Para-positronium, annihilation

Note that, as can be seen from the discussion in subsection 1.2.1, the contributions from the higher order annihilation modes are negligible at the present levels of precision. Thus, the rate for the annihilation of ortho-positronium into five gamma-rays is only 10-6 of that for three gamma-rays, with a similar value for the ratio of the rates for para-positronium annihilation into four and two gamma-rays. 

A follow-up study at O2 pressures below 0.05 atmospheres (Kakimoto, Hyodo and Chang, 1990), where the para-positronium to ortho-positronium conversion is suppressed because it occurs at a rate lower than that for para-positronium annihilation, yielded cross sections in good accord with the estimates given above. 

With position sensitive detectors the deviations from antiparallel emission of two annihilation photons can be observed. The small angles on the order of millirad are translated into two dimensional electron (or positronium) momentum distributions. The resolution is sufficient to distinguish positron from para-positronium annihilations and to determine the velocity distribution of positronium. 

PALS is based on the injection of positrons into investigated sample and measurement of their lifetimes before annihilation with the electrons in the sample. After entering the sample, positron thermalizes in very short time, approx. 10"12 s, and in process of diffusion it can either directly annihilate with an electron in the sample or form positronium (para-positronium, p-Ps or orto-positronium, o-Ps, with vacuum lifetimes of 125 ps and 142 ns, respectively) if available space permits. In the porous materials, such as zeolites or their gel precursors, ort/zo-positronium can be localized in the pore and have interactions with the electrons on the pore surface leading to annihilation in two gamma rays in pick-off process, with the lifetime which depends on the pore size. In the simple quantum mechanical model of spherical holes, developed by Tao and Eldrup [18,19], these pick-off lifetimes, up to approx. 10 ns, can be connected with the hole size by the relation ... 

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 the two conjugated atoms approach each other, the leptons might in principle annihilate before the hadrons do. We have found that this is not the case. Even though the annihilation reaction constant for para-positronium is larger than that for protonium, the probability of e+ — e annihilation at any given interhadronic distance R is weighted by the hadronic probability density at that distance. Because of that, the e+ — e annihilation occurs mainly at R 1 whereas the hadrons annihilate basically at R = 0. 

Positronium can exist in the two spin states, S = 0, 1. The singlet state (5 = 0), in which the electron and positron spins are antiparallel, is termed para-positronium (para-Ps), whereas the triplet state (5 = 1) is termed ortho-positronium (ortho-Ps). The spin state has a significant influence on the energy level structure of the positronium, and also on its lifetime against self-annihilation. 

In Chapter 1, the first order contributions to the annihilation rates from the dominant modes of decay of the S-states of both ortho- and para-positronium (for arbitrary principal quantum number nPs) were given as equations (1.5) and (1.6). These contributions are included in the following equations for the rates for the two ground states, which also contain terms of higher order in the fine structure constant, a ... 

Fig. 7.21. Angular correlation curves for mixtures of O2 and CI2 gases with an overall pressure of 120 atmospheres, (a) Pure O2, (b) O2 with 0.02 atmospheres of Cl2, (c) O2 with 0.05 atmospheres of CI2, (d) 02 with 0.2 atmospheres of CI2 and (e) O2 with 1 atmosphere of CI2. Goldanskii and Mokrushin (1968) attributed the components labelled Wi, W2 and W3 to the annihilation of thermalized para-positronium atoms (Wi, the narrow component), the annihilation of free positrons in O2 (W2) and the annihilation of positrons in the PsCl compound (W3). The intensity of the last, i.e. W3, grows progressively with the addition of CI2 to the O2 buffer.

The 2 dominant components are due to the annihilation of positrons in the sample MSSQ material independent of pores ( 0.5 ns) para-positronium (-0.1 ns). Ortho-positronium annihilations in the MSSQ cage structure occur with a -4 ns lifetime. Lifetimes of 10 ns and greater are due to positronium in pores and tend to increase with increasing porogen load. Open porosity is associated with a lifetime of -100 ns (80% case, dashed line). 

Para positronium two photon annihilations cause the narrow sharp feature in the center at zero momentum. The events at large momentum (> 4a.u.) are due to three photon annihilations. By adding lead filters between the sample and the detectors, the third photon is absorbed and only two photon events meet the sum energy restriction. 

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 ... 

The annihilation constant A is given as the number of annihilation events per unit density and unit time. It is obtained from the life time of positronium, which for the singlet state (para-positronium) is T2y = 1.25 X 10 ° s [13], and for the triplet state (ort/io-positronium) is = 1.42 X 10 s [14]. The positronium decay rate is related to the decay constant via... 

When an atom and its antiatom approach each other, the leptons might in principle annihilate before the hadrons do. This work finds that this is not the case. Although the annihilation reaction constant for para-positronium... 

Reaction of a positron with an electron gives a metastable positronium (Ps) particle, which may have antiparallel spins (para-positronium, p-Ps) or parallel spins (ort/jo-positronium, o-Ps). Within a polymer, the longer lifetimes of o-Ps may be related to the size, concentration and distribution of free volume elements. There have been a number of studies of PIM-1 by positron annihilation lifetime spectroscopy (PALS) [33-36]. 

Interest in the polarization correlation of photons goes back to the early measurements of the linear polarization correlation of the two photons produced in the annihilation of para-positronium which were carried out as a result of a suggestion by Wheeler that these photons, when detected, have orthogonal polarizations. Yang subsequently pointed out that such measurements are capable of giving information on the parity state of nuclear particles that decay into two photons. In addition, the polarization correlation observed in the two-photon decay of atoms is considered to be one of the few phenomena where semiclassical theories of radiation are inadequate and it is necessary to invoke a full quantum theory of radiation. The effect has also been used to demonstrate the phenomenon of quantum interference. ... 

The experiments using the annihilation of para-positronium have been reviewed elsewhere and this article concentrates on those in which the two photons are emitted from an atomic source. In order to understand fully the significance of these experiments, however, it is necessary to give some consideration to the underlying theory. The following discussion is not intended to be exhaustive and the reader is referred to the review articles by Clauser and Shimony, Pipkin and to the work of Aspect for further details. 

Positron Annihilation Spectroscopy (PALS) can investigate the free volume existing between polymer chains. The lifetime of particles (positrons) injected into a sample can thus provide information on the void structure existing in polymers and polymer blends. For immiscible polymers, free volume existing at the interface due to poor adhesion can be detected by PALS. In miscible polymers, densification due to favorable interactions may be capable of determination. This technique involves the injection of positrons into a polymeric system from a radioisotope capable of emitting positrons, such as Na. The positrons (positively charged electrons) combine with electrons to annihilate or to form a bound state called a positronium (Ps). If the spins of the positron and electron are antiparaUel, para-positroniums (pPS) with a lifetime of 0.125 ns are formed. If the spins of the positron and electrons are parallel, an orthopositronium (oPs) is formed with a lifetime of 1-5 ns. The oPs hfetime, Ts, is related to the free volume cavity in which the oPs is formed [388,389]. 

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). 

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