Doppler broadening parameters

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. 

Recent experiments determined the velocity state of the pionic hydrogen atom at the moment of the charge exchange reaction [23]. These results constrain the input parameters for the cascade calculations as well as the direct X-ray measurements from muonic hydrogen. The results of the cascade calculations can then be used to correct for the influence of the Doppler broadening. 

For the moment we shall consider the standard method for describing the Doppler-broadened linewidth—i.e. by using a simple lineshape parameter. By far the most common parameters used—called S and W—are defined... 

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... 

Figure 8.4 Doppler broadening lineshape parameter vs temperature in DyBa2Cu307 Yo.5Pro.5Ba2Cu307 and PrBa2Cu307. The arrow indicates Tc, From Jung et al [34,35].

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. 

MMW spectra possess a number of features that make direct readout of sample concentration from a measurement less than straightforward. Although the peak absorption coefficient of the sample may be determined in several ways itemised below. Equations 1.24 and 1.48 show that additional information about linewidth, temperature, occupation of vibrational states and even Doppler broadening is required to obtain the analyte concentration. Such calculations can be incorporated into any anal5dic program, but the parameters required are often not readily available in the literature and may need to be determined directly. 

Doppler broadened spectral line half width parameter... 

S(t) is quite independent of the external parameters of the atoms (positions and velocities) and is not submitted to Doppler-broadening. 

The definition of S- and w-parameters used to evaluate Doppler-broadening spectra. The symbols h/ kotau ai cl W2 denote areas (intensities) under specific sections of the Gaussian peak... 

The equilibriimi conditions of the FRC were measured by field probes, excluded flux loops, HeNe interferometry, etc. Thomson scattering and Doppler broadening of the CV 2271 A line were used to measure T and T. Figure 13 shows the temperature dependence on initial fill pressure as well as the classical equilibration between T and T. sej f-consistent set of parameters is... 

Early experiments with positrons were dedicated to the study of electronic structure, for example Fermi surfaces in metals and alloys [78,79], Various experimental positron annihilation techniques based upon the equipment used for nuclear spectroscopy underwent intense development in the two decades following the end of the Second World War. In addition to angular correlation of the annihilation of y quanta, Doppler broadening of the annihilation line and positron lifetime spectroscopy were established as independent methods. By the end of the 1960s, it was realised that the annihilation parameters are sensitive to lattice imperfections. It was discovered that positrons can be trapped in crystal defects i.e., the wavefunction of the positron is localised at the defect site until annihilation. This behaviour of positrons was clearly demonstrated by several authors (e.g., MacKenzie et al. [80] for thermal vacancies in metals, Brandt et al. [81] in ionic crystals, and Dekhtyar et al. [82] after the plastic deformation of semiconductors). The investigation of crystal defects has since become the main focus of positron annihilation studies. 

DB, Doppler broadening measurement of the annihilation line-shape parameter S ... 

In graphite furnace AAS, the damping constant, a, varies from 0.17 (Be resonance line, 234.9 nm) to 3.27 (Cs, 852.1 nm) for absorption lines and its value for emission lines, in the primary sources varies from 0.01 to 0.05. A relatively small value of the u-parameter means that the emission profile is primarily determined by the Doppler broadening. 

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