Doppler broadening experiments

These sketches serve to illustrate that there is structure in the photopeak which can yield information, albeit with relatively low resolution, on the details of electronic structure. Analysis routines have been developed which take account of the detailed shape of the peak, with a view to maximising the amount of information obtained in Doppler broadening experiments (see, e.g., [31]). We shall later that by decreasing background significantly, detailed analysis of the peak shape can yield considerable fruit. 

Natural linewidths are broadened by several mechanisms. Those effective in the gas phase include collisional and Doppler broadening. Collisional broadening results when an optically active system experiences perturbations by other species. Collisions effectively reduce the natural lifetime, so the broadening depends on a characteristic impact time, that is typically 1 ps at atmospheric pressure ... 

The arguments seen in section 2.3 suggest that resonant y-absorption should decrease at very low temperatures because the Doppler broadening of the y-lines decreases and may even drop below the value of the recoil energy. In his experiments with solid sources and absorbers, however, R.L. Mossbauer ([1] in Chap. 1) observed on the... 

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). 

In the first step of the experiment (with the 3-1 and the 4-1 transitions being measured at at least 3 different pressures) the width can be extracted from a simultaneous fit of all transitions, which keeps the different Doppler broadenings free, but leaves the resolution for the different transitions fixed at its known value. In addition the strong interaction width is assumed to be the same for all transitions. With this procedure a common value for the strong interaction width can be extracted with an accuracy of about 2.5%. 

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. 

But experiments to resolve the fine structure of the Balmer lines were difficult as you all know, resolution was impeded by the Doppler broadening of components. So ionized helium comes into the picture, because, as Sommerfeld s formula predicted, fine structure intervals are a function of (aZ)2, so in helium they are of order four times as wide as in hydrogen and one has more chance of resolving the Doppler-broadened lines. So PASCHEN [40], in 1916. undertook an extensive study of the He+ lines and in particular, 4686 A (n = 4->3). Fine structure, indeed, was found and matched against Sommerfeld s formula. The measurements were used to determine a value of a. But the structure did not really match the theory in that the quantum numbers bore no imprint of electron spin, so even the orbital properties - which dominated the intensity rules based on a correspondence with classical radiation theory - were wrongly associated with components, and the value of a derived from this first study was later abandoned. 

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. 

Here, (...) = J2pn ri. .. ri) is the appropriate combinedquantal and thermodynamic average (over the classical probabilities pn) related with the condensed matter system. M and n(p) are the mass and momentum distribution of the scattering nucleus, respectively, and ior = q2 /2 M is the recoil energy. For convenience, h = 1. Eq. (2) is of central importance in most NCS experiments, since it relates the SCS directly to the momentum distribution. Furthermore, n(p) is related to the nuclear wave function by Fourier transform and therefore, to the spatial localization of the nucleus. It takes into account the fact that, if the scattering nucleus has a momentum distribution in its ground state, the 5-function centered at uor will be Doppler broadened. 

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. 

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