Reasons for the deviation of I₁/I₃ and τ₁ from the expected lifetime parameters of positronium annihilation in polymers

High quality positron lifetime spectra were taken for several amorphous polymers. The spectra were analysed using the routine MELT which assumes continuous lifetime distributions, as well as the discrete-term analysis routine LIFSPECFIT. Disagreements between the analysed lifetime parameters and theoretical expectations, I₁/I₃I_p-Ps/I_{o- Ps}=1/3 and τ₁τ_p-Ps, which are well known, also appear in our results. The disagreements are distinctly larger using a discrete-term routine than when applying MELT (or CONTIN). From the analysis of computer-generated spectra, we found that these disagreements may be well understood by assuming a distribution of e⁺ lifetimes in addition to an o-Ps lifetime distribution, both of which can occur as consequence of size and shape distributions of free-volume holes in amorphous polymers (or of bubbles in molecular liquids). The disagreements appear to be due to the inability of the routines correctly to mirror very broad lifetime distributions. For broad distributions, MELT (and also CONTIN) delivers, as an artefact of the spectrum analysis, a distribution consisting of two narrow subpeaks instead of a single broad one. The lower subpeak of the e⁺ lifetime distribution may mix with the p-Ps lifetime component resulting in artificially large values for τ₁ and I₁. That is the reason for the unphysical increase of τ₁ and I₁ with decreasing I₃ observed in the analysed parameters of simulated as well as experimental spectra.