Electric dipole radiation

Situations will be encountered where the electric-dipole transition between two levels is allowed, and others where such a transition is forbidden. It will be seen that in the latter case, apart from magnetic-dipole radiation, electric-dipole radiation is nevertheless frequently observed, albeit very much weaker. We shall look at the conditions in which a forbidden transition partly ceases to be forbidden. 

State I ) m the electronic ground state. In principle, other possibilities may also be conceived for the preparation step, as discussed in section A3.13.1, section A3.13.2 and section A3.13.3. In order to detemiine superposition coefficients within a realistic experimental set-up using irradiation, the following questions need to be answered (1) Wliat are the eigenstates (2) What are the electric dipole transition matrix elements (3) What is the orientation of the molecule with respect to the laboratory fixed (Imearly or circularly) polarized electric field vector of the radiation The first question requires knowledge of the potential energy surface, or... 

To see how this result is used, consider the integral that arises in formulating the interaction of electromagnetic radiation with a molecule within the electric-dipole approximation ... 

The transition probability R is related to selection mles in spectroscopy it is zero for a forbidden transition and non-zero for an allowed transition. By forbidden or allowed we shall mostly be referring to electric dipole selection mles (i.e. to transitions occurring through interaction with the electric vector of the radiation). 

When monochromatic radiation falls on a molecular sample in the gas phase, and is not absorbed by it, the oscillating electric field E (see Equation 2.1) of the radiation induces in the molecule an electric dipole which is related to E by the polarizability... 

In the context of discussion of the Raman effect, Equation (5.43) relates the oscillating electric field E of the incident radiation, the induced electric dipole fi and the polarizability a by... 

Show that the 10.6 pm and 9.6 pm radiation from a CO2 laser is due to transitions allowed by electric dipole selection mles. 

If the electric dipole contribution dominates in the total SH response, the macroscopic response can be related to the presence of optically nonlinear active compounds at the interface. In this case, the susceptibility tensor is the sum of the contribution of each single molecule, all of them coherently radiating. For a collection of compounds, it yields ... 

The electromagnetic field of the incident radiation, E, may induce an electric dipole in the molecule, given by ... 

Application of the F-D theorem produced [122] several significant results. Apart from the Nyquist formula these include the correct formulation of Brownian motion, electric dipole and acoustic radiation resistance, and a rationalization of spontaneous transition probabilities for an isolated excited atom. 

For any molecular vibration that leads to infrared absorption, there is a periodic change in electric dipole moment. In case the direction of this change is parallel to component of the electric vector of the infrared radiation, absorption takes place otherwise it does not. In oriented bulk polymers, the dipole-moment change can be confined to specified directions. The use of polarised infrared radiation in such a case leads to absorption which is a function of the orientation of the plane of polarisation. The... 

W. Lukosz and R. E. Kunz, Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power, J. Opt. Soc. Am. 61, 1607-1614 (1977). 

If the transition is of an electric dipole nature, the interaction Hamiltonian can be written as // = p E, where p is the electric dipole moment and E is the electric field of the radiation. The electric dipole moment is given by p =, where r is the... 

According to Equations (5.14) and (5.15), we see that the probability of a particular transition depends on the electric dipole matrix element /x, given by Equation (5.12). These transitions, which are induced by interactions of the electric dipole element with the electric field of the incident radiation, are called electric dipole transitions. Therefore, electric dipole transitions are allowed when p- 0. 

Provided that a transition is forbidden by an electric dipole process, it is still possible to observe absorption or emission bands induced by a magnetic dipole transition. In this case, the transition proceeds because of the interaction of the center with the magnetic field of the incident radiation. The interaction Hamiltonian is now written as // = Um B, where is the magnetic dipole moment and B is the magnetic field of the radiation. 

Thus, the electric dipole a polarized emissions departing from the Ai level (in which the electric field of the emitted light is parallel to x or y) are those defined by the direct product Ai x L. An inspection of Table 7.6 shows that Ai X E = E, so that only A E emissions are allowed for a emitted radiation (as shown in Figures 7.7 and 7.8). 

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