Doppler broadening positron

In this section we introduce three techniques frequently encountered in positron physics, namely those used to measure annihilation lifetimes and the Doppler broadening (or Doppler shift) and angular correlation of the annihilation radiation. These techniques, or variants thereof, are encountered throughout the rest of this work, and here we briefly describe... 

The experimental techniques involved in measuring the angular correlation and the Doppler broadening of the two annihilation gamma-rays were introduced in section 1.3. These techniques rely on the fact that the motion of the positron-electron pair immediately prior to annihilation causes the two gamma-rays to be emitted in directions differing... 

The ability of angular correlation and Doppler broadening techniques to provide information concerning the momentum of an annihilating electron-positron pair was briefly discussed in section 1.3. Also, it... 

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). 

A broad overview of traditional methods and recent developments in experimental positron spectroscopy is presented. A discussion of the generation and detection of positrons and their annihilation radiation is followed by a survey of techniques used for positron lifetime measurement, Doppler broadening spectroscopy and angular correlation of annihilation radiation, and the opportunities presented by combining these methods (e.g. in age-momentum correlation) and/or extending their capabilities by the use of monoenergetic positron beams. Novel spectroscopic and microscopic techniques using positron beams are also described. 

This chapter will begin by looking at some of the hardware requirements for positron-based experiments and then move on to their application in the measurement of angular correlation, positron lifetimes and Doppler broadening parameters. We shall then look at the generation and application of beams of mono-energetic positrons. 

The main techniques used are positron annihilation lifetime spectroscopy (PALS) and the Doppler broadening (DB) or angular correlation (AC) techniques. The PALS parameters are the relative intensities (I j) and the... 

Measurements of the Doppler broadening of the annihilation radiation produced by various molecules has been related to annihilation at specific sites within molecules by Iwata, et al. [15]. Prom the observed 7-ray spectra, the line width of the dominate peak, which comes from valence electrons, was extracted. Thus, for each molecule there is a single measured quantity, the fine width. For a series of hydrocarbons, the observed fine widths were found to be linear in the fraction of electrons in C-C (or C-H) bonds. Each type of bond was assumed to contain two electrons. Prom a linear fit of this data, fine widths for the C-C and C-H bonds were extracted and found to be 2.06 and 2.42 keV, respectively. These agree reasonably with an old theoretical estimate in which the positron density was assumed to be constant over the molecule [16]. ... 

The terminology used here has been defined in preceding chapters. Treaties on positronium can also be found in Berko and Pendleton [2] and Rich [3]. Recent lifetimes are published by Gidley [4], Jean [5] and Yang and Jean [6] discuss positronium in open volume within polymers. Doppler broadening can be found in Saarinen [7] and Krause-Rehberg [8], Some aspects of positron porosimetry are presented rather briefly for lack of space. An upcoming review article will go into more details [9],... 

Temperature dependent work with positrons on porous materials is still in their infancy. Doppler broadening measurements have been published but suffer from the uptake of water (ice) [75],... 

It is possible to combine lifetime measurements with Doppler broadening techniques. In so-called Age-Momentum-Correlated measurements (AMOC), Doppler broadening information is collected as a function of time since positron implantation into the sample [76]. The energy loss mechanism for positronium as it traps in pores can be investigated. This might reveal material dependent effects that have not been included in any porosity studies by positrons. 

Figure 8.9 Variation with quenching temperature of, (a) positron lifetime, (b) Doppler broadened lineshape parameter, I, and (c) oxygen deficiency, as obtained from weight loss (+) and Tc (o) measurements. From Bharathi et al. [54].

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. 

A new spectroscopic method for the characterization of surface vacancy clusters is a combination of positron lifetime spectroscopy, which determines the size of vacancy clusters, and coincidence Doppler broadening of annihilation radiation, which gives information on where vacancy clusters are located [5, 6]. If these clusters are located on the surface of gold nanoparticles, namely the interface between the particle and host matrix, the surroundings of the clusters should include both particle atoms and the matrix atoms. Doppler broadening of annihilation radiation (DBAR) with two-detector coincidence should be able to reveal these atomic constituents, and therefore elucidate the location of vacancy clusters. 

AMOC allows time-dependent observations of the occupations and transitions of different positron states tagged by their characteristic Doppler broadening. Chemical reactions of positronium have been studied by beam-based AMOC as well as bound states between positrons (e+) and halide ions (cf. Sect. 2). 

In 1974, O.E. Mogensen and V.P. Shantarovich concluded from ACAR measurements on aqueous solutions of sodium chloride [15] that in this system a fourth positron state (in addition to p-Ps, free positrons and o-Ps) was formed, which they identified as an e+Cl bound state. The existence of such a bound state found support in several Doppler broadening and ACAR investigations on aqueous and non-aqueous solutions of halides and pseudohalides [16-20]. Since the commonly used expression bound state of positrons may lead to confusion with positrons bound in Ps, we refer to this fourth state as positron molecules and characterize it by the subscript M. 

The linewidth of annihilation from the free-positron state is Doppler-broadening measurements. In lifetime measurements the PsF component hides beneath the o-Ps component which has a similar lifetime. This is a case where the two-dimensional data analysis shows its great advantage As the Doppler broadening of each positron state is determined in its own time regime even positron states with similar features may be seperated from each other. Moreover, a tentative fitting procedure with only the three positron states as in pure water did not come to a satisfactory result with the AMOC histogram of the NaF solution. 

In Ar and even more pronounced, in Kr and Xe, the lineshape functions 5 (t) show indeed a clear shift of the juvenile Doppler broadening to higher positron ages (Figure 14.8). 

Mohamed, H.F.M. (2001) Study on polystyrene via positron annihilation lifetime and Doppler broadened techniques . Polymer, 42, 8013. 

Djourelov, N., Suzuki, T., Ito, Y, Shantarovich, V., and Kondo, K., Gamma and positron irradiation effects on polypropylene studied by coincidence Doppler broadening spectroscopy. Radial. Phys. Chem., 72, 687-694 (2005). 

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