Trapping of positrons

According to the currently accepted theory of positron in teractions with the entities present in these solutions, trapping of positrons by the aggregates, micelles, etc. would be the process responsible e.g. for the reduction in positronium formation observed upon micelle formation. They would therefore very closely resemble interactions of electrons in solution or gels used as solvents in liquid scintillation counting. 

The trapping of positrons by lattice defects is clearly established in Tl2Ba2CaCu20g by the occurrence of multi components in the lifetime spectra (Sundar et al. 1990a, Jean et al. 1989a) and in the lineshape (Pujari et al. 1989), and by deviations from the lifetime calculated for the defect-free structure (Barbiellini et al. 1994). 

The trapping of positrons in defects is based on the formation of an attractive potential at open-volume defects, such as vacancies, vacancy agglomerates, and dislocations. The main reason for this potential is the lack of a repulsive positively charged nucleus in such a defect. The sensitivity range for vacancy detection in metals starts at about one vacancy per 10 atoms. This extremely high sensitivity is caused by the fact that the positron diffuses about 100 nm through the lattice and... 

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... 

Recent advances in the production and storage of positrons and antiprotons have made it possible to think about the synthesis of atomic antimatter in the laboratory. Parallely, contemporary advances in cooling and trapping atoms have led to an unprecedented accuracy of spectroscopic measurments. The important difference between the spectroscopy of atoms and antiatoms is that in the latter case, because of annihilation, the sample must be isolated from the surrounding environment. 

Perhaps of more general applicability for the study of the properties of positronium is its production by the desorption of surface-trapped positrons and by the interaction of positrons with powder samples. According to equation (1.15) it is energetically feasible for positrons which have diffused to, and become trapped at, the surface of a metal to be thermally desorbed as positronium. The probability that this will occur can be deduced (Lynn, 1980 Mills, 1979) from an Arrhenius plot of the positronium fraction versus the sample temperature, which can approach unity at sufficiently high temperatures. The fraction of thermally desorbed positronium has been found to vary as... 

Traditionally, experimental values of Zeff have been derived from measurements of the lifetime spectra of positrons that are diffusing, and eventually annihilating, in a gas. The lifetime of each positron is measured separately, and these individual pieces of data are accumulated to form the lifetime spectrum. (The positron-trap technique, to be described in subsection 6.2.2, uses a different approach.) An alternative but equivalent procedure, which is adopted in electron diffusion studies and also in the theoretical treatment of positron diffusion, is to consider the injection of a swarm of positrons into the gas at a given time and then to investigate the time dependence of the speed distribution, as the positrons thermalize and annihilate, by solving the appropriate diffusion equation. The experimentally measured Zeg, termed Z ), is the average over the speed distribution of the positrons, y(v,t), where y(v,t) dv is the number density of positrons with speeds in the interval v to v + dv at time t after the swarm is injected into the gas. The time-dependent speed-averaged Zef[ is therefore... 

Fig. 6.6. Schematic illustration of the electrode structure of the positron trap of Greaves, Tinkle and Surko (1994). The variation of the electrical potential along the trap, together with the gas pressure in the various regions, is also shown. The letters A, B and C indicate energy-loss collisions of the positrons with the N2 buffer gas. Reprinted from Phys. Plasmas 1, Greaves et at, Creation and uses of positron plasmas, 1439-1446, copyright 1994, by the American Institute of Physics.

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. 

The positron-trap technique has been used to measure the annihilation rate of positrons interacting with a wide variety of molecules. The species investigated by Iwata et al. (1995) include many hydrocarbons, substituted (e.g. fluorinated and chlorinated) hydrocarbons and aromatics as mentioned in section 6.1, large values of (Zeff) (in excess of 106) were found for some molecules. Several distinct trends are exhibited in the data of Iwata et al. (1995). Though much of the detailed physics involved in the annihilation process on these large molecules is still unclear, the model of Laricchia and Wilkin (1997), described in section 6.1, may offer a qualitative explanation of the observations. 

As the density of a gas is increased and/or its temperature is lowered towards or below the critical temperature, Tc, new phenomena associated with the trapping and localization of positrons are sometimes encountered, indicating that many-body processes affect positron annihilation. We briefly describe these phenomena here, but a much more detailed treatment can be found in the review of Iakubov and Khrapak (1982). 

Iakubov, I.T. and Khrapak, A.G. (1982). Self-trapped states of positrons and positronium in dense gases and liquids. Rep. Prog. Phys. 45 697-751. 

If sufficient positrons can be confined, studies of particle transport within the plasma, etc., similar to those conducted with electrons can be carried out. It may be possible to use the enhanced detection possibilities afforded since positron-electron annihilations can be detected. An ultra-cold source of positrons would also have a variety of other applications.24 For example, it has been proposed to eject trapped positrons into a plasma as a diagnostic.25 Also, positrons initially in thermal equilibrium at 4.2K within a trap would form a pulsed positron beam of high brightness when accelerated out of the trap. 

Fig. 5.6 Resonance trapping of electrons (positrons) having excess kinetic energy in the gas and liquid phases.

The annihilation characteristics of a positron in a medium is dependent on the overlap of the positron wavefunction with the electron wavefunction [9]. From a measurement of the two photon momentum distribution, information on the electron momentum distribution can be obtained and this forms the basis of extensive studies on electron momentum distribution and Fermi surface of solids [9]. In the presence of defects, in particular, vacancy type defects, positrons are trapped at defects and the resultant annihilation characteristics can be used to characterize the defects [9, 10], Given these inherent strengths of the technique, in the years following the discovery HTSC, a large number of positron annihilation experiments have been carried out [11, 12]. These studies can be broadly classified into three categories (1) Studies on the temperature dependence of annihilation characteristics across Tc, (2) Studies on structure and defect properties and (3) Investigation of the Fermi surface. In this chapter we present an account of these investigations, with focus mainly on the Y 1 2 3 system (for an exhaustive review, see Ref. 11). 

In some of the experiments [30, 31], variation of lifetime uncorrelated with Tc, has been observed. This has prompted explanations for the observed temperature dependence of lifetime in terms of positron trapping behaviour... 

---