Shake-up ionization

Before discussing even more sophisticated photoionization correlated methods, we need to mention another area in which correlation is important, namely the shake-up processes. A shake-up ionization means that electrons are excited (or de-excited) while another is ejected, as shown in Figure 14. As the energy relative to the ground state M+ species is changed because of excitation upon ejection of the electron, such states typically appear as satellites on the principal photoelectron peak. In a favorable case, their intensity can be comparable to that for a primary ionization. In principle, there are an infinite number of such shake-ups which correspond to each primary ionization, but only a few will be intense enough to be observable. 

In the simplest unrelaxed orbital independent particle model, the energy of this particular shake-up ionization 4 (Figure 14) would be approximated by... 

Table 28 Core Ionization and Shake-up Energies (eV) for Some Heterocycles (73M130102)...

In this contribution, in order to illustrate tlie importance of shake-up bands for extended systems, we simulate and compare on correlated grounds the ionization spectra of polyethylene and poly acetylene, the most simplest systems one can consider to represent insulating or semi-conducting polymers. Conclusions for the infinite stereoregular chains are drawn by exU apolation of the trends observed with the first terms of the related n-alkane or acene series, CnH2n+2 and CnHn+2. respectively, with n=2, 4, 6 and 8. Our simulations are also compared to X-ray photoionization spectra (7) recorded on gas phase samples of ethylene, butadiene and hexatriene, which provide a clear experimental manisfestation of the construction of correlation bands (8-12). 

In principle, one can extract from G(ti)) the complete series of the primary (one-hole, Ih) and excited (shake-up) states of the cation. In practice, one usually restricts the portion of shake-up space to be spanned to the 2h-lp (two-hole, one-particle) states defined by a single-electron transition, neglecting therefore excitations of higher rank (3h-2p, 4h-3p. ..) in the ionized system. In the so-called ADC[3] scheme (22), elertronic correlation effects in the reference ground state are included through third-order. In this scheme, multistate 2h-lp/2h-lp configuration interactions are also accounted for to first-order, whereas the couplings of the Ih and 2h-lp excitation manifolds are of second-order in electronic correlation. 

The Si(k) term takes into account amplitude reduction due to many-body effects and includes losses in the photoelectron energy due to electron shake-up (excitation of other electrons in the absorber) or shake-off (ionization of low-binding-energy electrons in the absorber) processes. 

We have tacitly assumed that the photoemission event occurs sufficiently slowly to ensure that the escaping electron feels the relaxation of the core-ionized atom. This is what we call the adiabatic limit. All relaxation effects on the energetic ground state of the core-ionized atom are accounted for in the kinetic energy of the photoelectron (but not the decay via Auger or fluorescence processes to a ground state ion, which occurs on a slower time scale). At the other extreme, the sudden limit , the photoelectron is emitted immediately after the absorption of the photon before the core-ionized atom relaxes. This is often accompanied by shake-up, shake-off and plasmon loss processes, which give additional peaks in the spectrum. 

The selection rules appropriate for a shake-up transition are of the monopole type2, 76. The intensity of a shake-up peak depends on the overlap integral between the lower state molecular orbital from which the electron is excited (in the neutral molecule) and the upper state molecular orbital to which the electron is excited (in the core-ionized molecule). Consequently one expects transitions of the type au au, ag " ag> 7T nu, and irg - ng with g u and u - g transitions forbidden. 

As a first, trivial, example of the application of the overlap criterion, let us consider the possibility of a shake-up peak associated with the C Is ionization of the terminal carbon atom in nitroethane and the v - v transition of the nitro group in that molecule. In this case the core ionization occurs in a region of the... 

The core ionization of an atom stabilizes all the valence electrons in the atom. Depending on whether the electronic transition shifts electron density to or from an atom, the energy separation for a shake-up peak of that atom will be less than or greater than the energy of the neutral molecule ionization81. As an illustration of these effects, let us consider the shake-up spectra of formamide, H2NCH082. The principal transitions involved are the vl - n3 and 7r2 - 7r3 transitions. The tTj... 

We must also take into account two further factors. First, the fact that the transmission efficiency of the analyzer is a fimction of the kinetic energy (K.E.) of the photoelectrons in the ESCA-3 Vacumn Generators instrument the transmission is inversely proportional to the K.E. of the electrons (3a). Second, photoelectron yields must refer to total yield from a particular ionization process and this need not, for example, be just the area of the relevant peak. Account must be taken of all processes that divert electrons from the primary peak, e.g., shake-up, shake-oflF, and plasmon peaks. In some cases, e.g., emission from the Cu 2P3/2 level, the contribution of additional processes is small but in others, and emission from the Al(2p) shell is an example, the no-loss peak is substantially less than the true Al(2p) emission. 

Fig. 48. Orbitals involved in the low energy shake up satellites accompanying core ionization in polystyrene, poly-l-vinylnaphthalene and polyvinylcarbazole...

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