  Motivated by recent experiments, which give strong evidence for an excitonic
insulating phase in $\rm TmSe_{0.45}Te_{0.55}$, we developed a scheme to
quantitatively construct, for generic two-band models, the phase diagram of an
excitonic insulator. As a first application of our approach, we calculated the
phase diagram for an effective mass two-band model with long-range Coulomb
interaction. The shielded potential approximation is used to derive a
generalized gap equation controlling for positive (negative) energy gaps the
transition from a semi-conducting (semi-metallic) phase to an insulating phase.
Numerical results,obtained within the quasi-static approximation, show a
steeple-like phase diagram in contrast to long-standing expectations.
