Positronium reactions

An interesting aspect of Ps chemistry on fundamental grounds is the variety of possible reactions, although only some of these have been effectively characterized. Thus, Ps addition, substitution, tunneling and hot reactions have been suspected, but not proven to occur only Ps oxidation, bound-state formation and spin conversion reactions have been firmly proven. 

For decades, Ps chemistry has been quantitatively treated on the basis of a constant reaction rate coefficient (k )- It is only recently that the possibility of a time-dependent k has been examined. Therefore, the various known Ps reactions are presented in the following, before some fundamental aspects of Ps kinetics are discussed. 

I3(C) represents the hue, physical o-Ps intensity and A, is the free e+ decay rate constant. Similar equations hold for p-Ps, with subscript 1 instead of 3. 

The linear variation of 1/t3 with C expected from Eq. (14) has been verified in a very large number of cases. Furthermore, Eqs. 15 (l3m) and 16 

The use of DB or AC to characterize the reaction observed in PALS is compulsory as far as quantitative comparison of the experimental k with theoretical expressions is sought. 

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The results described in this section mark only the beginnings of positronium-atom(molecule) collision studies. Investigations in the intermediate energy range and the measurement of total cross sections of comparable, or better, accuracy should soon be available for a variety of targets. Extensions to both higher and lower positronium energies await developments in beam production and detection techniques. With an eye to the future, Charlton and Laricchia (1991) identified a number of positronium reactions which would be of interest to study, and we reproduce their list here ... 

Positronium reactions of a chemical nature form the third, and from the chemical aspect the most important, group of interactions. (It must be noted that certain types of the ortho-para conversion reactions are also of a chemical nature, e.g., the free radical reactions.) The main types of chemical reactions of positronium are illustrated by the following examples ... 

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. 

Outer-sphere electron transfer reactions involving the [Co(NH3)6]3+/2+ couple have been thoroughly studied. A corrected [Co(NH3)6]3+/2+ self-exchange electron transfer rate (8 x 10-6M-1s-1 for the triflate salt) has also been reported,588 which is considerably faster than an earlier report. A variety of [Co(NH3)g]3+/2+ electron transfer cross reactions with simple coordination compounds,589 organic radicals,590,591 metalloproteins,592 and positronium particles (electron/ positron pairs)593 as redox partners have been reported. 

The rearrangement reaction results in the formation of protonium and positronium in the final channel, according to... 

This inevitably leads to the annihilation of anti-particles from the bound states of protonium (Pn = pp) and positronium (Ps = e+e ). We found this reaction to be a very important mechanism for the loss of antihydrogen [26, 27, 29]. 

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. 

The final method which is proving of value is the gas-cell technique, in which use is made of the natural peaking of the positronium formation cross section in the direction of the incident positrons (see Chapter 4 for further discussion of this feature) for the reaction described by equation (1.12). This method was pioneered independently by Brown (1985, 1986), and by Laricchia and Charlton and coworkers (Laricchia et al., 1986, 1987b, 1988), who have shown that a tunable positronium beam with narrow energy width can be produced by the capture reaction in gases. Further discussion of this technique, and some applications in atomic physics, can be found in section 7.6. 

As the positron energy is raised above the positronium formation threshold, EPs, the total cross section undergoes a conspicuous increase. Subsequent experimentation (see Chapter 4) has confirmed that much of this increase can be attributed to positronium formation via the reaction (1.12). Significant contributions also arise from target excitation and, more importantly, ionization above the respective thresholds (see Chapter 5). In marked contrast to the structure in aT(e+) associated with the opening of inelastic channels, the electron total cross section has a much smoother energy dependence, which can be attributed to the dominance of the elastic scattering cross section for this projectile. 

Although, as described in section 1.5, positronium can be formed when positrons interact with many different media, in this chapter we are mainly concerned with the reaction... 

The formation of excited states of positronium, usually termed Ps, through reaction 4.2, can make significant contributions to erPs. This has already been discussed briefly in the theoretical section 4.2 and in subsection 4.4.3, where we saw that excited state positronium is thought to dominate alkali metals. Here we describe the only experiment to date which has directly detected excited state positronium formation in gases, namely that of Laricchia et al. (1985). 

Use of the charge-exchange mechanism, reaction (8.13), to produce antihydrogen was first proposed by Deutch et al. (1986), and subsequently it was shown that the cross section for this process could be obtained by applying the charge conjugation and time reversal operators to the process of positronium formation in positron-hydrogen collisions (Humberston et al., 1987, and see section 4.2). Under time reversal, the positronium formation process equation (4.5) becomes... 

Deutch, B.I., Charlton, M., Holzscheiter, M.H., Hvelplund, P., Jprgensen, L.V., Knudsen, H., Laricchia, G., Merrison, J.P. and Poulsen, M.R. (1993). Antihydrogen synthesis by the reaction of antiprotons with excited state positronium atoms. Hyperfine Interactions 76 153-161. 

Mogensen, O.E. (1974). Spur reaction model of positronium formation. J. 

The above reactions require that two plasmas of opposite charge (antiprotons and positrons) are trapped and brought into contact. Alternatively, recombination by crossing a beam of positronium (either in the ground state or in low-lying excited states) with antiprotons has been proposed (see references [23,24,25,26]) ... 

Many other attempts to observe this new excited state of positronium have been made. Indications of correlated, equal energy, two-photon decay with a summed energy of 1062 keV have been found by DANZMANN et al. [22] in the same reaction as produced the electron-positron pairs. [15, 18, 19] The authors believe that this line, at a new, fourth energy, may belong to the same neutral system which produced the correlated electron-positron pairs. [22]... 

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). 

Now let us estimate the low boundary, Wiow, of the Ore gap in molecular liquids. Because the Ore process is just an electron-transfer reaction, we assume that no rearrangement of molecules occurs and, therefore, the final positronium state will be quasi-free (formation of the bubble requires much longer time). The corresponding Born-Haber cycle is the following ... 

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