Doppler broadening measurements

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],... 

In the field of positronium chemistry AMOC combines the positronlifetime analysis which is especially sensitive to detect long-lived ortho-positronium (o-Ps) with the Doppler-broadening-measurement technique which is particularly suitable for the observation of the para-positronium (p-Ps) state with its characteristic narrow momentum distribution. In addition,... 

The linewidth of annihilation from the free-positron state is 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. 

The above discussion is presented merely to give an idea of the types of EUV detectors and their applications in use on present fusion plasma experiments. It is by no means an exhaustive list of possibilities. Indeed, several different detectors are in use or being planned in future experiments. Resistive anode encoders will probably see more use in fusion experiments as they become commercially available. However, the low count rates available ( 10 to 10 sec-1) will result in these detectors being used mostly for line profile studies (e.g., ion temperature measurements via Doppler broadening measurements). Intensified CCD arrays (back-illuminated or otherwise), vidicon or CID systems, lens-coupled intensifiers, and anode detectors have all seen some use on tokamak experiments or are planned for the near future, but have not been widely used as yet. However, in terms of availability, pixel format, dynamic range, insensitivity to magnetic fields, compact package, and moderate cost, the IPDA remains the most versatile multichannel EUV detector for plasma spectroscopy. 

The 2Y-annihilation of positrons produces two correlated photons. On the other hand, hoth lifetime spectroscopy and Doppler-broadening measurements need only one of them. This suggests an evident possibility, that is, the combination of the two measurements. To achieve this goal, a three-photon coincidence system is required. In the system, one of the detectors measures the energy of an annihilation photon, and the other two determine the lifetime of the corresponding positron. 

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

Figure 4.36 a Typical Doppler-broadening spectrum, and b scheme of a Doppler-broadening measurement system... 

It would appear that measurement of the integrated absorption coefficient should furnish an ideal method of quantitative analysis. In practice, however, the absolute measurement of the absorption coefficients of atomic spectral lines is extremely difficult. The natural line width of an atomic spectral line is about 10 5 nm, but owing to the influence of Doppler and pressure effects, the line is broadened to about 0.002 nm at flame temperatures of2000-3000 K. To measure the absorption coefficient of a line thus broadened would require a spectrometer with a resolving power of 500000. This difficulty was overcome by Walsh,41 who used a source of sharp emission lines with a much smaller half width than the absorption line, and the radiation frequency of which is centred on the absorption frequency. In this way, the absorption coefficient at the centre of the line, Kmax, may be measured. If the profile of the absorption line is assumed to be due only to Doppler broadening, then there is a relationship between Kmax and N0. Thus the only requirement of the spectrometer is that it shall be capable of isolating the required resonance line from all other lines emitted by the source. 

There are well-exploited connections between experimental phenomena and electron momentum densities. Inelastic scattering [167,181-184] of high-energy electrons, X rays, or y rays by electrons in a molecule allows us to measure the electron momentum density of the molecule. The observable is the intensity of the Compton scattering at wavelengths shifted, by a Doppler broadening-like... 

In conclusion, the observed spectrum of an isolated Doppler-broadened line, along with some well-known constants and the easily measured temperature, contains all the information needed to determine the response function. Application details for this method are available in the literature (Jansson, 1968, 1970). 

For simplicity, suppose that we have an emission spectrum consisting of a single, predominantly Doppler-broadened line. This spectrum may be taken as an approximation to the case of widely separated and nonoverlapping lines of equal intensity. Again for simplicity, now consider the typical emission spectrum to be continuous, not sampled. Thus q(x) is given by q(x) = q0 exp( —x2) for a typical line, where q0 is the peak height. We have chosen the abscissa to be measured in either wavelength or wave number relative to a typical line center. For illustrative purposes only, the x interval for the observation is taken to be 2 Ax. If the line is centered in this interval at x = 0, we can never have q(x) < exp ( — Ax2). 

State-resolved inelastic scattering for a wide range of incident conditions ( ), d,) are measured for this system by combining molecular beam techniques with (2 + 1) ion TOF REMPI detection of the scattered molecules [58]. Energy transfer parallel to the surface is measured from the Doppler broadening of the REMPI spectra. Trapping... 

Figure 21-17 Relative bandwidths of hollow-cathode emission, atomic absorption, and a monochromator. Linewidths are measured at half the signal height. The linewidth from the hollow cathode is relatively narrow because the gas temperature in the lamp is lower than a flame temperature (so there is less Doppler broadening) and the pressure in the lamp is lower than the pressure in a flame (so there is less pressure broadening).

Even in a molecule the size of benzene the resolution achieved in this way is sufficient to investigate the dynamic behavior of individual rotational states. For this it is necessary to eliminate the Doppler broadening of the rovibronic transitions. Two methods have been applied (i) the elimination of Doppler broadening in a Doppler-free two-photon-transition and (ii) the reduction of Doppler broadening in a molecular beam. Measurements of the dynamic behavior have been performed in the frequency [3] and time domain [4]. We will briefly summarize the results from high-resolution measurements and discuss the conclusions on the intramolecular decay mechanism. Then it will be discussed how the intramolecular dynamics is influenced by the attachment of an Ar or Kr atom to the benzene molecule, leading to a weakly bound van der Waals complex. 

The measurements of 2s — Is transitions in magnetically trapped hydrogen have achieved a relative accuracy of one part in 1012 [21] by means of two-photon spectroscopy which eliminates the first-order Doppler broadening. It is hoped that this technique will allow the measurement of the Is — 2s transition with the accuracy limited only by the shape of the transition line dictated by quantum electrodynamics, i.e. to a few parts in 1015. Further, if the center of the Is — 2s line could be determined with the accuracy of a few parts in 103 of its width, the relative accuracy for this transition would increase to a few parts in 1018. 

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 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). 

Photon Correlation. Particles suspended in a fluid undergo Brownian motion due to collisions with the liquid molecules. This random motion results in scattering and Doppler broadening of the frequency of the scattered light. Experimentally, it is more accurate to measure the autocorrelation function in the time domain than measuring the power spectrum in the frequency domain. The normalized electric field autocorrelation function g(t) for a suspension of monodisperse particles or droplets is given by ... 

In the case of the 1S-3S transition in hydrogen and for an estimated velocity of v=3km/s, the shift is Av =l4A kHz. We can t measure the velocity distribution by observing the Doppler broadened 1S-2P transition at 121 nm with a colinear laser beam, because the production of Lyman-a radiation is very difficult. In 1991 a method to compensate or at least to measure this effect was proposed by F. Biraben [7]. The basic idea is to apply a transverse magnetic field B in the atom-laser interaction region. This field has two effects ... 

The iT20Ne(6h — 5g) transition is an ideal case for a calibration line, because no Doppler broadening occurs from Coulomb deexcitation for the noble gas Ne as is the case for diatomic molecules like N2. Therefore, the line shape reflects exclusively the response of the spectrometer. The resolution achieved is 26 (seconds of arc), which is close to the theoretical limit of 22 for the chosen geometry. The line width of the TrN(5g — 4/) transition, measured to 50 , is dominated by Coulomb deexcitation [21]. 

---