Dipole forbidden resonance

Using Eqs. (2.13), (2.14), and (3.12), we get an expression for Ig s) that determines the inelastic cross section of a dipole-forbidden resonance near the point of a phase transition ... 

The Stokes region of a dipole-forbidden resonance is formed by long-range interparticle interactions. According to our model, an essential change of EELS correlational structure takes place close to the critical point where the correlational radius tends to infinity. This effects corresponds qualitatively to those of section III. A. 

Thus in the Stokes neighborhood of a dipole-forbidden resonance formed by long-range interparticle correlations, the correlational structure of EELS takes changes close to the phase separation critical point. In the asymptotic anti-Stokes neighborhood, the correlational behavior is independent of the critical point behavior. 

Resonance Raman spectroscopy has been applied to studies of polyenes for the following reasons. The Raman spectrum of a sample can be obtained even at a dilute concentration by the enhancement of scattering intensity, when the excitation laser wavelength is within an electronic absorption band of the sample. Raman spectra can give information about the location of dipole forbidden transitions, vibronic activity and structures of electronically excited states. A brief summary of vibronic theory of resonance Raman scattering is described here. 

Here, e and e represent slow and fast electrons, respectively, and the superelastic collision may preferentially produce the A resonant excited state because A — A is a strong dipole transition. (Note that inelastic cross sections for electron-atom collisions are generally larger for dipole-allowed transitions compared to dipole-forbidden transitions.) Since the ground state density N is high, the electron excitation of A following Eq. (7) is fast ... 

The simplest aromatic molecule, benzene, is characterized by a lowest absorption band that is located relatively far in the ultraviolet (37,800 cm ) and is dipole forbidden ( B2 in Dg/,). The same applies to the second absorption band ( Bi at 46,500 cm ). The lowest-energy allowed transition ( Ei ) is located at about 52,700 cmAll these transitions are well outside the range where their resonance Raman spectra can be studied in detail by present-day techniques. However, some preresonance data are available (Ziegler and Albrecht, 1977 Ohta and Ito, 1977b Ito et al., 1978), which allow a partial analysis of vibronic coupling channels in benzene. 

The benzene preresonance Raman spectra show also fairly strong activity of the first overtone of mode Vi4(b2 ). This mode is dipole forbidden and thus cannot directly obtain its intensity through coupling of B2 with the ground state as discussed in Section IX,D. However, it is possible to formulate several higher-order vibronic coupling schemes that yield such overtone activity, depending on which state is the resonant state. The Raman intensity probably derives from the dipole allowed 2 transition... 

Figure 9 Three-level atoms with dipole transitions 1,2>- 3) in the Lambda configuration. The dipole forbidden transition between two metastable states 1> and 2) are coupled to each other via microwave transition (a), or Raman transition (b), or two-photon transition (c) with effective half Rabi frequency Qo Another optical field is resonantly coupled to the dipole transition 2)- 3> with half Rabi frequency Qi. The two cavity fields 012 are amplified from Rabi sidebands on the dipole transition 1)- 3>.

Short range transfer by exchange mechanism occurs when donor and aceer. electronic wavefunctions spatially overlap. The rate follows diflusion-contro",. kinetics if donor and acceptor energy levels are in near resonance. Transit forbidden by dipole-dipole mechanism may occur by exchange mechanism, e.g... 

In the remainder of this section, we will consider only electric-dipole transitions. These are the strongest transitions, and account for most of the observed atomic and molecular spectroscopic transitions. (Magnetic-dipole transitions occur in magnetic-resonance spectroscopy.) When the integral d vanishes, we say that a transition between states n and m is forbidden. 

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