Probability density function from experimental positron annihilation lifetime spectra

Abstract

A inversão de espectro experimental de vida média de aniquilação de pósitron foi realizada com o intuito de se obter a função densidade de probabilidade. A resolução do aparelho, juntamente com ruído experimental foram considerados na resolução deste problema mal-colocado. O método de decomposição em valores singulares, movendo-se o limite entre os subespaços foi a formulação teórica empregada para calcular a função densidade de probabilidade. O complexo Al(dpm) 3 , sistema considerado no presente trabalho, apresenta três picos no espectro invertido, indicando a presença de para-positrônio, pósitron livre e orto-positrônio. As posições previstas foram 0,1042 ns, 0,3542 ns e 1,3958 ns, respectivamente. Como o presente método fornece a distribuição das espécies, é possível também prever a relativa importância de cada espécie no espectro. As áreas obtidas foram: 13%, 32%, 55%. Ambos resultados, posição dos picos e áreas relativas, bem como a distribuição dos tempos de meia-vida, podem fornecer informações importantes para experimentalistas.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 orthoPositronium. 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.

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