Measurement of 18O concentration profiles using resonant nuclear reactions

Abstract

A convolution procedure is described for the determination of ¹⁸O diffusion profiles from data taken using the nuclear reaction ¹⁸O(p, α)¹⁵N. A Van de Graaff generator is used as a source of protons. Three types of concentration profile for the reacting species are considered: a step function, an error function and a thin-film-diffusion function. These are convoluted with functions that represent the spread and straggling of the proton beam, and the shape of the resonance capture cross section. The fit with the measured curve of resonant alpha yield against proton energy is estimated by a x² analysis. The concentration profile parameters are varied so as to minimize x². The analysis has proved successful in measuring oxide thicknesses on chromium and oxygen diffusion profiles in TiO₂ and Cr₂O₃, and sample experiments are described.