Density matrices of superfluid helium-4. I

Calculation of density matrices for the ground state of interacting boson systems is performed on the basis of the method suggested before. Many-particle correlations are taken into account. General expression is found which makes it possible to reduce the calculation of density matrices in any approximation to simple parametric differentiation. Perturbation theory for the logarithm of the density matrix is developed in such a way that each term includes one more summation over the wave vector than the preceding term. Corrections are explicitely calculated the expressions for which include the double summation over the wave vector. This corresponds to taking into account the contributions of three-particle correlations and those four-particle correlations in the wave function which can be represented by means of the double Fourier series.