Analysis of positron annihilation lifetime data by numerical laplace inversion with the program CONTIN

Abstract

The performance of the program CONTIN [Stephen W. Provencher, Comput. Phys. Commun. 27 (1982) 229], modified to solve Fredholm integral equations with convoluted kernels of the type that occur in the deconvolution and analysis of positron annihilation lifetime data, is investigated with computer-simulated test data. The method avoids direct determination of the instrument resolution function by employing the decay curve of a reference material with a well-known single lifetime. CONTIN employs a constrained, regularized least-squares analysis to calculate a continuous annihilation-rate probability density function (pdf) which is the most parsimonious solution that is consistent with the experimental data and prior knowledge. The performance of the algorithm for extracting positron annihilation lifetime information was evaluated by using several measures of the information content of the data described by Schrader and Usmar [in: Positron Annihilation Studies of Fluids, ed. S. Sharma (World Scientific, Singapore, 1988) p. 215]. The quality of the CONTIN reconstruction of the annihilation-rate pdf is strongly dependent on the information content of the data and is greatly improved as the total number of counts in the data set is increased. Nevertheless, the method provides excellent estimates of the intensities and mean lifetimes of peaks in the annihilation-rate pdf, even when the total counts in the data set are relatively low (10 5–10 6). The sensitivity of the algorithm to systematic errors in the data, including errors in the instrument resolution function, shifts in the positron of the zero-time channel of the sample and reference data and contamination of the reference decay by additional lifetime components was also evaluated. Errors in the FWHM of the instrument resolution function and shifts in the zero time channel as small as 1 10 to 1 5 of the channel width of the instrument generate additional spurious peaks in the annihilation-rate pdf and introduce errors in the lifetime parameters of the short-lived components.