Particle-hole excitations in normal liquidHe3

Abstract

The dynamic form factor $S(Q,E)$ in liquid $^{3}\mathrm{He}$ is evaluated in the momentum-transfer range $2\ensuremath{\le}Q\ensuremath{\le}5$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ for comparison with neutron scattering measurements. In this momentum range the neutrons excite chiefly interacting single particle-hole ($p\ensuremath{-}h$) excitations but no collective excitations. $S(Q,E)$ is calculated within an extended random-phase approximation (RPA) and the single $p\ensuremath{-}h$ energy spectrum and $p\ensuremath{-}h$ 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 $Q=2$ ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ are well described by a single $p\ensuremath{-}h$ excitation spectrum having effective mass ${m}^{*}\ensuremath{\approx}1$, a strongly negative spin-symmetric $p\ensuremath{-}h$ interaction and a nearly zero spin-antisymmetric interaction. This comparison also suggests that the $p\ensuremath{-}h$ 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.