Helium photoionization cross-sections

XPS. As indicated in Figure 1, core-level B.E. s are characteristic of individual atoms and so one obtains an atomic identification directly from the determined B.E. value. In addition, the core-level photoionization cross-sections are reasonably well-established, both theoretically (13) and experimentally (14), and since the core-levels are atomic in nature, there are no significant variations with chemical environment of the atoms, which means that the atom composition analysis can be made quantitative. All elements which have core-levels, i.e., everything but hydrogen and helium can be detected, though the magnitude of the cross-sections and hence the relative sensitivities to the different elements varies by 102. 

Figure 8.1 Theoretical values for the Is photoionization cross section of helium. L, V, and A indicate the length, velocity, and acceleration forms of the dipole matrix element, respectively. From [Mar67], using data from [SWe63].

As an example, the Is photoionization cross section in helium calculated for the three forms of the dipole matrix element is shown in Fig. 8.1, and the deviations can be clearly seen. 

Y. Komninos, C.A. Nicolaides, Many-electron approach to atomic photoionization Rydberg series of resonances and partial photoionization cross sections in Helium, around the n=2 threshold, Phys. Rev. A 34 (1986) 1995. 

Figure 11 Experimental and theoretical (dashed line) photoionization cross sections of helium.

Fig. 22. Calculations of the double photoionization cross section a for helium by Carter and Kelly, ref. 107. Curves labelled LOL(LOV) are lowest order length (velocity) results for the kskp channel. Curves labelled L(V) are length (velocity) results containing higher-order corrections for both kskp and kpkd channels. Curve labelled BJ is dipole-velocity result from Byron and Joachain, ref. 106.

Fig. 23. Double photoionization cross section of helium. Length (solid curve) and velocity (dashed curve) calculated by Carter and Kelly, ref. 107. Experimental data (dots) from Bizau et al., ref. 120.

Section 6.2). An example of such a calibration measurement is shown in Fig. 1.18 where Is photoionization in helium with the energy-independent p value of p = 2 was selected. The angle-dependent intensity varies between a maximum and a minimum value. Within these limits, at a certain angle partial cross section. The above relation requires for this case that... 

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... 

Cross sections for Is photoionization in helium and for 2p photoionization in neon [BWu95] ... 

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