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A new quantum-theoretical derivation of the elastic and inelastic scatteringprobability of He atoms from a metal surface, where the energy and momentumexchange with the phonon gas can only occur through the mediation of thesurface free-electron density, shows that the Debye-Waller exponent is directlyproportional to the electron-phonon mass coupling constant $\lambda$. Thecomparison between the values of $\lambda$ extracted from existing data on theDebye-Waller factor for various metal surfaces and the $\lambda$ values knownfrom literature indicates a substantial agreement, which opens the possibilityof directly extracting the electron-phonon coupling strength in quasi-2Dconducting systems from the temperature or incident energy dependence of theelastic Helium atom scattering intensities.

The electron-phonon coupling strength at metal surfaces directly determined from the Helium atom scattering Debye-Waller factor