Positron trapping

Referring again to Figure 1.8(a), the surface-trapped positron shown there is bound by an energy Eb. It has been shown many times (e.g. 

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... 

As outlined by Wolf (1993) and Holzscheiter et al. (1996), similar considerations to those described above also apply to recombination in traps, and in particular the nested Penning-trap scheme (see below), again with appropriate assumptions regarding the speed distributions of the trapped positrons and antiprotons and their degree of spatial overlap. As an example, Holzscheiter et al. (1996) argued that the recombination rates are of the order of one per second (though dependent upon Ee) for 106 positrons and 105 antiprotons trapped in a volume of 1 cm3. 

Annihilation at positron energies below the threshold for Ps formation, which used to be measured for a variety of high-density gases, can now be measured by introducing low-pressure gas in the presence of a cloud of trapped positrons, thus avoiding the density-dependent effects. It has become possible even to use a positron beam to determine the annihilation cross section as a function of the positron energy. 

The exact electric potentials and potential steps applied to the electrodes are crucial to maximize the number of trapped positrons eventually confined in... 

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. 

An unmoderated, 1 mCi source of 22Na was used in the UW experiments. The positrons vary in total kinetic energy between 0 and 544 keV and travel along magnetic field lines into the trap. Positrons available for trapping are those whose kinetic energy parallel to the magnetic field is within a 1 meV window. Approximately 6 x 10-5 of the emitted positrons were estimated to be within this window.26... 

Although our primary goal is to produce sufficient positrons for antihydrogen production, it is useful to examine the plasma that will be formed and to see if trapped positrons may also be useful for plasma studies. A single component plasma can be confined within a trap. As with two component plasmas, the Debye length... 

In our initial experiments with trapped positrons, if we achieve densities of order n = 108/cm3 with N = 107 positrons in the trap at T = 4.2 K, we will clearly have a plasma in the sense of Eqs. (2) and (4). The Debye length will be much smaller than the dimension of the positron cloud. Correlations will be important since T 0.3. This may make it possible, for example, to study particle transport for a plasma with n 3D 1. To produce a classical plasma for study, the positrons can easily be heated using... 

The PAES mechanism, first demonstrated in 1987 [1], can be outlined as follows (1). A positron implanted at low energy diffuses to and gets trapped at the surface. (2). A few percent of the trapped positrons annihilate with core electrons leaving atom in excited state. (3). The atom relaxes via emission of an Auger electron. The PAES mechanism is contrasted with that of electron induced Auger Spectroscopy (EAES) in Figurel2.1. 

The total annihilation rate, X, of the surface trapped positrons is found from the following equation ... 

Another positron state is formed when free volume-type crystal defects are present in the metal crystal. The positively charged ionic cores are missing from these defects, so, usually they are effective traps for any positive particle, including the positron in our case. Thus, in most metals, vacancies, vacancy clusters, dislocations, and grain boundaries localize some or all of the free positrons and produce another positron state, the trapped positron. These localized positrons still can meet conducting electrons, but ionic cores are out of their reach. Accordingly, their annihilation characteristics differ from those of free positrons significantly. Different kinds of traps all have their own characteristic annihilation parameters but these parameters are very close to each other. 

In a real system, the positron exists in different states. It may annihilate either with valence or conduction electrons of the bulk. These processes give rise to a bulk annihilation rate Ab. It may also be trapped in various defect states Dj where the electron density is smaller than in the bulk, i.e. a single vacancy, a cluster of vacancies, dislocations, impurities etc. Each defect state will be characterized by an annihilation rate Dj- In a vacancy-like defect the trapped-positron lifetime is increased compared to free positrons aimihilating in the bulk, as the electron density is locally reduced. Each defect state leads to a different lifetime Tdj = 1/Ap,. 

For the experimental determination of viv, it is necessary to independently measure the absolute concentration of monovacancies in the specimen. Such experiments were performed at elevated temperatures, where the equilibrium concentration of monovacancies is high enough to make the contribution from trapped positrons to the PL spectrum significant [110]. Kluin et al. [107] have correlated positron lifetime, dilatometry and lattice parameter experiments. Another way is to perform electron irradiation at low temperature [109]. The irradiation-induced Frenkel pairs are frozen in the lattice, and their concentration may be obtained by measuring the residual resistivity and dividing it by the resistivity of a Frenkel pair. 

In order to elucidate whether such a precipitate can trap positrons, the positron affinities A+ for the host material and the precipitate were calculated [154], The A+ values were found to be relatively high and the positron lifetimes very short for perfect MC carbides. This fact confirms that perfect MC (M s Cr, V, Ti, Mn, Fe, Zr, Nb) carbides are very dense materials that cannot trap positrons when embedded in the Fe matrix. In general, from a PAS point of view, radiation damage can be interpreted as a combination of radiation-induced point defects, dislocations and small vacancy clusters [129,130] that occur mainly in the region of the precipitate-matrix interface. 

The longer positron lifetime in each test film corresponds to the poatrons trapped in the potential defects (microvoids) in the test films. These microvoids result firom fluctuations in the packing density of the macromolecular diains. The sizes of these microvoids arc too small for the formation and localization of positronium atoms. However, fi ee positrons can be trapped at these sites with subsequent annihilation. The radii of the microvoids (R) in nanometers and the trapped positron lifetime (tj) in nanoseconds are related as foOows ... 

This equation differs from the conventional model (6) for positronium-for-ming media in having l/2.5r instead of l/2r as the left hand side term. This form has been dictated by the following considerations (a) The positron annihilation in polyimides reportedly (7) differs considerably from that observed in most polymers. It proceeds from the free or trapped positron states without the formation of positronium atoms (b) Positron lifetime spectra in all of the polyimides (PMDA, BFDA, BTDA and 6FDA-based polyimides etc.) investigated in this laboratory exhibit only two lifetime components. The shorter lifetime (r,) ranges from 100 to 300 picoseconds and arises firom free positron... 

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