Double photoionization helium

J.-Z. Tang, I. Shimamura, Double photoionization of helium at low photon energies, Phys. Rev. A 52 (1995) R3413. 

A.S. Kheifets, I. Bray, Photoionization with excitation and double photoionization of the helium isoelectronic sequence, Phys. Rev. A 58 (1998) 4501. 

A.K. Kazansky, P. Selles, L. Malegat, Hyperspherical time-dependent method with semi-classical outgoing waves for double photoionization of helium, Phys. Rev. A 68 (2003) 052701. 

Depending on the individual orbital angular momenta /a and tb involved, the summation can go up to infinity. Such a situation occurs for double photoionization in helium where the 1P° state of the continuum pair wavefunction can be obtained by an unlimited coupling of individual orbital momenta (esep, sped, edef,...). However, in the case of photon-induced two-step double ionization the formulation... 

Table 4.1. The lowest A-coefficients neededfor the description of double photoionization in helium according to equ. (4.68).

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 content of this angular factor is in agreement with two selection rules derived rigorously for vanishing intensity in helium double photoionization [MBr93] ... 

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... 

Starting from a different treatment of double photoionization in helium, based on properties of the wavefunctions in the threshold region, and special coordinates (hyperspherical coordinates) for the description of the correlated motion of the electrons, different predictions for this 0 parameter have been obtained (see [HSW91, KOs92] with references therein).)... 

Figure 4.44 Illustration of energy- and angle-resolved two-electron emission following direct double photoionization in helium at 80 eV photon energy using linearly polarized light (electric field vector along the x-axis). Both electrons are detected in a plane perpendicular to the photon beam direction, the direction of one electron (ea) is fixed at a = 180°, = 150° and a = 90° (first, second and third columns in the figure), while...

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