Radiation dipole

When an electronic charge is oscillating, it emits electromagnetic radiation [1]. It this section we will consider the electromagnetic field emitted by a point-like oscillating dipole, which also describes quite well the field emitted by molecules, which are much smaller then the electromagnetic wavelength. 

Let s consider a point-like dipole jio located at ro = 0 and oscillating with frequency co. In the most general case /to is a complex vector. It has a polarization field given by  

This point-like dipole can be thought to generate external source terms, namely a charge density given by Eq. (1.8) and a current density given by Eq. (1.9). Using the Fourier transformation we have  

The electric and magnetic fields in the free-space can be directly obtained from Eqs. (1.107,1.110)  

Thus the free-space d3 dic Green s function relates the electric field in the free-space at point r with the source dipole at point ro. The magnetic field is instead easier derived from Eq. (1.210). 

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Dipol-kraft,/. dipole force, -messung,/. dipole measurement, -strahlung, /. dipole radiation. 

For a fundamental transition to occur by absorption of infrared dipole radiation, it is necessary that one or more of these integrals (and consequently the intensity) be nonzero. It follows from the selection rule given above that in order that a transition be infrared active p must have the same symmetry properties as at least one of x, y, or z. 

Both p and / are ratios of a power emitted at position z relative to that for an isolated dipole p refers to total power (light plus heat) whereas / refers to radiated power only, derived by integrating the fixed-amplitude dipole radiated intensity 5 [given by Eq. (7.34) without the PT normalization in the denominator] over An steradians. 

Unlike the near-field dyadic of Forster, which has no frequency dependence, the dyadics appearing in the above expression are explicitly frequency-dependent due to the range of the interaction. In particular, T p is the appropriate dyadic with the sphere in place, and fdip is the dyadic in the absence of the sphere. Although Td,p is easily obtained from dipole radiation theory, f,p must be obtained bv solvine the appropriate boundary value problem. When one considers that T( d, ra, co) - id is the electric field at the acceptor [see Eq. (8.14)], it becomes apparent that A(co) 2 is simply a ratio of intensities. For the case of transition moments which are normal to the surface as depicted in Figure 8.19, the numerator of Eq. (8.21) reduces to... 

A giant dipolar resonance (GDR) exists in the majority of photoabsorption and photonuclear reactions. This resonance energy corresponds to the fundamental frequency for absorption of electric dipole radiation by the nucleus acting as a whole. It can be envisioned as an oscillation of neutrons against the protons in a nucleus. The GDR occurs at energies of 20-24 MeV in light material and of 13-15 MeV in heavy nuclei. A compendium of the GDR parameters is found in Ref [3]. 

The dipole moment p = emaE0e, 0 tex of an ideal dipole, located at z = 0 and illuminated by an x-polarized plane wave is0exp(/ kz — iut)ex, oscillates with the frequency of the applied field therefore, the dipole radiates (i.e., scatters) an electric field E, (Stratton, 1941, p. 453)... 

For quadrupole radiation, they estimate P 2x 10-9, whereas for magnetic-dipole radiation their result was P 2 x 10-8. The experimental values lie in the range of 10 7 to 10 5. From these estimates, one concludes that the probability of significant electric-quadrupole and higher-order-multipole radiation is very small indeed. The magnetic-dipole radiation is weak but probably is of some importance, particularly in cases where the electric-dipole emission is strictly prohibited. 

The probability per unit time for a single ion embedded in a crystal excited to state K to deexcite by spontaneous emission of electric-dipole radiation to a lower state M has been given by Axe (28) as... 

A) with respect to the operation of inversion about the origin of the system. The electric dipole operator is antisymmetric (A) with respect to inversion at a point of symmetry. The electric quadrupole operator is inversion symmetric (S). A transition is allowed if the product function in the expression for transition moment is symmetric for electric dipole radiation and antisymmetric for electric quadrupole radiation. 

Electric dipole radiation is the most important component involved in normal excitation of atoms and molecules. Ttu electric dipole operator has the form TejXf where e is the electronic charge in esu and xt is the displacement vector for the jth electron in the oscillating electromagnetic field. 

Content. After a brief overview of molecular collisions and interactions, dipole radiation, and instrumentation (Chapter 2), we consider examples of measured collision-induced spectra, from the simplest systems (rare gas mixtures at low density) to the more complex molecular systems. Chapter 3 reviews the measurements. It is divided into three parts translational, rototranslational and rotovibrational induced spectra. Each of these considers the binary and ternary spectra, and van der Waals molecules we also take a brief look at the spectra of dense systems (liquids and solids). Once the experimental evidence is collected and understood in terms of simple models, a more theoretical approach is chosen for the discussion of induced dipole moments (Chapter 4) and the spectra (Chapters 5 and 6). Chapters 3 through 6 are the backbone of the book. Related topics, such as redistribution of radiation, electronic collision-induced absorption and emission, etc., and applications are considered in Chapter 7. 

Note that the radiation field is dependent on one angle only, namely the angle 9 subtended by the acceleration r and radius arm vector R the dependence enters Eq. 2.60 as (sin 9)2 which is characteristic of the familiar dipole radiation pattern. It is, therefore, straightforward to integrate Eq. 2.60 over a spherical surface R2 f dQ where dQ = sin 9 d9 dtotal power emitted,... 

Classical dipole radiation. Usually, we will be dealing with radiation emitted (or absorbed) by dipoles. In the simplest case, a dipole may be thought of as a point charge q positioned a distance r away from the origin of a Cartesian frame the dipole moment p is then given by... 

J. Schafer and W. Meyer. Collision induced dipole radiation of normal hydrogen gas in frequency range of the cosmic background. In J. Eichler, I. V. Hertel, and N. Stolterfoht, eds., Electronic and Atomic Collisions,... 

For a fundamental transition to occur by absorption of infrared dipole radiation (see Section 5.3) it is necessary that one or more of the integrals... 

Selection rules also arise on considering the point-group symmetry of tfo(Qeq). In the case of electric dipole radiation the perturbation Y, which describes the interaction with the radiation field, may be expressed in terms of the x, y, z components of the dipole moment operator r. The operators (t) transform as the x, y, or z components of r. 

The angular distribution of the intensity of electromagnetic radiation is given by specific analytic functions written in terms of an angle, W(Q,mi), relative to the quantization axis, Z, and the magnetic quantum number, mi. The patterns depend on the order of the multipole, dipole, quadra pole, and so forth, but they are the same for electric and magnetic transitions with the same order. For example, the angular distributions for dipole radiation are... 

Figure 9.8 Schematic diagram of how angular correlations occur. Panel (a) shows the angular distribution of dipole radiation for Am = 0 and Am = +1. Panel (b) shows the magnetic substates populated in a y y2 cascade from J = 0 to J = 1 to J = 0. When -y, defines the Z axis, then the mi = 0 state cannot be fed and one has only Ami = + 1 and Am2 = +1, causing y2 to have an anisotropic distribution relative to 71 shown in panel (c). [From Marmier and Sheldon, 1969.] Copyright 1969 Academic Press. Reprinted by permission of Elsevier.

Prompt y-ray emission competes with or follows the last stages of prompt neutron emission. These photons are emitted in times from 10 15-10 7s. Typical y-ray multiplicities of 7-10 photons/fission are observed. These photons, as indicated earlier, cany away 7.5 MeV. This y-ray yield is considerably larger than one would predict if y-ray emission followed neutron emission instead of competing with it. Because of the significant angular momentum of the fission fragments ( 7-10 h) even in spontaneous fission, photon emission can compete with neutron emission. The emitted y rays are mostly dipole radiation with some significant admixture of quadrupole radiation, due to stretched El transitions (J/= 7, — 2). 

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