Positron spatial distribution

The evolution of the positron spatial distribution /(r t) is conventionally described by the diffusion-annihilation equation [72]... 

SR is emitted by any electrically charged particle (usually an electron or positron) moving at nearly relativistic velocities (v c) along a curved trajectory of large radius (i.e. large compared to atomic or molecular dimensions). The spatial distribution of the radiation depends on the linear velocity of the particle and is emitted tangentially to the plane of the trajectory. 

At the end of the slowing-down by ionization and electronic excitation, the spatial distribution of e+ coincides with the distribution of the blob species (i.e., exp(-r2/o )). Such a subionizing positron having some eV of excess kinetic energy may easily escape from its blob because there is no Coulombic interaction between the blob and the e+ (the blob is electrically neutral). It is expected that by the end of thermalization, the e+ distribution becomes broader with the dispersion ... 

Fig. 5.3 The spatial distribution of the positron density at the Ps formation stage when an external electric field E is imposed. efn is that part of the positron density that is bound within the blob and not biased by the external electric field. is the part perturbed by the field. The depth of the trapping potential is about several tenths of eV.

Further developments in this field would probably be forthcoming with more precise studies of the energetics of Ps formation, and measurements of the work functions for e+ and Ps using low-energy positron beams. Better understanding may come from studies of Ps formation at different temperatures and external electric fields (determination of e+ mobility, investigation of the positron-blob interaction, e+ thermalization parameters and its spatial distribution). 

Various forms of spectroscopy have been applied to in situ studies of catalysis, and it is appropriate to cite a few examples. FT-IR is frequently employed for in situ investigations. The experimental configurations used can be either transmission studies of free-standing catalyst wafers [2] or diffuse reflectance measurements on samples in catalytic reaction chambers 13]. In situ Raman spectroscopy has also been applied [4]. X-rays have been used to study catalysts in situ, either by powder diffraction methods [5,6] or XAFS [7]. In situ imaging techniques are beginning to be applied to the measurement of spatial distributions and residence times in catalytic reactors. A recent example of this method employed positron-emission tomography [8]. 

Richard J-C, Factor P, Welch LC, Schuster DP. Iinaging the spatial distribution of transgene expression in the lungs with positron emission tomography. Gene Ther 2003 10 2074-2080. 

Positron emission tomography (PET) is a quantitative and noninvasive technique that enables in vivo investigations of cellular and molecular processes (Dufort et al., 2010). This technique assesses the 3D spatial distribution of special tracers, incorporating positron emitting radioactive isotopes injected into the body (Hoff, 2005). 

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. 

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