Photoionization differential

A detailed derivation of the photoionization differential cross-section expression, leading ultimately to the angular distribution in Eq. (4), is provided in Appendix A. This will help provide a detailed understanding of the photoelectron dynamics that determine the angular distribution parameters, as will be discussed in a subsequent section, but for now it may help develop the reader s appreciation of this phenomenon to provide a simple, if necessarily inexact, mechanical analogy. 

Sometimes, membrane inlets are operated at the same temperature as the IMS ceU, and sometimes they are operated at elevated temperatures. More recently, advantages of controlling the temperature of the membrane separate from that of the cell have been reported. The primary advantage of temperature-controlled membranes for sample introduction to an IMS is the ability to concentrate the sample and then heat the membrane to provide low-resolution separations as the analytes diffuse through the membrane. One application of this active membrane technology is the detection of benzene in water by photoionization differential mobility spectrometry. " Drawbacks of using membranes are rednced sensitivity, increased response times, and longer clearance times (i.e., memory effects). 

J.-Z. Tang, I. Shimamura, Differential cross sections for photoionization of He, J. Electron Spectrosc. Related Phenomena 79 (1996) 259. 

The thus determined wavefunctions of the continuous spectrum of the atom A encage in C60, combined with the wavefunctions of the ground state of the free atom A, are used in determining the total and differential photoionization cross sections of the encaged form. 

Starting in a manner similar to the treatment of single photoionization described in Section 2.1, double photoionization in helium caused by linearly polarized light will be treated first with uncorrelated wavefunctions. A calculation of the differential cross section for double photoionization then requires the evaluation... 

Figure 4.43 Energy- and angle-resolved triple-differential cross section for direct double photoionization in helium at 99 eV photon energy. The diagram shows the polar plot of relative intensity values for one electron (ea) kept at a fixed position while the angle of the coincident electron (eb) is varied. The data refer to electron emission in a plane perpendicular to the photon beam direction for partially linearly polarized light (Stokes parameter = 0.554) and for equal energy sharing of the excess energy, i.e., a = b = 10 eV. Experimental data are given by points with error bars, theoretical data by the solid curve.

The matrix element Mfi derived so far for the differential cross section of double photoionization in helium is based on uncorrelated wavefunctions in the initial and final states. For simplicity the initial state will be left uncorrelated, but electron correlations in the final state will now be included. The significance of final state correlations can be inferred from Fig. 4.43 without these correlations an intensity... 

Collecting together the information contained in equs. (4.78) and (4.81), the triple-differential cross section for double photoionization can be represented as... 

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