Helium double-differential cross section

Fig. 10.12. Primary-electron double differential cross section for electron-helium ionisation. Experimental data are due to Muller-Fiedler et al. (1986) (open circles) and Avaldi et al. (1987a) (full circles). Full curves, distorted-wave Born approximation (McCarthy and Zhang, 1989). Cases illustrated are (a) Eq = 100 eV, Ef = 73.4 eV(A), 71.4 eV(B), 55.4 eV(C) (b) Eq = 300 eV, Ef = 235.4 eV (cross section multiplied by 100) (A), 271.4 eV(B) (c) Eq = 500 eV, Ef = 471.4 eV(A), 435.4 eV(B). From McCarthy and Zhang (1989).

L. Malegat, P. Selles, A.K. Kazansky, Absolute differential cross sections for photo double ionization of helium from the ab initio hyperspherical R-matrix method with semiclassical outgoing waves, Phys. Rev. Lett. 85 (2000) 4450. 

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... 

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