Inversion of experimental positron annihilation lifetime spectra was carried out to obtain the probability density function. Apparatus resolution together with experimental noise was taken into consideration while solving this ill posed problem. The singular value decomposition approach, moving the boundary between the subspaces was the theoretical formulation to calculate the probability density function. For the system considered, the Al(dpm)3 complex, three peaks will be presented in the inverted spectra, indicating the presence of the para-Positronium, the free positron and the ortho-Positronium. The predicted positions were, 0.1042 ns, 0.3542 ns and 1.3958 ns, respectively. Since the present approach gives the distribution of the species, it was possible also to predict the relative importance of each species in the spectra. The areas found correspond to: 13%, 32%, 55%. Both these results, position of the peaks and the areas, together with the half-life distribution can provide important information for experimentalists.
probability density function; positron annihilation lifetime espectra; singular value decomposition
