  A detection technique for ultra-high energy cosmic rays, complementary to the
fluorescence technique, would be the use of the molecular Bremsstrahlung
radiation emitted by low-energy ionization electrons left after the passage of
the showers in the atmosphere. In this article, a detailed estimate of the
spectral intensity of photons at ground level originating from this radiation
is presented. The spectral intensity expected from the passage of the
high-energy electrons of the cascade is also estimated. The absorption of the
photons in the plasma of electrons/neutral molecules is shown to be negligible.
The obtained spectral intensity is shown to be $2\times10^{-21} $W cm$^{-2}$
GHz$^{-1}$ at 10 km from the shower core for a vertical shower induced by a
proton of $10^{17.5}$ eV. In addition, a recent measurement of Bremsstrahlung
radiation in air at gigahertz frequencies from a beam of electrons produced at
95 keV by an electron gun is also discussed and reasonably reproduced by the
model.
