  A new quantum-theoretical derivation of the elastic and inelastic scattering
probability of He atoms from a metal surface, where the energy and momentum
exchange with the phonon gas can only occur through the mediation of the
surface free-electron density, shows that the Debye-Waller exponent is directly
proportional to the electron-phonon mass coupling constant $\lambda$. The
comparison between the values of $\lambda$ extracted from existing data on the
Debye-Waller factor for various metal surfaces and the $\lambda$ values known
from literature indicates a substantial agreement, which opens the possibility
of directly extracting the electron-phonon coupling strength in quasi-2D
conducting systems from the temperature or incident energy dependence of the
elastic Helium atom scattering intensities.
