Electric fields positron annihilation

It is interesting to compare the properties of positive electrons, positrons, with the properties of electrons in nonpolar liquids. Values of the mobility of positrons, )x +, are now available for a few liquids. Early measurements for in -hexane ranged from 8.5 to 100 cm /Vs [181,182]. In a recent study, the Doppler shift in energy of the 511-keV annihilation gamma ray in an electric field was utilized to measure the drift velocity. This method led to fi+ = 53 cm /Vs in -hexane and 69 cm /Vs in 2,2,4-trimethylpentane [183]. Interestingly, these values are comparable to the mobilities of quasi-free electrons in nonpolar liquids. 

In cases where the annihilation rate, and hence Zef[, is a rapidly varying function of the positron energy, as with xenon (Schrader and Svetic, 1982), the simplification introduced above is not valid and the solution to equation (6.15) must be used. The functional form for f(v) given in equation (6.17) was used by Campeanu and Humberston (1977b) to investigate the variation of the equilibrium value of (Zeff) with electric field and temperature, and their results for the former are shown in Figure 6.3. 

In this section we review the results from positron annihilation experiments, predominantly those performed using the lifetime and positron trap techniques described in section 6.2. Comparisons are made with theory where possible. The discussion includes positron thermalization phenomena and equilibrium annihilation rates, and the associated values of (Zeff), over a wide range of gas densities and temperatures. Some studies of positron behaviour in gases under the influence of applied electric fields are also summarized, though the extraction of drift parameters (e.g. mobilities) is treated separately in section 6.4. Positronium formation fractions in dense media were described in section 4.8. 

Several studies have been made of the behaviour of low energy positrons in gases under the influence of a static electric field e. The broad aim of this work has been to study the diffusion and drift of positrons in order to understand better the behaviour of the momentum transfer and annihilation cross sections at very low energies. The theoretical background has been given in section 6.1, and the diffusion equation with an... 

The effect of an electric field on positrons annihilating in dense helium gas at low temperatures was investigated by Canter and coworkers (Ruttenberg, Tawel and Canter, 1985 Tawel and Canter, 1986). This work centred on the localization phenomena responsible for the clustering behaviour of helium atoms around the positron in dense helium gas, as illustrated in Figure 6.12. The aim of the studies was to test the hypothesis of Canter et al. (1980), supported by Azbel and Platzman... 

The broken-line portion of the v+/(Zeg) curve, which attains a maximum and then falls, was explained by Bose, Paul and Tsai (1981) in terms of the formation of positronium due to positron heating in the electric field, so that the apparent value of Z s) rises as the amount of positronium formation increases. At high electric fields nearly all the positrons form positronium and do not annihilate at the foil. 

When an electric field was applied across the chamber some positrons annihilated prematurely, following field-induced drift to one of the electrodes. In this case the free-positron component of the lifetime spectrum was field dependent the maximum drift time, rmd, was given by the end-point of the lifetime spectrum and was due to thermalized positrons which had traversed the entire drift length l. The drift speed was then v+ = 1/rmd and the mobility could be found from... 

Davies, S.A., Charlton, M. and Griffith, T.C. (1989). Free positron annihilation in gases under the influence of a static electric field. J. Phys. B At. Mol. Opt. Phys. 22 327-340. 

Singh, V. and Grover, P.S. (1987). Computer-aided analysis of electric and magnetic field effects on positron annihilation in argon. J. Phys. B At. 

Fig. 3.4. (a) The electric field dose to the proton (composed of three quarks) is so strong that it creates matter and antimatter (shown as electron-positron pairs). The three quarks visible in scattering experiments represent the valence quarks, (b) One of the radiative effects in the QED correction of the c order (see Table 3.1). The pictures show the sequence of the events from left to the right A photon (wavy line on the left) polarizes the vacuum and an electron-positron pair (solid lines) is created, and the photon vanishes. Then the created particles annihilate each other and a photon is created, (c) A similar event (of the order in QED), but during the existence of the electron-positron pair the two particles interact by exchange of a photon, (d) An electron (horizontal solid line) emits a photon, which creates an electron-positron pair, that annihilates producing another photon. Meanwhile the first electron emits a photon, then first absorbs the photon from the annihilation, and afterwards the photon emitted by itself earlier. This effect is of the order c in QED. 

This means that, e.g., the annihilation of a positron with an electron can be described as if an electron came to the point of collision, emitted two or three photons and then went out backwards in space-time. In field theory such incoming and outgoing particles are described as particle currents in (some) analogy with the electric current in the above example the incoming electron and positron constitute a lepton current. 

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