Catastrophe theory and resonance line shapes in atom-surface scattering

The measured high-resolution energy profile of a selective adsorption reson ance in the scattering of He atoms from NaCl(001) is found to exhibit a mix ed-extrema structure reminiscent of a Fano-type function. An analysis of th e topological properties of the resonance line shape as a function of the s urface temperature reveals a behavior which is isomorphic to the simplest e lementary catastrophe, the fold catastrophe. As the crystal temperature app roaches the surface Debye temperature Theta(D) of NaCl the resonance profil e undergoes a transition in its topology according to the behavior of the f old catastrophe. The analysis is sufficiently general in order to be extend ed to any resonant scattering event displaying Fano-type profiles. [S0163-1 829(99)00633-5].