Catastrophe theory and resonance line shapes in atom-surface scattering

The measured high-resolution energy profile of a selective adsorption resonance in the scattering of He atoms from NaCl(001) is found to exhibit a mixed-extrema structure reminiscent of a Fano-type function. An analysis of the topological properties of the resonance line shape as a function of the surface temperature reveals a behavior which is isomorphic to the simplest elementary catastrophe, the fold catastrophe. As the crystal temperature approaches the surface Debye temperature Theta(D) of NaCl the resonance profile undergoes a transition in its topology according to the behavior of the fold catastrophe. The analysis is sufficiently general in order to be extended to any resonant scattering event displaying Fano-type profiles. [S0163-1829(99)00633-5].