The characteristic function method in surface diffusion

In surface diffusion, one of the key observables is the so-called intermediate scattering function which is measured directly from the helium spin echo surface technique. This function is shown to be a characteristic function of probability theory; in fact, it is the central dynamical measurement which clearly emphasizes that the relationship between the structure and dynamical process is a central goal in condensed matter physics. It is also the generating function of the moments and cumulants of the jump distribution function at any order; in particular, the second order which is related to the diffusion coefficient. Furthermore, the frequency moments or sum rules are also calculated from this scattering function and are written in terms of the total jumping rate. The role played by this function, when helium atoms are used for probing adsorbates (here we assume non-interacting adsorbates or very low surface coverages), is essential to clearly show some important differences with respect to neutron scattering. In order to illustrate this new approach, the method of the characteristic function, we have focused on the incoherent tunneling of H and D on a Pt(111) surface. This analysis has led us to some discrepancies with respect to the diffusion coefficient values previously reported. Finally, an extension to jumps beyond nearest neighbors is also considered theoretically.