Investigation of the temperature dependence of the Bose condensate density in helium 4 in relation to the superconductivity phenomenon

The experimental results on the relative-density temperature dependence of the Bose-condensate (BC) and on the mean kinetic energy per atom in a liquid hellium-4 are discussed. The investigation has been carried out by studying the spectra of inelastic neutron scattering at the momentum transfers k=12 - 14 A-1 at the temperatures of 1.2 -4.2 K. The experimental data have been analyzed by means of the two-gaussian and one-gaussian models. The BC relative density is estimated by the method of two-gaussian expansion of spectra of neutrons scattered by liquid helium. The temperature dependence has a singularity at T0. BC is observed at TT0 within the accuracy of an experiment and mathematical data processing. The BC relative density at T→0 makes up 0.022+-0.002, the temperature of the Bose condensation coinciding with that of the lambda-transition