Electronic transition energies, matrix

Figure 33. Pressure dependence of the electronic transition energies of [Cu(dieten)2](BF4)2 polycrystalline (left panel) and in polyvinyl pyridine matrix (right panel).

If ionization of a core level X in an atom A in a solid matrix M by a primary electron of energy Ep gives rise to the current Ij (XYZ) of electrons produced by the Auger transition XYZ, then the Auger current from A is... 

UV-vis spectra of matrix-isolated intermediates are not so informative as matrix IR spectra. As a rule, an assignment of the UV spectrum to any intermediate follows after the identification of the latter by IR or esr spectroscopy. However, UV-vis spectra may sometimes be especially useful. It is well known, for example, that the energy of electronic transitions in singlet ground-state carbenes differs from that of the triplet species. In this way UV spectroscopy allows one to identify the ground state of the intermediate stabilized in the matrix in particular cases. This will be exemplified below. 

If the nuclear matrix element does not depend on the electron kinetic energy, as we have assumed so far, then a plot of the reduced spectral intensity, the left-hand side, versus the electron kinetic energy will be a straight line that intercepts the abscissa at the Q value. Such a graph is called a Kurie plot, and an example is shown in Figure 8.3. This procedure applies to allowed transitions (see below). There are correction terms that need to be taken into account for forbidden transitions. 

One-electron submatrix elements of the spherical functions operator occur in the expressions of any matrix element of a two-electron energy operator and the electron transition operators (except the magnetic dipole radiation), that is why we present in Table 5.1 their numerical values for the most practically needed cases /, / < 6. 

While calculating matrix elements of various items of the energy operator or electron transition quantities in relativistic approximation we shall... 

Usually, the first way is utilized in practice. This is due to the well developed mathematical technique necessary, by the presence of the expressions for both the matrix elements of the energy operator and of the electronic transitions in various coupling schemes. However, the second method is much more universal and easier to apply, provided that there are known corresponding transformation matrices. Now we shall briefly describe this method. 

As we have seen while considering energy spectra, the energy levels of free atoms are always degenerate relative to the projections M of the total angular momentum J. Further we shall learn that the characteristics of spontaneous electronic transitions do not depend on them. Let us define the line strength of the electronic transition of any multipolarity k as the modulus of the relevant matrix element squared, i.e. 

As we have seen in Chapter 11, the energy levels of atoms and ions, depending on the relative role of various intra-atomic interactions, are classified with the quantum numbers of different coupling schemes (11.2)— (11.5) or their combinations. Therefore, when calculating electron transition quantities, the accuracy of the coupling scheme must be accounted for. The latter in some cases may be different for initial and final configurations. Then the selection rules for electronic transitions are also different. That is why in Part 6 we presented expressions for matrix elements of electric multipole (Ek) transitions for various coupling schemes. 

These are produced by autoionization transitions from highly excited atoms with an inner vacancy. In many cases it is the main process of spontaneous de-excitation of atoms with a vacancy. Let us recall that the wave function of the autoionizing state (33.1) is the superposition of wave functions of discrete and continuous spectra. Mixing of discrete state with continuum is conditioned by the matrix element of the Hamiltonian (actually, of electrostatic interaction between electrons) with respect to these functions. One electron fills in the vacancy, whereas the energy (in the form of a virtual photon) of its transition is transferred by the above mentioned interaction to the other electron, which leaves the atom as a free Auger electron. Its energy a equals the difference in the energies of the ion in initial and final states ... 

---