New results are reported that facilitate and improve trajectory reconstruction algorithms in positron emission tomography. By applying the ab initio methods to common e/sup +//M systems, we address (1) positron range effect in biological tissue and (2) the distribution of non-collinear effect in annihilation /spl gamma/ trajectories. To that aim, a suite of ab initio programs is developed that treats (N/sub p/p, N/sub e/e, e/sup +/) on the same footing including the total spin of the system. Bound-state energies, annihilation rates and momentum distributions have been computed with the accurate MRD-CI methods for several prototype biological molecules. In addition, related data available in the literatures are shortly summarized and reviewed. While many of recent PET improvements elaborate on detectors and TOF measurements, this work deals with PET resolution limits on the side of the measured system.