The Interrelation of Physics and Mathematics in Ion-Neutralization Spectroscopy

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Abstract
Because the Auger neutralization of an ion at a solid surface involves two electrons, the kinetic-energy distribution of electrons ejected in the process is related to the convolution of two transition-density functions involving electronic-state-density and transition-probability factors. This fact interrelates the physics and the mathematics of the problem in an important and interesting way. Knowledge of how the physics puts limitations on the functions involved which make deconvolution mathematically tractable and how the mathematical procedures provide information concerning the physics is absolutely essential to the successful operation of the ion-neutralization spectroscopy. The nature of possible spurious structure introduced by the mathematics has led to the devising of tests for such features. It is shown that these test procedures are entirely adequate for the "peaked" functions encountered. Some discussion of inversion procedures is provided in the appendices.