Thermal Dilepton Radiation from Finite Fireball

We analyze the dilepton emission rates from the hot pion gas confined to a finite space-time volume. Two models of pion(+) pion(-) annihilation to dileptons are under consideration. The first model mimics an extreme influence of the dense hadron environment on the rho-meson mean free path and mean life time. The second model deals with the standard concept of vector meson dominance when the hadron medium is not accounted. Our results indicate that the dilepton rates are finite in the low invariant mass region M<2m_\pi. It is found that the rates experience an enhancement in the electron-positron production when invariant mass tends to the "real" threshold M=2m_e. The breaking of the detailled energy-momentum conservation in favour of the integral one due to broken translation invariance is discussed.