Pick off annihilation

These traps, (Fig. 6) and similar effects in the motion of holes and other charges through polymers, would eventually be correlated also with such structural probes as positron lifetimes in macromolecular solids. Extensive recent studies of positron lifetime are based on positronium decay. In this, the lifetime of o-positronium (bound positron-electron pair with total spin one) is reduced from about 140 nanoseconds to a few nanoseconds by "pick-off annihilation" in which some unpaired electron spins in the medium cause conversion quenching of orthopositronium to para-positronium. The speed of the t2 effect is supposed, among other things, to represent by pick-off annihilation the presence of defects in the crystalline lattice. In any case, what amounts to empty space between molecules can then be occupied by orthopositronium.(14,15,16) It is now found in linear polyethylene, by T. T. Wang and his co-workers of Bell Laboratories(17) that there is marked shift in positron lifetimes over the temperature range of 80°K to 300°K. For... 

An important feature of o-Ps in polymers is that these particles tire preferentially formed or trapped in holes or regions of low electron density. The annihilation rate of o-Ps is proportional to the overlap of the positron and the pick-off electron wavefunctions and therefore the lifetime of o-Ps will depend on the size of the hole. The relative number of o-Ps pick-off annihilations is related to the number of suitable free volume sites in the polymer [3]. 

Fig. 7.16. The pick-off annihilation rate (q)p, see equation (7.11), for ortho-positronium in 4 He gas at various temperatures, observed by Hautojarvi and Rytsola (1979). At the lowest temperature (q)p is almost independent of density, indicating stable bubble formation. The behaviour gradually changes to that of free ortho-positronium, indicated by the straight line whose slope corresponds to (iZeff) = 0.125 (see table 7.2). The data at 77 K are due to Fox et al. (1977).

The p-Ps has a shorter lifetime than o-Ps and it annihilates into two photons, while o-Ps annihilates into three photons. The intrinsic lifetime is 0.125 ns and 142 ns for the free p-Ps and o-Ps, respectively. In ordinary molecular media, the electron density is low enough so that Ps can pick off electrons from the media that have anti-parallel spin to that of the positron, and undergo two-photon annihilation. This is called the pick-off annihilation of Ps. The pick-off annihilation of o-Ps not only occurs in the form of two-photon annihilation, it also shortens the o-Ps lifetime from 142 ns (free o-Ps) to a few ns. The pick-off annihilation lifetime of o-Ps in molecular systems is about one order of magnitude greater than in crystalline or metallic media. Experimental determination of o-Ps lifetime is one of the most useful methods for positron and positronium chemistry. This is because o-Ps lifetime contains information about electron density, which governs the basic properties of chemical bonding in molecules. It is also controlled by the physical structure of molecules. 

Further support to the model should be found by examining the values of F], as deduced from AC or DB measurements since p-Ps annihilates in an intrinsic mode, this parameter should reflect directly the average Ps kinetic momentum. However, the data on F, are usually poorly defined [61, 64], so that the correlation with y is more conveniently sought using experimental values of r3, provided that the momentum distribution of the valence electrons participating in the o-Ps pick-off annihilation is reasonably solvent independent. Such a correlation has been effectively found for a variety of solvents at various temperatures [61], leading to ... 

The chance for pick-off annihilation can be altered dramatically by impurities and paramagnetic elements like fluorine. A large electron density either prevents the formation of positronium altogether. 

It turns out that the positronium signal from the pores is very small and quite comparable to MSSQ with less than 10% porogen. Either positronium rarely forms and traps the pores, or the positronium-wall interaction is much stronger and causing pick-off annihilation within a few bounces, rather than thousands of bounces as in the case of MSSQ. 

Positrons emitted for a radioactive source (such as 22Na) into a polymeric matrix become thermalized and may annihilate with electrons or form positronium (Ps) (a bound state of an electron and positron). The detailed mechanism and models for the formation of positronium in molecular media can be found in Chapters 4 and 5 of this book. The para-positronium (p-Ps), where the positron and electron have opposite spin, decays quickly via self-annihilation. The long-lived ortho positronium (o-Ps), where the positron and electron have parallel spin, undergo so called pick-off annihilation during collisions with molecules. The o-Ps formed in the matrix is localized in the free volume holes within the polymer. Evidence for the localization of o-Ps in the free volume holes has been found from temperature, pressure, and crystallinity-dependent properties [12-14]. In a vacuum o-Ps has a lifetime of 142.1 ns. In the polymer matrix this lifetime is reduced to between 2 - 4 ns by the so-called pick-off annihilation with electrons from the surrounding molecule. The observed lifetime of the o-Ps (zj) depends on the reciprocal of the integral of the positron (p+(rj) and electron (p.(r)) densities at the region where the annihilation takes place ... 

A number of positron annihilation studies with carbon materials [10-12] have shown the existence of three lifetime components the longest-lived component with a mean lifetime from 1000 to 5000 ps resulted from pick off annihilation of the orthopositronium atoms formed in the samples the intermediate component having a mean lifetime between 350 and 400 ps has been assigned to annihilation of positrons by interaction with the electron density at the surface and near-surface regions, and the shortest-lived component, with mean lifetime from 140 to 225 ps, comes from positron annihilation with 7t-electrons in the bulk of the graphite structure. 

Shantarovich, V. P., On the role of free volume in pick-off annihilation and positronium chemical reactions chemistry, J. Radioanal. Nucl. Chem., 210, 357-369 (1996). 

Once o-Ps is conflned in a hole it stays there colliding many times on the wall until an electron, having anti-parallel spin to the e" spin, in the wall meets e" and is annihilated (pick-off annihilation). Theoretically the rate of this pick-off annihilation is proportional to the overlap integral of the e wave function with those of external electrons. In a simple but useful model a spherical potential well is assumed for the hole and the external electrons are dealt with as an electron layer pasted over the wall with a thickness A R. The o-Ps lifetime is then given as (3) ... 

It has been seen that pick-off annihilation is a general means of annihilation, occurring in all types of material and media. Since the positron of the positronium is annihilated here by the electrons of the medium, it is to be expected that a connection exists between the rate of annihilation and the structure of the molecules in the medium, as well as the interactions between them, and thus information indicative of the liquid structure may also be obtained. 

The dependence of pick-off annihilation on the various parameters was also studied in solutions and liquid mixtures. 

In aqueous solutions of hydroxy acids it was observed that the pick-off annihilation was predominantly a function of the molar density, being nearly additive [Ta 69]. 

In contrast, when methanol-water and dioxane-water mixtures were examined and the literature data for other alcohol-water mixtures were analyzed, it could be concluded that there is a significant deviation from additivity in alcohol-water mixtures [Le 72]. A simple correlation can be deduced between the rate of pick-off annihilation and the molar volume, with the assumption that the cross-section of annihilation is a linear function of the molar fraction in the mixture, i.e., it is additive ... 

Further investigations disclosed a fundamental correlation between the rate constant Xp) of the pick-off annihilation observed in liquids and the surface tension (y) of the liquids ... 

Correlations could further be deduced from the dependence of the rate of pick-off annihilation on temperature and viscosity [Le 73a] the square root of the lifetime of the pick-off annihilation was found to vary linearly with the absolute temperature and with the reciprocal of the viscosity. Hence, the temperature and viscosity dependences of the pick-off annihilation could be described well even in associating liquids, where other theories were inapplicable. 

A theoretical explanation of the close correlation between pick-off annihilation and the surface tension is given by the bubble model . According to this model, a small bubble develops around the Ps atom, owing to the repulsion potentials arising between the molecules of the medium and the neutral Ps atom formed in liquids. The surface tension acting on the surface of the bubble tends to decrease the surface area, and thus the resulting radius of the bubble will depend on the equilibrium of the opposing forces. 

The most general interaction between Ps and materials is the so-called pick-off annihilation. It occurs in every material, although sometimes together with other o-Ps interactions. This interaction is based on the fact that the positron of the triplet positronium atom can undergo 2y-annihilation with an opposite-spin electron of a colliding molecule. Thus, the positron-electron pair, which annihilates at the end, is in singlet state (S = 0) instead of the original S = 1... 

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