Particle-hole excitations in normal liquidHe3

The dynamic form factor $S(Q,E)\mathrm{}$ in liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is evaluated in the momentum-transfer range $2\le Q\le 5$ ${\mathrm{\AA }}^{-1\mathrm{}}$ for comparison with neutron scattering measurements. In this momentum range the neutrons excite chiefly interacting single particle-hole ($p-h$) excitations but no collective excitations. $S(Q,E)\mathrm{}$ is calculated within an extended random-phase approximation (RPA) and the single $p-h$ energy spectrum and $p-h$ interaction needed in the RPA is provided by the Galitskii-Feynman-Hartree-Fock (GFHF) theory of liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. The GFHF is a first-principles theory having no adjustable parameters with only the pair interatomic potential as input. Comparison with experiment suggests that the excitations at $Q=2\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$ are well described by a single $p-h$ excitation spectrum having effective mass $m^{*}\approx 1$, a strongly negative spin-symmetric $p-h$ interaction and a nearly zero spin-antisymmetric interaction. This comparison also suggests that the $p-h$ spectrum is well represented by the GFHF spectrum, the real part of the interaction by the Galitskii-Feynman (GF) $T$ matrix, but that the imaginary part of the GF $T$ matrix is too large.