Selection rules emission spectra

Moseley found that each K spectrum of Barkla contains two lines, Ka and K(3, and that the L spectra are more complex. Later important work, especially by Siegbahn,38 has shown that M, N, and O spectra exist and are more complex in their turn. Relatively numerous low-intensity lines are now known to exist in all series. Fortunately, the analytical chemist can afford to ignore most of these low-intensity lines in his practical applications of x-ray methods at present. It generally suffices for him to know that x-ray spectra at their most complex are enormously simpler than emission spectra involving valence electrons, and that most x-ratr lines are satisfactorily accounted for on the basis of the simple selection rules that govern electron transitions between energy states. 

As seen from (12) and Fig. 6, the peaks in the excitation anisotropy spectrum indicate a small angle between the absorption and emission transition dipoles suggesting allowed 1PA transitions while valleys indicate large angles between these two dipoles, suggesting a forbidden 1PA transition. Due to selection rules for symmetrical cyanine-like dyes, the valleys in the anisotropy spectrum could indicate an allowed 2PA transition as demonstrated in Fig. 6. Thus, an excitation anisotropy spectrum can serve as a useful guide to suggest the positions of the final states in the 2PA spectra. 

As a result of the atomic nature of the core orbitals, the structure and width of the features in an X-ray emission spectrum reflect the density of states in the valence band from which the transition originates. Also as a result of the atomic nature of the core orbitals, the selection rules governing the X-ray emission are those appropriate to atomic spectroscopy, more especially the orbital angular momentum selection rule A1 = + 1. Thus, transitions to the Is band are only allowed from bands corresponding to the p orbitals. 

However, in the sodium atom, An = 0 is also allowed. Thus the 3s —> 3p transition is allowed, although the 3s —> 4s is forbidden, since in this case A/ = 0 and is forbidden. Taken together, the Bohr model of quantized electron orbitals, the selection rules, and the relationship between wavelength and energy derived from particle-wave duality are sufficient to explain the major features of the emission spectra of all elements. For the heavier elements in the periodic table, the absorption and emission spectra can be extremely complicated - manganese and iron, for example, have about 4600 lines in the visible and UV region of the spectrum. 

In the ideal case of free Eu + ions, we first must observe that the components of the electric dipole moment, e x, y, z), belong to the irreducible representation in the full rotation group. This can be seen, for instance, from the character table of group 0 (Table 7.4), where the dipole moment operator transforms as the T representation, which corresponds to in the full rotation group (Table 7.5). Since Z)° x Z) = Z) only the Dq -> Fi transition would be allowed at electric dipole order. This is, of course, the well known selection rule A.I = 0, 1 (except for / = 0 / = 0) from quantum mechanics. Thus, the emission spectrum of free Eu + ions would consist of a single Dq Ei transition, as indicated by an arrow in Figure 7.7 and sketched in Figure 7.8. 

If we start with excited molecules or atoms, we can observe spontaneous emission— generation of light as the atom or molecule drops down to a lower energy level. Equation 8.1 also dictates the possible frequencies in the emission spectrum. Spontaneous emission in general gives radiation in all directions, and the selection rules are almost the same as in Equation 8.4. The only difference is that we must have An < 0 for the final state to be lower in energy than the initial state. 

So far, this discussion of selection rules has considered only the electronic component of the transition. For molecular species, vibrational and rotational structure is possible in the spectrum, although for complex molecules, especially in condensed phases where collisional line broadening is important, the rotational lines, and sometimes the vibrational bands, may be too close to be resolved. Where the structure exists, however, certain transitions may be allowed or forbidden by vibrational or rotational selection rules. Such rules once again use the Born-Oppenheimer approximation, and assume that the wavefunctions for the individual modes may be separated. Quite apart from the symmetry-related selection rules, there is one further very important factor that determines the intensity of individual vibrational bands in electronic transitions, and that is the geometries of the two electronic states concerned. Relative intensities of different vibrational components of an electronic transition are of importance in connection with both absorption and emission processes. The populations of the vibrational levels obviously affect the relative intensities. In addition, electronic transitions between given vibrational levels in upper and lower states have a specific probability, determined in part... 

Additional information on electronic structure may be obtained from the x-ray emission spectra of the SiOj polymorphs. As explained in Chapter 2, x-ray emission spectra obey rather strict selection rules, and their intensities can therefore give information on the symmetry (atomic or molecular) of the valence states involved in the transition. In order to draw a correspondence between the various x-ray emission spectra and the photoelectron spectrum, the binding energies of core orbitals must be measured. In Fig. 4.12 (Fischer et al., 1977), the x-ray photoelectron and x-ray emission spectra of a-quartz are aligned on a common energy scale. All three x-ray emission spectra may be readily interpreted within the SiO/ cluster model. Indeed, the Si x-ray emission spectra of silicates are all similar to those of SiOj, no matter what their degree of polymerization. Some differences in detail exist between the spectra of a-quartz and other well-studied silicates, such as olivine, and such differences will be discussed later. 

The very different spectra of iodine obtained under continuum and discrete resonance-Raman conditions are illustrated in Fig. 11 for resonance with the B state, whose dissociation limit is 20,162 cm . In the case illustrated of discrete resonance-Raman scattering, Xl =514.5 nm, and specific re-emission results from an initial transition from the v" = 1 vibrational, J" = 99 rotational level of the X state to the v = 58, J = 100 level of the B state, i.e. the transition is 58 - l" R(99). Owing to the rotational selection rule for dipole radiation, AJ = 1, a pattern of doublets appears in the emission. Clearly, the continuum resonance-Raman spectrum of iodine (Xl = 488.0 nm) is very different from the discrete case spectrum. The structure, which arises from the 0,Q, and S branches of the multitude of vibration-rotation transitions occurring, can be analysed in terms of a Fortrat diagram, as done for gaseous bromine (67). 

Information regarding the normal modes of a polyatomic molecule, which are not IR active, may often be obtained from the Raman spectrum. Raman spectroscopy is an inelastic-scattering technique rather than requiring the absorption or emission of radiation of a particular energy. The selection rule differs from the IR in that it is required that the incident electric field of the radiation can induce a changing dipole moment of the molecule. This results in a different symmetry requirement for the normal modes of vibration to be Raman active, since it now depends on the polarizability of the molecule. 

Consider the Menon-Agarwal approach to the Autler-Townes spectrum of a V-type three-level atom. The atom is composed of two excited states, 1) and 3), and the ground state 2) coupled by transition dipole moments with matrix elements p12 and p32, but with no dipole coupling between the excited states. The excited states are separated in frequency by A. The spontaneous emission rates from 1) and 3) to the ground state 2) are Tj and T2, respectively. The atom is driven by a strong laser field of the Rabi frequency il, coupled solely to the 1) —> 2) transition. This is a crucial assumption, which would be difficult to realize in practice since quantum interference requires almost parallel dipole moments. However, the difficulty can be overcome in atomic systems with specific selection rules for the transition dipole moments, or by applying fields with specific polarization properties [26]. 

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