  The aim of this work is to investigate how energy depends on the two-body
interaction potential in Bose-Einstein condensation (BEC) phenomena. An
equation of state is obtained which is valid both for low and high energy BEC,
through the application of a revised form of quantum statistics. An extension
of the singularity conditions describing the state of BEC is given, in order to
consider interactions between particles due to a central interatomic potential.
  From the singularity conditions of the corresponding system of hard-sphere
bosons and the equation for the energy of the system in its ground state, the
equation of state connecting temperature, density and energy in BEC is deduced,
with upper and lower limits for the energy depending on the form of the central
interaction potential. It is shown that high energy mode is allowed in the case
of Coulomb type interaction only, low energy mode in the case of non-Coulomb
type interaction. Numerical results are then derived for low energy BEC,
occurring in neutral matter, with application to He-4 and alkali-metal atoms,
and in the case of high energy BEC occurring in systems of charged bosons, with
application to atomic nuclei.
