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53 degrees 70 degrees aG(Q Airy functions approximately assume atom-surface potential atom-surface scattering azimuthal angle azimuthal scan bound state energies boundary conditions Bragg diffracted calculations Chemical Physics class F collision corresponding curve Debye-Waller constant Debye-Waller factor Debye-Waller scaling define diffracted beams diffracted intensities elastic exp(i(K experimental fluorine free beam Green function hard corrugated hard wall incident atom incident polar angle inelastic effects isolated resonance Journal of Chemical kQzz laterally averaged potential lineshape Lippmann-Schwinger equation lower graph matrix elements maximum non-resonant particles peak phonon phonon wavevector Polar scan propagator quantum Quantum Mechanics Rayleigh wave Re(b reciprocal angstroms reciprocal lattice vectors reciprocal vector Reference repulsive resonant features RESONANT SCATTERING THEORY resonant vector S-Matrix scattered intensity scattering amplitude selection rule solve specular beam specular intensity substitute surface corrugation surface potential Surface Science term theoretical unitarity upper graph wave wavefunction wavevector