Dipole intensity

Equation (2.44) indicates that for the delocalized model, the transition dipole intensity ratio is related to 0 Bm. To obtain ()Bi Bm at various temperatures, we utilize Breton s data regarding the angles between the electronic transition moments of the four BChls and the normal axis of the membrane. The calculated %BlBm are listed in Table IV. 

Figure 7.6. Intensity emitted at supercritical angle 6 = 70° into the glass versus dipole distance z for dipoles oriented perpendicular to the interface. The solid lines show the properly normalized (fixed-power dipole) intensities for the bare glass and Al film surfaces. The dashed line shows the exponentially decaying intensity that would be obtained for bare glass by omitting the required normalization PT in Eq. (7.34). All optical parameters are the same as in Figure 7.3.

In going to complexes lacking a center of inversion (i.e., noncentrosymmetric), the dx.2 v2 orbital can mix with the 4p-orbitals of the metal. From the above discussion, the Is — 4p transition is electric dipole allowed. In the X-ray region, electric dipole intensity is 100-fold higher than electric quadrupole intensity thus, a few percent of 4p mixing into a d-orbital can have a large effect on the pre-edge intensity. 

Notice a very important feature of equation (6.334). Electronic transitions do not depend for their intensity on the presence of a permanent electric dipole moment in the molecule, so that they exist for both homonuclear and heteronuclear diatomic molecules. This is in contrast to rotational and vibrational transitions which have electric dipole intensity only in heteronuclear molecules (apart from one extraordinary exception for the II2 molecule, described in chapter 10.)... 

The subscripts 1 and 2 refer to the Br and Li nuclei respectively. This Hamiltonian differs from that used previously for CsF, equation (8.282), only through the additional quadrupole term and the explicit addition of a Stark effect term. Although the weak electric fields (a few V cm ) used in this work were employed mainly to transfer electric dipole intensity into the resonance transitions, the resulting Stark shifts were measurable because of the extremely small linewidths obtained (about 300 Hz). 

The origin of the electric dipole intensity for the AMj = 1 transitions studied merits further consideration. If the static magnetic field is 5 kG, the motional electric field has a magnitude of approximately 3 V cm-1 and is perpendicular to the applied magnetic field. This electric field mixes a state [./, Mj) with the states. J 1, Mj 1) and in order to obtain non-zero electric dipole transition moments for the transitions. /. Mj) o IJ, Mj 1), the oscillating electric field must be applied parallel to the static magnetic field. 

Using (8.432) and (8.433) the Stark energies for J = 2, S2 = 2 can be readily calculated and the results are presented in figure 8.50 the initial splitting of the /1-doublets was determined from the electric resonance study to be 7.351 MHz for the v = 0 level. In small electric fields the parities of the states are essentially preserved, and transitions between the /1-doublets have their full electric dipole intensities. At higher electric fields, however, the opposite parity states are mixed and the electric dipole intensity decreases. It follows that so far as the intensities of the electric resonance transitions are concerned, low electric fields are desirable. On the other hand, Stern, Gammon,... 

There are three other possible transitions, indicated by dashed lines in figure 11.58, which have comparable magnetic dipole intensities but were not observed experimentally. Table 11.6, however, shows that for the levels involved in these transitions, little or no photo-alignment is to be expected. The experimental and calculated transition frequencies are given in table 11.8, together with the determined values of the molecular constants. 

Botschwina s calculations on HCN, HCP, and CjNj [118] included IR (vibrational dipole) intensities. Compared against experimental values, the use of correlated wavefunctions seems to have given better results than the use of SCF wavefunctions. In some cases, SCF significantly overestimated the intensities relative to correlated wavefunction values. 

The first two terms vanish on account of the orthogonality properties of either nuclear or electronic wavefunctions. The surviving third term, proportional to the square of the very small coefficient of the second term in (3.6), gives a splitting about proportional to the mixed-in dipole intensity, with no contribution by the higher multipoles. This allows many puzzling features of the crystal spectra of such transitions to be explained. In physical terms the small resonance effects reflect the low rate of intermolecular exchange of vibrational, as opposed to electronic, motion. 

Refinements in vuv spectroscopy W, aided by the development of synchrotron radiation (7 ) and equivalent-photon electron-impact ( ) tunable light sources, and closely related advances in photoelectron, fluorescence-yield, and electron-ion coincidence spectroscopy measurements of partial cross sections (9), have provided the complete spectral distributions of dipole intensities in many stable diatomic and polyatomic compounds. Of particular importance is the experimental separation of total absorption and ionization cross sections into underlying individual channel contributions over very broad ranges of incident photon energies. 

CD and absorption intensities of these transitions. On the other hand, the Q3(tiu), Qi+ (tiu), and Qg(t2u) vibrational modes will be effective in mixing the Tiu excited state with the T g and Tp g excited states. This will lead to a redistribution of electric dipole intensity out of the Aig->-Tiu transition and into the Aig->-Tig and Aig->-T2g jl-d transitions. 

Calculating the dipole intensities, with resonances included, requires one step in addition to the procedure described above. After the matrix representation of the effective dipole moment operator is calculated, in the same basis as was used to set up the block-diagonal Hamiltonian matrix, the similarity transformation that diagonalizes the Hamiltonian matrix is applied to the dipole moment matrix. The intensity of the transition... 

Making no distinction between the electric and magnetic dipole intensity mechanism, the absorption coefficient for left and right circularly polarized light for a transition <— A is written as (see Eq. (158) and Section 3.2.2)... 

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