  Atom scattering is becoming recognized as a sensitive probe of the
electron-phonon interaction parameter $\lambda$ at metal and metal-overlayer
surfaces. Here, the theory is developed linking $\lambda$ to the thermal
attenuation of atom scattering spectra (in particular, the Debye-Waller
factor), to conducting materials of different dimensions, from quasi-one
dimensional systems such as W(110):H(1$\times$1) and Bi(114), to quasi-two
dimensional layered chalcogenides and high-dimensional surfaces such as
quasicrystalline 2ML-Ba(0001)/Cu(001) and d-AlNiCo(00001). Values of $\lambda$
obtained using He atoms compare favorably with known values for the bulk
materials. The corresponding analysis indicates in addition the number of
layers contributing to the electron-phonon interaction that is measured in an
atom surface collision.
