Photoionization double

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

T.N. Rescigno, W. Vanrose, D.A. Homer, F. Martin, C.W. McCurdy, First principles study of double photoionization of H2 using exterior complex scaling, J. Electron Spectros. Relat. Phenom. 161 (2007) 85. 

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. 

Figure 1.3 Illustration of the two classes of two-electron processes caused by photoionization using magnesium as an example, using, on the left the model-picture of Fig. 1.1 and on the right an energy-level diagram (not to scale) (a) direct double photoionization in the outer 3s shell (b) 2p inner-shell photoionization with subsequent Auger decay where one 3s electron jumps down to fill the 2p hole and the other 3s electron is ejected into the continuum (Auger electron). The wavy line represents the incident photon (which is often omitted in such representations) electrons and holes are shown as filled and open circles, respectively arrows indicate the movements of electrons continuum electrons are classified according to their kinetic energy e.

This expression disentangles the properties of the light polarization (coefficients /9, ( 1)), the geometry of two-electron emission (coefficients B t2(Ka, Kb)) and the dynamical parameters of the double photoionization process (coefficients A(ku k2, k)). The pkq(El) are the statistical tensors of the incident light which describe its polarization properties in the electric dipole approximation represented by 1. For linearly polarized light in which the electric field vector defines the z-axis of the coordinate frame, one has only two non-vanishing components given by (see equ. (8.99b))t... 

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).)... 

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

Double photoionization in the outer shell of rare gases by a single photon is an important manifestation of electron correlations. One specific aspect which has received much attention over the years is double photoionization in the vicinity of the double-ionization threshold. On the theoretical side, this attention is due to the possibility of deriving certain threshold laws without a full solution of the complicated three-body problem of two electrons escaping the field of the remaining ion. On the experimental side, the study of threshold phenomena always provides the challenge for mastering extremely difficult experiments. 

Here the quantity U is an effective potential that contains three contributions the kinetic energy for the radial movement of the electrons (in the coordinate a), a centrifugal potential energy, and the Coulomb potential energy — C(a, 12)/R of the system. In the present context of double photoionization it is this Coulomb energy which determines the features of two-electron emission (in atomic units) ... 

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 ... 

Table 5.3. Data relevant for double photoionization in the outer 3p shell of argon.

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