A potential detection technique of ultra-high energy cosmic rays would be the use of the molecular Bremsstrahlung radiation emitted by low-energy electrons left after the passage of the showers in the atmosphere. The emission mechanism is expected from quasi-elastic collisions of electrons produced in the shower by the ionisation of the molecules in the atmosphere. Given the low energy of the ionisation electrons, GHz photons resulting from this emission mechanism are expected to be emitted

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... ropically. This would allow for mapping the ionisation content along the showers through the intensity of the microwave signals detected at ground, in the same way as done for the fluorescence technique. In this contribution, a detailed calculation of the spectral intensity of photons at ground level originating from the transitions between unquantised energy states of free ionisation electrons is presented. The obtained spectral intensity is shown to be 4.0 10 −26 W m −2 Hz −1 at 10 km from the shower core for a vertical shower induced by a proton of 10 17.5 eV. The detectability of the derived spectral intensities with the current experimental setups is discussed.