In the present work we have shown experimentally that the light emissi
on intensity from a STM tunneling junction depends exponentially on th
e tunneling distance, and we believe that the decay constant is equal
to the mean wave vector of the surface plasmons excited by the tunneli
ng electrons. Our estimation of the plasmon phase velocity shows that
this is about two times smaller than the Fermi velocity of the electro
ns inside the metal. Theoretically, we have developed a description of
the phenomenon based on resonant Cherenkov interaction between the tu
nneling electrons and the propagating surface plasmons. Our calculatio
ns of the dispersion law of the surface plasmons and the quantum effic
iency for plasmon emission by the tunneling electrons are in qualitati
ve agreement with the experimental data.