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The Temperature Dependence of the Static Structure Factor for Liquid 4He Below Tλ

The temperature dependence of the structure factor S(k, T) is studied based on an assumption that the anomalous behaviour of S(k, T) below Tλ is due to thermally excited rotons and phonons. The calculation of S(k, T) is performed with the help of the HNC-equation from a model density matrix of Penrose which in turn is obtained from a quasiparticle Hamiltonian describing elementary excitations of liquid helium (both phonons and rotons). The results are in qualitative agreement with recent neutron and X-ray scattering experiments below Tλ. The theoretical temperature correction is used to deduce S(k, T = 0) separately from the most recent X-ray and neutron scattering experiments.