Detectors exponential factor

The damping factors take into account 1) the mean free path k(k) of the photoelectron the exponential factor selects the contributions due to those photoelectron waves which make the round trip from the central atom to the scatterer and back without energy losses 2) the mean square value of the relative displacements of the central atom and of the scatterer. This is called Debye-Waller like term since it is not referred to the laboratory frame, but it is a relative value, and it is temperature dependent, of course It is important to remember the peculiar way of probing the matter that EXAFS does the source of the probe is the excited atom which sends off a photoelectron spherical wave, the detector of the distribution of the scattering centres in the environment is again the same central atom that receives the back-diffused photoelectron amplitude. This is a unique feature since all other crystallographic probes are totally (source and detector) or partially (source or detector) external probes , i.e. the measured quantities are referred to the laboratory reference system. 

A linear dependence between detector response and the amount of sample entering the detector is expected for phosphorus. The response for sulfur is inherently nonlinear and is described by 1(82) = A [S]", where 1(82 ) is the detector response, A an experimental constant, [8] the mass flow rate of sulfur atoms, and n an exponential factor. The theoretical value for n is 2, but in practice, values between 1.6 and 2.2 are frequently observed for the single flame FPD. Non-optimized flame conditions, compound-dependent decomposition, hydrocarbon quenching, and competing flame reactions that lead to de-excitation all contribute to this deviation. Decoupling the... 

The X-ray absorption factor (A) counts the decrease in density of characteristic X-rays from emitting location to detector. The absorption follows an exponential relationship as shown in Equation 2.2. 

The factor exp ( — At) gives the response of the detectors. If the flux undergoes a step increase, as shown in Fig. 14.28, the signal will rise exponentially to its saturated value. If the flux goes down suddenly, the signal will decay... 

The signal response time is important for the safe localization of leaks. It states the time period after spraying helium on the leak until the leak detector indication reaches a defined level (63% of final equilibrium value). Figure 8.3 shows the typical exponential trace of the signal rise. The response time can be calculated from the parameters of the system under test. The critical factors are the volume of the system and the total pumping speed of the installed vacuum pumps. Typical response times of chemical plant systems are in the range of several seconds up to a few minutes. 

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