Surface diffusion: The intermediate scattering function seen as a characteristic function of probability theory

Abstract: In surface diffusion, one of the key observables is the so-called intermediate scattering function which is measured directly from the surface technique called Helium spin echo. In this work, we show that this function can be seen as a characteristic function of probability theory. From the characteristic function, the moments and cumulants of the probability distribution function of the position of the adsorbate are straightforward obtained in an analytical way; in particular, the second order which is related to the diffusion coefficient. In order to illustrate this simple theory, we have focused on the incoherent tunneling of H and D on a Pt(111) surface where only jumps between nearest neighbor sites have been reported experimentally. Finally, an extension to jumps to more than nearest neighbors has also been considered.