THE DISPERSION OF HE-3 QUASI-PARTICLES IN HE-II FROM NEUTRON-SCATTERING

In an inelastic neutron scattering (INS) experiment on He-3-He-4 mixtu res one observes, besides the photon-roton mode which is barely modifi ed by the admixture of He-3, an additional excitation at lower energie s which is interpreted as quasi-particle-hole excitations of a nearly free Fermi gas. We reanalyse INS data of x3 = 1% and 4.5% mixtures at various pressures to extract the mean energy omega(q) of the fermions. In the momentum range 9 < q < 17 nm-1 (above 2k(F)) omega(q) follows very closely the relation omega(q) = A2q2+ A4q4 at all concentrations, pressures and temperatures observed In a 4.5 % mixture (T(F) almost-e qual-to 0.3 K), measurements were performed for temperatures in the ra nge 0.07 < T < 0.9 K. We find both A2 and A4 to be strongly temperatur e dependent. For the interpretation of thermodynamical properties, the single particle energy epsilon(k) is parametrized as epsilon(k) = eps ilon0 + 1/(2m).k2.(1 + gammak2). Neglecting interactions between ferm ions, we calculate from the free-particle epsilon(k) the scattering fu nction S(q, omega) and the mean value of the fermion peak energy omega (q) = integral omegaS3(q, omega) domega/integral S3(q, omega) domega. We find that omega(q) follows closely epsilon(q), deviating at most by 10%. A comparison to the measured A2 and A4 directly yields m(x3, p, T) and gamma(x3, p, T). In the limit x3 = 0, p = 0 and T = 0, the den sity 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-Bradley e t al. are well represented by our model at T < 0,5 K.