Positron-molecule lifetimes

The lifetimes of the positron-molecule states rM (see Table 14.2) are considerably longer than that of the free positrons (rc+= 400 ps). rM is longest for PsF, which has the smallest number of electrons in its shell, and, hence, the lowest electron density, and decreases with increasing number of electrons. Seeger and Banhart [25] give an upper limit for the lifetime of positron states where no o-Ps is involved ... 

For water, with rp = (140 2) ps and t0 = (1886 2) ps, we get Tm = 580 ps. The positron-molecule lifetimes exceed this limit for all halides examined. As data analyses with positron-molecule lifetimes fixed below this limit were definitely not successful, we are confessed that the long lifetimes are a hard experimental fact. However, we have not yet come to a satisfactory explanation what makes the positrons survive this long in the neighborhood of the halide ions. Possible explanations could involve the spin similar to the effect in o-Ps, or electron depletion due to charge effects in the hydration sphere around the halide ions. 

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... 

When a positron encounters normal matter it eventually annihilates with an electron after a lifetime which is inversely proportional to the local electron density. In condensed matter lifetimes are typically less than 500 ps, whilst in gases this figure can be considered as a lower limit, found either at very high gas densities or when the positron forms a bound state or long-lived resonance with an atom or molecule. 

In the section on excitation we shall treat only electronic transitions thus rotational and vibrational processes in molecules are excluded. As will be described in Chapter 6, information on these latter processes has been derived from positron lifetime and other experiments. Our theoretical discussion will mainly concern excitation of the lower levels of... 

Independent of whether or not a well-defined crossover temperature can be observed in NS data above Tg, it has been well known for a considerable time that on heating a glass from low temperatures a strong decrease of the Debye-Waller factor, respectively Mossbauer-Lamb factor, is observed close to Tg [360,361], and more recent studies have confirmed this observation [147,148,233]. Thus, in addition to contributions from harmonic dynamics, an anomalously strong delocalization of the molecules sets in around Tg due to some very fast precursor of the a-process and increases the mean square displacement. Regarding the free volume as probed by positron annihilation lifetime spectroscopy (PALS), for example, qualitatively similar results were reported [362-364]. 

A positron in an electronic media can pick up an electron and form a neutral atom called Positronium (Ps) [9], The existence of Ps and its chemical reaction with molecules was detected from annihilation photons in 1951 [10], Ps is formed in most molecular systems. Due to the different combinations of positron and electron, there are two states of Ps the para-Ps (p-Ps) from the anti-parallel spin, and the ortho-Ps (o-Ps) from the parallel spin combination. The lifetime and the annihilation events for p-Ps and o-Ps are very different from each other, as given by electromagnetic theory. Figure 1.1 shows basic physical properties of Ps and compares them with the H atom, although it should not be considered an isotope of H (see problems 1.5 and 1.6 and answers at the end of this chapter). 

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. 

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 positron, having given off its energy by interaction with matter, may coexist with an electron for a short time in the form of a positronium atom (c e ) before annihilation occurs. Absorption of other short-lived elementary particles such as muonS pions, kaons or sigma particles may lead to substitution of protons or electrons, respectively, in atoms or molecules, with the result of formation of so-called exotic atoms or molecules. Although the lifetime of these species is very short... 

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... 

In recent years, positron annihilation lifetime (PAL) spectroscopy has been demonstrated to be a special sub-nanometer probe to determine the free-volume hole size, fraction and distribution in a variety of polymers (4-9). In this technique, measured lifetimes and relative intensities of the positron and positronium, Ps (a bound atom which consists of an electron and a positron), are related to the size and fraction of sub-nanometer holes in polymeric materials. Because of the positive-charge nature, the positron and Ps are repelled by the ion core of polymer molecules and trapped in open spaces, such as holes, free volumes, and voids. The observed... 

The most general interaction, which occurs in all materials, is pick-ofT interaction. The essence of this is that positron of the positronium atom in the triplet state is annihilated not by its own electron, but undergoes 2y-annihilation with some antiparallel-spin electron of a molecule encountered during collision with the molecules of the medium. As a result of the interaction, the lifetime of the ortho-positronium is shortened, although, because of the shielding effect of its own electron, not to the extent that it would have been if it had been destroyed in free annihilation. Pick-off interaction occurs to a significant extent particularly in the condensed phase. 

Since positronium formation and positronium reactions can he easily identified by positron lifetime measurements this technique has been applied to the steady of micelles, reversed micelles, microemulsions, liquid crystals, and microphase changes occurring in these systems. By adding probe molecules to these solutions it is also possible to study their location in e.g., micelles. 

In order to obtain rate constants for the reaction of Ps (or positrons) with substrate molecule or to follow changes in the reactivity of a certain medium towards Ps the two photon annihilation rate (see above) has to be determined. This is accomplished by positron lifetime conventional fast-slow y y coincidence methods. 22... 

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