Free positrons

Positron annihilation lifetime spectroscopy (PALS) provides a method for studying changes in free volume and defect concentration in polymers and other materials [1,2]. A positron can either annihilate as a free positron with an electron in the material or capture an electron from the material and form a bound state, called a positronium atom. Pnra-positroniums (p-Ps), in which the spins of the positron and the electron are anti-parallel, have a mean lifetime of 0.125 ns. Ortho-positroniums (o-Ps), in which the spins of the two particles are parallel, have a mean lifteime of 142 ns in vacuum. In polymers find other condensed matter, the lifetime of o-Ps is shortened to 1-5 ns because of pick-off of the positron by electrons of antiparallel spin in the surrounding medium. 

In solids the free positron lifetime r lies in the approximate range 100-500 ps and is dependent upon the electron density. Following implantation, the positrons are able to diffuse in the solid by an average distance L+ = (D+t)1//2, where D+ is the diffusion coefficient. This quantity is usually expressed in cm2 s-1 and is of order unity for defect-free metallic moderators at 300 K (Schultz and Lynn, 1988). The requirement of very low defect concentration arises because the value of D+ is otherwise dramatically reduced owing to positron trapping at such sites. 

The results obtained by the Texas group (Fornari, Diana and Coleman, 1983 Diana et al., 1986b) are discussed below along with those obtained by the Bielefeld group, whose apparatus is shown schematically in Figure 4.13. In this case the manner of detecting positronium depended upon method (iii) outlined above, i.e. detection of the ions formed without an accompanying free positron in the final state. 

Before the advent of low energy beams, the only means of investigating positron interactions with atoms and molecules was to study their annihilation. Information could thereby be obtained directly on the annihilation cross section but only indirectly for other processes such as elastic scattering. In this chapter we consider the annihilation of so-called free positrons in gases. The fate of positrons which have formed positronium prior to annihilation is treated in Chapter 7. 

Fig. 6.5. Examples of positron lifetime spectra for (a) argon and (b) xenon gases. The argon data are for a density of 6.3 amagat at 297 K. The channel width is 1.92 ns. In (a), (i) shows the raw data, (ii) shows the signal with background removed, (iii) shows the free-positron component and (iv) shows the fitted ortho-positronium component. In (b), the spectrum for xenon is for room temperature and 9.64 amagat and has a channel width of 0.109 ns. The inset shows the fast components as extracted and discussed by Wright et al. (1985).

Once the background is subtracted, the component of the spectrum due to the annihilation of ortho-positronium is usually visible (see Figure 6.5(a), curve (ii) and the fitted line (iv)). The analysis of the spectrum can now proceed, and a number of different methods have been applied to derive annihilation rates and the amplitudes of the various components. One method, introduced by Orth, Falk and Jones (1968), applies a maximum-likelihood technique to fit a double exponential function to the free-positron and ortho-positronium components (where applicable). Alternatively, the fits to the components can be made individually, if their decay rates are sufficiently well separated, by fitting to the longest component (usually ortho-positronium) first and then subtracting this from the... 

The instantaneous free-positron annihilation rate is particularly useful where it is time dependent (i.e. on the shoulder region) it is... 

Fig. 6.10. Mean positron annihilation rate (denoted here as Af) at various gas densities for N2 and Ar gases at different temperatures. Key A, N2 at 130 K , Ar at 160 K A, N2 at 297 K , Ar at 297 K. The original sources for these measurements are given by Heyland et al. (1986). The broken line indicates the linear rise expected, equation (6.3), for a constant (Zeff) of 27. Reprinted from Physics Letters A119, Heyland et al., On the annihilation rate of thermalized free positrons in gases, 289-292, copyright 1986, with permission from Elsevier Science.

Fig. 6.12. An example of the effect of self-trapping in clusters on the free-positron annihilation rate. The right-hand side is for 4He at 5.7 K and 7.2 K, whilst the left-hand data are for 3He at 4.2 K and 5.7 K (Hautojarvi et al, 1977).

The positron-trap technique has been used by Surko and coworkers to measure the Doppler broadening of the 511 keV line for positrons in helium gas. This method does not have the drawback of the experiment described above, in which both positronium and free-positron events overlap on the angular distribution curves here the positrons are thermalized prior to the introduction of the gas and therefore cannot form positronium. A comparison of the theoretically predicted and experimentally measured Doppler spectra (Van Reeth et al., 1996) is shown in Figure 6.16. The theoretical results were obtained from the variational wave functions for low energy positron-helium scattering calculated by Van Reeth and Humberston (1995b) see equations (3.75) and (3.77). 

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... 

Fig. 6.19. (a) The free-positron component with electric fields applied to 0.26... 

The experiments were performed at two values of the magnetic field, 0.375 T and 0.425 T, and at various densities of N2 gas with small admixtures of isobutane to quench the free-positron component (see subsection 6.3.2). Al-Ramadhan and Gidley (1994) derived a quantity A(p) from their measured values of A Ps and Ao-ps, for the mixed and unmixed ortho-positronium states respectively, at a gas density p given by... 

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.

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. 

Positron chemistry is a specific field which aims at determining which solutes react with e+ to form a bound-state, comparing the related constants and studying the effects of temperature [3, 5, 6, 13, 18, 25, 46-48]. The results are scarce, because the bound-states can only be characterized through AC or DB experiments, which are less used than PALS as it seems, the lifetimes of all e+ bound-states known are very close to those of the free positrons, so that PALS cannot sufficiently distinguish these two states and is therefore unable to provide useful information. 

The last exponential factor takes into account a possibility of the free-positron annihilation occuring during the Ps formation time, ips (on the order of some picoseconds) with the annihilation rate 1/t2 (< 2 ns-1). Obviously, the contribution from this factor is negligible. In nonpolar molecular media at room temperature rc is 300 A. Typical thermalization lengths b of electrons are < 100 A. Thus, the Onsager factor, 1 — err, is also very close to unity. Therefore, to explain observable values of Ps yields, which never exceed 0.7, we must conclude according to Eq. (11) that the terminal positron spur contains on average 2 to 3 ion-electron pairs. 

Theoretical arguments are twofold. On one hand, one may expect that e+ also gets solvated over a time comparable with r . Mobility of solvated particles drastically drops and they simply do not have enough time to meet each other during the free-positron lifetime ( 0.5 ns). Really, corresponding diffusion displacement of e+ is smaller than e+ thermalization... 

It should be noted that the S parameters of both o-Ps pick-off and free-positron annihilation are lower than that of the Si substrate, because positrons predominantly annihilate with electrons of oxygen in the Si02 network. Only p-Ps self-annihilation has a higher S value than that of Si. The S parameter observed in conventional Doppler- broadening-of-annihilation radiation is the average of p-Ps, o-Ps, and free-positron annihilation. Therefore, if the Ps fraction decreases due to the presence of defects, impurities, etc., the intensity of the narrow momentum component due to p-Ps self-annihilation decreases, and as a result the averaged S parameter decreases. 

At very low temperatures (typically below 150K) the o-Ps intensity increases as a function of exposure time for a large number of polymers. This increase in the o-Ps yields at very low temperature is explained by the reaction of free positrons with trapped electrons produced by the previously injected positrons [77],... 

In polymer systems, positron chemistry can occur if the e+ is able to attach itself to a particular atom or group. Halogenated polymers, radicals and certain electron rich unsaturated structures have the capability of forming stable species of the form (e+,R ), with free positrons. These processes can lead to quenching and inhibition of Ps formation. 

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