Exact limiting relation between the structure factors in neutron and x-ray scattering

The ratio of the static matter structure factor measured in experiments on coherent X-ray scattering to the static structure factor measured in experiments on neutron scattering is considered. It is shown theoretically that this ratio in the long-wavelength limit is equal to the nucleus charge at arbitrary thermodynamic parameters of a pure substance (the system of nuclei and electrons, where interaction between particles is pure Coulomb) in a disordered equilibrium state. This result is the exact relation of the quantum statistical mechanics. The experimental verification of this relation can be done in the long wavelength X-ray and neutron experiments.Comment: 7 pages, no figure

Coexistence of the "bogolons" and the one-particle spectrum of excitations with a gap in the degenerated Bose gas

Properties of the weakly non-ideal Bose gas are considered without suggestion on C-number representation of the creation and annihilation operators with zero momentum. The "density-density" correlation function and the one-particle Green function of the degenerated Bose gas are calculated on the basis of the self-consistent Hartree-Fock approximation. It is shown that the spectrum of the one-particle excitations possesses a gap whose value is connected with the density of particles in the "condensate". At the same time, the pole in the "density-density" Green function determines the phonon-roton spectrum of excitations which exactly coincides with one discovered by Bogolyubov for the collective excitations (the "bogolons").Comment: 8 pages, no figure