  We carefully analyse the contribution to the oscillations of a metallic
gravitational antenna due to the interaction between the electrons of the bar
and the incoming gravitational wave. To this end, we first derive the total
microscopic Hamiltonian of the wave-antenna system and then compute the
contribution to the attenuation factor due to the electron-graviton
interaction. As compared to the ordinary damping factor, which is due to the
electron viscosity, this term turns out to be totally negligible. This result
confirms that the only relevant mechanism for the interaction of a
gravitational wave with a metallic antenna is its direct coupling with the bar
normal modes.
