Analysis of positron annihilation lifetime data by numerical Laplace inversion: Corrections for source terms and zero-time shift errors

Abstract

Abstract We have recently described modifications to the program CONTIN [S.W. Provencher, Comput. Phys. Commun. 27 (1982) 229] for the solution of Fredholm integral equations with convoluted kernels of the type that occur in the analysis of positron annihilation lifetime data [R.B. Gregory and Yongkang Zhu, Nucl. Instr. and Meth. A290 (1990) 172]. In this article, modifications to the program to correct for source terms in the sample and reference decay curves and for shifts in the position of the zero-time channel of the sample and reference data are described. Unwanted source components, expressed as a discrete sum of exponentials, may be removed from both the sample and reference data by modification of the sample data alone, without the need for direct knowledge of the instrument resolution function. Shifts in the position of the zero-time channel of up to half the channel width of the multichannel analyzer can be corrected. Analyses of computer-simulated test data indicate that the quality of the reconstructed annihilation rate probability density functions is improved by employing a reference material with a short lifetime and indicate that reference materials which generate free positrons by quenching positronium formation (i.e. strong oxidizing agents) have lifetimes that are too long (400–450 ps) to provide reliable estimates of the lifetime parameters for the shortlived components with the methods described here. Well-annealed single crystals of metals with lifetimes less than 200 ps, such as molybdenum (123 ps) and aluminum (166 ps) do not introduce significant errors in estimates of the lifetime parameters and are to be preferred as reference materials. The performance of our modified version of CONTIN is illustrated by application to positron annihilation in polytetrafluoroethylene.