Theory of Brueckner and Sawada applied to a many-boson model

The Bassichis–Foldy model of a simple interacting boson is solved numerically and the results are compared with those obtained by the Bogoliubov approximation and by the Brueckner–Sawada t-matrix formalism. In the normal region, contrary to the widely held view, the Brueckner–Sawada approximation for the energy of the ground state is not reliable for strong, well-behaved, repulsive forces. The Bogoliubov approximation, on the other hand, remains valid for a wide range of values of the coupling constant. In the inverted region, the attractive force causes a population inversion in the levels of the system. For this case a modified Brueckner–Sawada approximation is developed. This method is applied to the calculation of the transition point and the energies of the ground and the first excited states of the system. Here most of the predictions of the modified Brueckner–Sawada approximation are quite accurate. By a simple change in the Bassichis–Foldy model it is shown that even, for two bosons there can be a phase transition. In this model, the derivative of the ground state energy with respect to the coupling constant is discontinuous at the transition point.