wide range of physical parameters andfor other physical systems.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Dynamic properties and the roton mode attenuation in the liquid 3He: an ab initio study within the self-consistent method of moments