Fast Fourier transform deconvolution of positron annihilation Doppler-broadened lineshapes

A fast Fourier transform method for the deconvolution of positron annihilation Doppler-broadened lineshapes and their decomposition into different components is described. Different filters are tested on the positron annihilation line for two different systems which can be described as a superposition of three components, two Gaussian curves and an inverted parabola, convoluted with a measured resolution function; Cu containing a high proportion of krypton precipitates and physisorbed oxygen on graphite. Special attention is paid to the effect of filtering on narrow and on parabolic components, both of which need higher Fourier coefficients to be described fully. In the case of oxygen on graphite, which has a narrow component due to the annihilation of para-positronium comparison is made with analysis by repeated numerical convolution of modelled lineshapes. (author)