Journal of Physics A. Mathematical and General vol:30 issue:14 pages:4895-4913
The theory of Bogoliubov contains the prescription of replacing the ground-state mode a(0)/root V by a constant b. In a previous contribution, we showed that the Bogoliubov model was thermodynamically unstable. We stabilized this model by adding 'forward scattering' terms. In this paper we exploit the fact that it is not compulsary to take b equal to c = (a(0))/root V. We show that if b = c the Bogoliubov theory does not have a satisfactory thermodynamics. We prove that it is possible to make a proper choice of the ground-slate mode. i.e. b as a function of c, in order to obtain the correct excitation spectrum and thermodynamically a second-order phase transition, as is compulsory for a theory of superfluidity.