THE DIRECT INVERSION OF HELIUM ATOM SCATTERING (HAS) DIFFRACTION SPECTRA

Abstract

An algorithm that provides direct, efficient ND polynomial factorization is presented to solve the numerical issues that arise during the direct inversion of helium atom scattering (HAS) diffraction spectra. For an n-variate polynomial the algorithm directly deflates the polynomial to n-single variable equations by evaluating the ratio of pairs of polynomial coefficients. Error estimation of the coefficients of the 1D polynomials is then performed automatically using standard 1D search techniques. The effectiveness of the technique is demonstrated against bi- and trivariate polynomials and an approximate range of validity for error prone polynomials is demonstrated. To demonstrate the effectiveness of the technique, HAS diffraction spectra for the low coverage (2 × 1)-H/Pd(311) system have been analyzed using direct inversion and have revealed that H binds in a three-fold hollow site.