A dense Bose fluid at zero temperature: condensation and clusters in liquid He-4

We present a full set of wave equations describing a dense Bose fluid, applicable both to non- ideal gases and to liquid 4He. The phonon spectrum in liquid 4He is found and the fraction of condensed particles is calculated at zero temperature for a wide range of densities. The theory also yields the ground-state energy for the quantum liquid 4He in agreement to high accuracy with Monte Carlo simulations and experimental data at low pressure. We also present the derivation of a generalized Hartree-Fock equation describing roton clusters in low temperature liquid 4He, allowing us to confirm that, at low enough temperatures and for a wide range of pressures, the stable clusters consist of 13 bound atoms.