The dispersion of³He quasiparticles in He II from neutron scattering

Abstract

In an inelastic neutron scattering (INS) experiment on³He-⁴He mixtures one observes, besides the photon-roton mode which is barely modified by the admixture of³He, an additional excitation at lower energies which is interpreted as quasi-particle-hole excitations of a nearly free Fermi gas. We reanalyse INS data ofx ₃=1% and 4.5% mixtures at various pressures to extract the mean energy$\hat \omega _q$ of the fermions. In the momentum range 9<q<17 nm⁻¹ (above 2k _F )$\hat \omega _q$ follows very closely the relation$\hat \omega _q$=A ₂ q ²+A ₄ q ⁴ at all concentrations, pressures and temperatures observed. In a 4.5% mixture (T _F ≈0.3 K), measurements were performed for temperatures in the range 0.07<T<0.9 K. We find bothA ₂ andA ₄ to be strongly temperature dependent. For the interpretation of thermodynamical properties, the single particle energy ε _k is parametrized as ε _k =ε_o+1/(2ms*) ·k ₂ · (1+γk ²). Neglecting interactions between fermions, we calculate from the free-particle ε _k the scattering functionS(q, ω) and the mean value of the fermion peak energy ω _q =∫ ωS ₃(q, ω)dω/∫S ₃(q, ω)dω. We find that$\hat \omega _q$ follows closely ε _q , deviating at most by 10%. A comparison to the measuredA ₂ andA ₄ directly yieldsms* (x ₃,p, T) and γ(x ₃,p, T). In the limitx ₃=0,p=0 andT=0, the density and concentration dependence of the inertial mass is in excellent agreement with values found by Sherlock and Edwards. The temperature dependence of the specific heat data from Greywall and Owers-Bradleyet al. are well represented by our model atT<0,5 K.