Results on the quasiparticle model for liquid He4 at finite temperatures

Within the interacting-quasiparticle model, we find several identities expressing the thermal energy H in terms of parameters entering the thermal-neutron scattering function S(q,ω) and an unknown interaction term. A new form for S(q,ω) at finite T is found which should be useful in analyzing neutron experiments. The only approximations are that the self-energies ij(q,ω) are independent of ω, and that the density ρq→ is linear in the boson operators αq→† and αq→ of the model.