Dipole processes

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. 

As shown in Example 5.2, magnetic dipole transitions are much weaker than electric dipole transitions. Nevertheless, when a radiative transition is forbidden by an electric dipole process, it may happen due to a magnetic dipole process. In fact. 

Different interactions for exchange of magnetization between the proton pools were proposed, which are through-space dipole-dipole processes, " ... 

Melamed et al. (136) describe laser oscillation in uranyl-sensitized neodymium-doped barium crown glass. They believe that the energy migrates from the uranyl to the neodymium by an electric dipole-dipole process. The results of their measurements on the uranyl lifetime, uranyl-neodymium-transfer time, and the quantum efficiency are summarized in Table VII. 

It is clear, however, from the discussion involving Eqs. (7)—(9) and from the sudden approximation sum rule that the spectrum associated with the photoionization of a core electron should not, in fact, necessarily consist only of a single line some data observed for RbCl and RbF (40) are shown in Fig. 16. The narrow peaks are the Rb 4s24 6(1S) - -4s14 >6(2S) excitation and the broad peaks, approximately equal in intensity, arise from multiple electron excitation , that is, the production of final states such as 4s24 4 s(2S), where n > 5. Even though the photoemission event is just a one-electron dipole process, multiple excitation can occur because the wavefunction of the instantaneous intermediate state of the (TV—1)-electron ion [Eq. (7)] has overlap with wavefunctions of such multiply excited states that is, i has components which are eigenfunctions, n(N—1), of multiply... 

Thus different luminescence takes place after activation in air and in vacuum. As it was already mentioned, in the apatite structure Ca5(P04)3F there are two types of Ca site Ca(l) with C3 symmetry and Ca(II) with Cs symmetry. The Dq- Fq transition has been reported to exist in cases where the site symmetry allows an electric dipole process Cs, C , Cnv This is consistent with the conclusion that the centers with the main line at 574 nm belongs to Ca(II) site with Cs symmetry, while the asymmetry of the crystal field is lower for the center with the main line at 618 nm. The ratio between Dq- Fo and Dq- F2 which are forced electric dipoles to Dq- Fi which is magnetic dipole tells us about the synunetry of the site in which Eu + is situated (Blasse and Grabmaier 1994 Reisfeld 1973). In fluor-apatite activated in air the ratio is higher meaning a lower synunetry Ca(II) site, while in namral fluorapatite or synthetic one activated in vacuum the ratio is lower... 

The resonant cross-section is normally dominated by electric dipole processes for which L = 1 and M = 1, such as the 2p3/2 —> 5di/2 transition that occurs at the Lm edge in the lanthanides. For such a transition the scattering amplitude may be written as... 

For Hubbard chains with V t> t, the ground state becomes a spin wave, with p = 0 for all n, and dipole processes are suppressed Eq. (42) then decreases as and the bond orders vanish when only virtual transfers are possible. Dipole-allowed transitions from B are still possible to A states with a C + C pair, however, in the manifold of states within t of ib U. Such excitations in Eq. (43) go as t /U in units of Eib. The only even-parity excited state, mAg, considered in the essential states model [146,147] for NLO is just above IB, which changes the sign of the left-hand side of Eq. (43) and implies [100] a strong two-photon resonance in the THG spectrum (Fig. 6.11) around 3o 3 eV. Vanishing 2A contributions in the essential states model also point to strong correlations, when 2A is a spin state based on two triplets. The intermediate nature of molecular correlations is again apparent correlations place 2A and nA far below the band limit, but the intense linear absorption is far from spin waves. 

Nuclear magnetic dipole relaxation interactions may occur with other nuclei, or with unpaired electrons. These processes usually dominate the relaxation of spin - nuclei. Both intra- and intermolecular interactions may contribute to dipole-dipole nuclear relaxation times. The value of due to the intramolecular dipole-dipole process is proportional to the sixth power of the internuclear separation. Consequently, this process becomes rather inefficient in the absence of directly bonded magnetic nuclei. However, it follows that a measurement of can be provide an estimate of internuclear separation that can be of chemical interest. The nuclear Overhauser effect (NOE) depends upon the occurrence of dipole-dipole relaxation processes and can similarly provide an estimate of internuclear separation. 

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