The characteristic function method in surface diffusion

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. 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 also a central goal in condensed matter physics. 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. Furthermore, the frequency moments or sum rules are also calculated from the intermediate scattering function. The role played by this function, when Helium atoms are used for probing adsorbates, is essential to clearly show some important differences which are genuine of this scattering with respect to nuclear scattering. In order to illustrate this 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, leading to some discrepancies for the diffusion coefficient values previously reported. Finally, an extension to jumps to more than nearest neighbors has also been considered.