Density matrix of superfluid4He and temperature dependence of the static structure factor

We have computed properties of superfluid⁴He on the basis of a new density matrix which is based on a shadow wave function for the roton excitation. We deduce the separate contribution of kinetic and potential energy to a roton and find that a roton lowers the potential energy of the system. We find that S (k; T) and g(r; T) have an anomalous T dependence as found experimentally and the extra correlations present at finite T are induced by rotons. By computing the condensate fraction n₀(T) we find that the Cummings et al relation between g(r; T) and n₀(T) is violated and that it leads to a value of n₀(T) larger of the true one.