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.
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