Photoionization description

For many years, investigations on the electronic structure of organic radical cations in general, and of polyenes in particular, were dominated by PE spectroscopy which represented by far the most copious source of data on this subject. Consequently, attention was focussed mainly on those excited states of radical ions which can be formed by direct photoionization. However, promotion of electrons into virtual MOs of radical cations is also possible, but as the corresponding excited states cannot be attained by a one-photon process from the neutral molecule they do not manifest themselves in PE spectra. On the other hand, they can be reached by electronic excitation of the radical cations, provided that the corresponding transitions are allowed by electric-dipole selection rules. As will be shown in Section III.C, the description of such states requires an extension of the simple models used in Section n, but before going into this, we would like to discuss them in a qualitative way and give a brief account of experimental techniques used to study them. 

The first approximation to the description of Rydberg levels treats the benzene ion-core as a monopole. This description is known not to be quantitatively accurate. Calculations which include the symmetry of the molecular ion, and the charge delocalization, lead to an energy level spectrum in much better agreement with experiment. Thus, it seems unlikely that the geometric structure of the molecular ion can be completely neglected in the study of photoionization. 

These general remarks on the process of electron emission following photoionization lead us to a description of the experimental set-up used (spin-detection... 

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

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).)... 

To talk of a 2pm photoelectron suggests an underlying single-particle description, but this is not necessarily the case. Here and in the following it is understood to be a shorthand notation for photoionization leading to the 2p 1 2P3/2 final ionic state. 

For a detailed description of the RPA method in atomic photoionization the reader is referred to [ACh75, Wen84, Amu90], but the following points are mentioned here ... 

In this general formulation no information is required concerning the underlying coupling scheme used for the description of the photoionization channels. 

We have already shown that excitation energies can be diagrammatically decomposed to yield simpler quantities such as ionization potentials and electron affinities plus some remaining diagrams. MB-RSPT permits the use of this treatment for even more complex processes. In this section, we present the applicability of the theory to double ionizations observed in Auger spectra as well as excitations accompanying photoionization (shake-up processes) observed in ESCA and photoelectron spectroscopy. A detailed description of this approach is given in Refs.135,136. Here we shall present only the formal description. 

The authors of [315] applied linearly polarized synchrotron radiation (45-66 nm) for ionization, which corresponds to photon energy from 18.76 eV (threshold) + 0.7 eV up to 27 eV. The measured V values, as dependent on photon energy, changed correspondingly from 0.052 down to approximately half the value, which made it possible to determine the value of r within the range 0.4-0.7. Further improvement of the experiment and refinement of the theoretical description was carried out in [179]. Accounting for the hyperfine and spin-rotational interaction effect made it possible to refine the photoionization channel relation r, which yielded values of 0.2-0.4 for photon energies between threshold and 32 eV. 

We turn now to a more detailed description of the photoionization probe step in order to clarify the ideas presented above. Time-resolved photoelectron spectroscopy probes the excited-state dynamics using a time-delayed probe laser pulse that brings about ionization of the excited-state wave packet, usually with a single photon... 

In conclusion, much interest is presently focussed on the dynamics and excitation spectra of transition-metal carbonyls and adsorbate systems, and I have little doubt that the problems discussed in this section will be understood before long. However, the problem of first principles descriptions of photoionization spectra of these systems will remain a very important field of application of many-body theory for a long time to... 

Sofar the imaging results of Fig. 3.1 were discussed in very classical terms, using the notion of a set of trajectories that take the electron from the atom to the detector. However, this description does not do justice to the fact that atomic photoionization is a quantum mechanical proces. Similar to the interference between light beams that is observed in Young s double slit experiment, we may expect to see the effects of interference if many different quantum paths exist that connect the atom to a particular point on the detector. Indeed this interference was previously observed in photodetachment experiments by Blondel and co-workers, which revealed the interference between two trajectories by means of which a photo-detached electron can be transported between the atom and the detector [33]. The current case of atomic photoionization is more complicated, since classical theory predicts that there are an infinite number of trajectories along which the electron can move from the atom to a particular point on the detector [32,34], Nevertheless, as Fig. 3.2 shows, the interference between trajectories is observable [35] when the resolution of the experiment is improved [36], The number of interference fringes smoothly increases with the photoelectron energy. 

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