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Since the decomposition of positron lifetime spectra requires solving an ill-posed and inverse problem, the accurate knowledge of the spectrometer's instrument response function is crucial for extracting the true underlying physical information of the phenomenon under investigation. In general, the instrument response function is modelled by a superposition of Gaussian functions, since an analytical solution for the convolution with an exponential distribution function exists and, hence, the characteristic lifetimes and its corresponding contributions can be obtained by non-linear least-squares fitting. In contrast, the iterative least-squares re-convolution approach determines the best fit of the recorded lifetime spectrum by re-convoluting a sum of N expected exponential decays with the numerical data of the experimentally obtained instrument response function. For a laboratory setup, two methods exist to estimate the shape of the instrument response function from experiment: (1) the direct method using a Co-60 isotope and an indirect method by graphically deconvoluting the monoexponential lifetime spectrum obtained from Bi-207. For both variants, the energies of the incident gamma-rays are considerably different to the energies accompanying the creation (1274 keV) and annihilation (511 keV) of a positron using Na-22: Co-60 (1173 keV, 1333 keV), Bi-207 (570 keV, 1064 keV). Here we present a detailed study on the basis of plastic scintillators regarding the spectra decomposability by using the re-convolution technique with experimentally obtained instrument response functions. We can clearly show that beyond incident gamma-ray energy differences, the Compton scattering effects and pile-up events represent the limiting factors in this approach.

acta physica polonica. a

Limitations on the Positron Lifetime Spectra Decomposability Applying the Iterative Least-Square Re-Convolution Method Using the Instrumental Responses Obtained from 207Bi and 60Co