Bogoliubov approximation as a second-order approximation in the spectral-density method. II

A method, based on the second-order approximation in the spectral-density approach, which avoids the difficulties which appear in the Bogoliubov approximation for an interacting Bose system is discussed. The prescriptions are indicated under which, starting from the original number-conserving Hamiltonian, the known Bogoliubov results and the possibility to obtain corrections to those results emerge in a natural way. Explicit calculations are made at zero temperature for a high-density Bose model with a repulsive soft core and a strong attraction between the particles and the self-consistence of the above prescriptions is explicitly proved. (author)