Positronium formation probability

The positronium formation probability Lq-ps is strongly reduced by the presence of electron acceptor groups in the polymer, since these groups trap free electrons that have been excited in the spur of the injected positrons, which otherwise could have formed positronium together with the positron [2, 4, 5]. 

Fig. 29.1 shows the PALS analysis of a 650 nm epoxy film on an Au substrate, which demonstrates that the dependence of Iq-ps on the average positron implantation depth. 7o-Ps is quite constant at 28% over a depth interval between 50 and 400 nm. Above 400 nm, lo.ps is significantly reduced. Some of the positrons with implantation depths above 650 nm penetrate into the metal substrate or even deeper into the silicon wafer. Neither in metal nor in sihcon is positroni-um formed. Therefore, the positronium formation probability Iq-ps is reduced by the number of positrons penetrating the substrate. 

Fig. 29.1 PALS analysis of an unaged epoxy thin film on an Au substrate. Ortho-positronium formation probability Ps is given as a function of average positron implantation depth.

Two series of cellulose samples, Avicel and Whatman CFll cellulose ball-milled powders with different crystallinity are studied below Tg temperature by using positron annihilation lifetime spectroscopy. A good correlation is found between ortho-positronium formation probability and crystallinity as measured by Fourier transform -infrared spectroscopy. Sub-nanometer hole distributions are found to be narrowed as a function of milling time. These are interpreted in terms of microstructural changes of cellulose. 

Probably the most accurate positron-hydrogen s-wave phase shifts are those obtained by Bhatia et al. (4974), who avoided the possibility of Schwartz singularities by using a bounded variational method based on the optical potential formalism described previously. These authors chose their basis functions spanning the closed-channel Q-space, see equation (3.44), to be of essentially the same Hylleraas form as those used in the Kohn trial function, equation (3.42), and their most accurate results were obtained with 84 such terms. By extrapolating to infinite u in a somewhat similar way to that described in equation (3.54), they obtained phase shifts which are believed to be accurate to within 0.0002 rad. They also established that there are no Feshbach resonances below the positronium formation threshold. 

The most accurate theoretical results for positronium formation in positron-helium collisions in the energy range 20-150 eV are probably those of Campbell et al. (1998a), who used the coupled-state method with the lowest three positronium states and 24 helium states, each of which was represented by an uncorrelated frozen orbital wave function... 

A semi-quantitative picture of positronium formation in a spur in a dense gas was developed by Mogensen (1982) and Jacobsen (1984, 1986). If the separation of the positron from an electron is r, and there is assumed to be only one electron in the spur (a so-called single-pair spur), then the probability of positronium formation in the spur, in the absence of other competing processes, can be written as [1 — exp(—rc/r)] here rc is the critical, or Onsager, radius (Onsager, 1938), given for a medium of dielectric constant e by... 

The lifetimes given above relate to positronium in vacuum. In the medium a new possibility of destruction appears the positron bound in Ps can annihilate with one of strange electrons having appropriate (opposite) spin orientation. The process is called pick-off and leads to two quantum annihilation. If the medium is paramagnetic, another process shortening the o-Ps lifetime is possible the interaction with magnetic moments can transform o-Ps into p-Ps, which decays almost immediately (conversion process). Both e and Ps can participate in chemical reactions with molecules of the medium changing the Ps formation probability... 

The results of the PALS investigations of the aging behavior of thin epoxy films are presented here. The decisive parameters of the PALS analysis for polymers are the formation probability lo.ps of ortho-positronium and its average lifetime To-ps- While lo-Ps predominantly represents the effectivity of the electron acceptor groups in the polymer, Tq.ps is directly correlated with the sizes of the free-volume voids. 

For the first time, aging investigations of thin epoxy films have been performed with the PALS beam technique in combination with other experimental techniques. The main quantities for the characterization of polymers with PALS are the average lifetime Tq-ps of ortho-positronium and its formation probability... 

The most interesting information from the chemical point of view may be obtained by measurement of the distribution of the lifetimes of the positrons or positronium atoms. In addition to the lifetime, this method also gives a measure of the relative probability of ort/io-positronium formation as a separable parameter. Hence, from the lifetime distribution, information is obtained not only on the rates of the chemical reactions and other interactions of the positronium, but also on the probability of positronium formation, e.g., the extents of the possible inhibitory processes. The only deficiency of the method is that it does not provide a possibility for simple differentiation between ortho-para conversion processes and the chemical reactions, since both processes cause a decrease in the lifetime. 

In addition, an effect resulting in inhibition of positronium formation was also observed during the development of the strongly polar pyridine-iodine complex. It is probable that a reaction competing with positronium formation occurs between the positrons and the negative charge localized on the molecule, and this causes the inhibitory effect. 

In order to determine the effect of the microstructure of the solution on the beta counting efficiency in toluene -Triton mixtures in a first series of experiments the positron annihilation parameters were determined in toluene - Triton mixtures containing various amounts of water. As can be seen from Eigs. 11 and 12, where the Parameter l2 which is correlated to the formation probability of thermal positronium, is plotted as a function of Triton (in the presence of 0 and 2 % water) concentration, increasing amounts of Triton reduce I2 to a semi-plateau value, while X2, the annihilation rate of the thermal positronium, changes only slightly. A more detailed plot of I2 at lower Triton concentration reveals that I2 remains constant up to 20 mM or 10 mM Triton in solutions containing 0 or 2 % water, respectively. 

According to Ore, the probability of positronium formation (Pps) can be estimated as follows ... 

The leptonic annihilation is nevertheless observable in hydrogen-antihydrogen collisions. Its main appearance is, however, due to indirect processes, namely the intermediate formation of positronium as a consequence of rearrangement collisions. In that case the leptons are likely to annihilate with a certain time delay after hadronic annihilation. This is because regardless the final state of positronium its life time is longer than that of the most probable final state of protonium with N = 23. 

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