Ground State Energy of Bose Particle System

The ground state energy of the Bose particle system at low densities is investigated by using a method based on summing the terms of conventional perturbation series, giving rise to the lowest order with respect to density. The summation is shown to be greatly simplified if the scattering matrix is introduced, and a simple example is demonstrated for the repulsive square well potential by calculating a few terms of the series, first directly and secondly with the aid of scattering matrix. The final result is shown to be valid both for weak and strong interactions and the calculation is carried out analytically for some types of potential function. The connection of the method with the pseudopotential method and with the Brueckner theory is investigated, and some problems associated with the attractive interactions are discussed. (auth)