Triple differential cross section

Fig. 5.8. The triple differential cross section for positron impact ionization of atomic hydrogen, expressed as a function of the energy of the ejected electron. The scattered positron and electron both emerge in the direction of the incident...

Recently, Kover and Laricchia (1998) reported the first measurement of d3(Tj+ /riOidQ2d/f. the triple differential cross section for positron collisions. Molecular hydrogen was chosen as the target for positrons at... 

On the grounds of very general symmetry arguments the triple differential cross section for two-electron emission following photon impact can be represented as... 

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.

In order to elucidate how the total cross section for double photoionization, equ. (5.76), can be derived from the triple-differential cross section, equ. (4.84b), the necessary integration steps will be listed (for details see [HSW91]). Assuming for simplicity completely linearly polarized incident light with the electric field vector defining the reference axis, the triple-differential cross section from equ. (4.84b) including also a constant of proportionality can be reproduced here ... 

Starting with the parametrization for two-electron emission given in equ. (4.68), and using equ. (4.67) which relates the bipolar spherical harmonics to spherical harmonics attached to the actual directions ka = a, electron emission, the triple differential cross section for two-electron emission can be rewritten as... 

Eph is the photon energy, and Ej++ is the energy necessary for double ionization. The -function restricts the energies to Eb = Eexc — Ea, so equ. (4.62a) is replaced by the triple-differential cross section (TDCS)... 

The so-called triple-differential cross section is the measure of the probability that in an (e,2e) event an incident electron of momentum ko and energy Eo produces two electrons of energy and momenta and kj, k in the solid angles and respectively. It is the... 

The differential cross section (6.60) is sometimes called the triple differential cross section because it is differential in two solid angles and one energy. In the absence of spin analysis it provides the most-detailed information about the ionisation mechanism, but it is impracticable to study it over the full kinematic range available to a three-body final state. It is more informative to study it as a function of one variable in restricted kinematic regions. 

The most complicated example ever calculated by us was the system on Ar which is a gas-type experiment published by Schulz et al. [6], Fig. 2 gives the results of the experiment and our calculation [7,8] for the triple differential cross section to observe at least two X-rays after the collision from either Ar (P a) or S (Pjs) or one X-ray of both types (Psa)- In this case we adapted even the correlation diagram according to the occupation of the levels during the collision. 

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