  We calculate dilepton production rates from a fireball adapted to the
kinematical conditions realized in ultrarelativistic heavy ion collisions over
a broad range of beam energies. The freeze-out state of the fireball is fixed
by hadronic observables. We use this information combined with the initial
geometry of the collision region to follow the space-time evolution of the
fireball. Assuming entropy conservation, its bulk thermodynamic properties can
then be uniquely obtained once the equation of state (EoS) is specified. The
high-temperature (QGP) phase is modelled by a non-perturbative quasiparticle
model that incorporates a phenomenological confinement description, adapted to
lattice QCD results. For the hadronic phase, we interpolate the EoS into the
region where a resonance gas approach seems applicable, keeping track of a
possible overpopulation of the pion phase space. In this way, the fireball
evolution is specified without reference to dilepton data, thus eliminating it
as an adjustable parameter in the rate calculations. Dilepton emission in the
QGP phase is then calculated within the quasiparticle model. In the hadronic
phase, both temperature and finite baryon density effects on the photon
spectral function are incorporated. Existing dilepton data from CERES at 158
and 40 AGeV Pb-Au collisions are well described, and a prediction for the
PHENIX setup at RHIC for sqrt(s) = 200 AGeV is given.
