Shake-up effects

One can therefore, in general, not separate the relaxation and shake up effects induced by the hole from the corresponding effects induced by the photoelectron. These considerations are particularly important in the photoionization threshold region where the speed of the photoelectron is relatively low. 

Sinha ejt al /135/ also applied the Haque-Mukherjee formalism for IP calculations, but they envisaged a more general computational strategy where not only the principal IP values at the outer and inner valence region but also the satellite peaks with dominant shake-up effects were aimed at. For this, they included all the hole orbitals upto the inner valence region as active. Since the dimension of the model space for the one-hole valence problem is just equal to the number of hole orbitals, it may at first appear surprising that satellite peaks can at all be obtained in this scheme in addition to the main peaks. We should, however, note that the CC equations are inherently non-linear in nature. In fact, at any n-valence level the eq. (7.3.18) involves quadratic... 

Shake-up effects may start to contribute from the II2 peak. That may be the reason why the measured peak is higher than calculated and also the reason the intensity beyond the II2 peak is strong. 

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. 

The OVGF function method provides a quantitative account of ionisation phenomena when the independent-particle picture of ionisation holds and as such is most applicable in the treatment of outer-valence orbitals. It provides an average absolute error for vertical ionisation energies below 20 eV of 0.25 eV for closed shell molecules. The TDA and ADC(3) methods allow for the breakdown of one particle picture of ionisation and so enable the calculation of the shake up spectra. The ADC(3) is correct up to 3rd order, is size consistent and includes correlation effects in both the initial and final states. 

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. 

Shake-up and shake-off losses are final state effects, which arise when the... 

The term S0 k) in (6-9) is a correction for relaxation or final state effects in the emitting atom, such as the shake-up, shake-off and plasmon excitations discussed in Chapter 3. The result of these processes is that some absorbed X-ray quanta of energy hv are converted not into photoelectrons of kinetic energy hv-Eb, but into electrons with lower kinetic energy as well. 

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... 

Core electron ejection normally yields only one primary final state (aside from shake-up and shake-off states). However, if there are unpaired valence electrons, more than one final state can be formed because exchange interaction affects the spin-up and spin-down electrons differently. If a core s electron is ejected, two final states are formed. If a core electron of higher angular momentum, such as a 2p electron, is ejected, a large number of multiplet states can result. In this case it is difficult to resolve the separate states, and the usual effect of unpaired valence electrons is... 

Shake up - shake off satellites. Monopole excited states energy separation with respect to direct photoionization peaks and relative intensities of components of singlet and triplet origin. Short and longer range effects directly (Analogue of UV). 

Comparison of the UV spectrum of polystyrene in the 2600 A region with that of toluene shows a close relationship in terms of both extinction coefficients and vibronic fine structure. The effect of para substituents is most conveniently characterized by the shift in the band corresponding to the a0-o transition. The comparison of substituent effects on the electronic excited states of thepara substituted polystyrenes parallels those for the corresponding para substituted toluenes. Such a correlation would only be expected if the tr - n transitions were effectively localized within a given pendant group of the polymer system. This conclusion is reinforced by the observation that polystyrene and toluene show similar shake up structure in their ESC A spectra with respect to both band profiles and intensities (when due... 

This may be derived from experimental data by analyzing the first order inductive shift in non alternants and second order shift in alternants. Both substituent constants are therefore intimately related to substituent effects on the it - n dipole excited states. Figure 44 shows the correlation with the shake up intensities. The trends displayed are quite striking and leave little doubt that the satellites arise from it->it excitations. 

Similar effects have also been observed for solids and seem to become a very important source of information, because for a given ion the satellites are found to depend in intensity, position and shape on the type of ligand in transition metal complexes 24,13s,im, 174,175) Thus in many cases the study of shake-up peaks has provided additional evidence for a specific oxydation state 17> and will certainly increase our understanding of crystal and ligand field effects. 

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