Abstract
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 ${\ensuremath{\Theta}}_{D}$ 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.
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