Transition quadrupole

FIGURE 10.18 Comparison of (a) Raman scattering process and (b) gradient-field Raman (GFR) scattering process. ED and EQ denote electric dipole and electric quadrupole transitions, respectively. 

Fig. 3.38. Absorption of N2-Ar in the fundamental band of N2 [111]. Nitrogen and argon densities were both 19 amagat room temperature measurement ( ) the solid line represents a fit based on the stick spectrum and a J-independent quadrupole transition moment. In pure nitrogen, an almost identical spectrum was obtained.

O branch). The measurement is given by the dots. The curve drawn was constructed from the envelopes of the stick spectrum of N2 (which is well known from Raman studies). The curve approximates the measurement quite closely. In order to fit the experimental line shape one had to take the dependence of the quadrupole transition moments on the rotational quantum number into account. 

J. Litvin. Collision-induced absorption in the fundamental band of CH4. Determination of the quadrupole transition moment. J. Chem. Phys., 115 8852, 2001. 

Electric-quadrupole transition, 123,127 Electromagnetic radiation, 114-117. See also Radiation, electromagnetic Electromagnetic spectrum, 115 Electronic energy, 57,64,148 Electronic spectra, 130, 296-314 of diatomics, 298-306 and molecular structure, 311 of polyatomics, 71-72, 73, 75, 306-314 selection rules for, 297-301, 306-307 Electronic structure of molecules, 56-76 Electron spectroscopy for chemical analysis (ESCA), 319-320 Electron spin resonance (ESR), 130, 366-381... 

Transitions due to such matrix elements are called electric-quadrupole transitions. Since the wavelength of ultraviolet light is about 103 times the size of atoms, electric-quadrupole transitions are about 1/106 the intensity of electric-dipole transitions. 

What about parity in electric-quadrupole and magnetic-dipole transitions The quantities (3.58) are even functions. Hence for electric-quadrupole transitions, parity remains the same. Magnetic-dipole transitions involve angular momentum operators. For example, consider Lz = -ih(xd/dy — yd/dx). Inversion of coordinates leaves this operator unchanged. Hence for magnetic-dipole transitions, parity remains the same. 

It is possible to distinguish the electric dipole and electric quadrupole transitions from the magnetic dipole ones using the following selection rules (for a detailed treatment of the selection rules see ref. 556—560). 

Experimental transition quadrupole moments, Qt, were obtained from the reduced electric quadrupole transition probabilities, B(E2), according to the expression... 

In this section we want to estimate the foreseeable systematic line shifts of the atomic reference in an indium frequency standard and compare indium to the alkali-like candidate ions like mercury, ytterbium, barium or strontium that rely on electric quadrupole transitions of the type Si/2 —> >5/2 Line shifts may be caused by the motion of the ion, by electric and magnetic fields, by radiation or by collisions. Values for the shifts will be given as dv/v, relative to the In+ transition frequency of v = 1267 THz. 

In the NBS work, the transition of interest for a frequency standard is the Hg+ 5d 6s Si 5d 6s 5/2 quadrupole transition at 281.5 nm shown in Fig. 1. The 5/2 level has a lifetime of 86 ms, corresponding to a natural width of 1.8 Hz. Use of the single photon quadrupole transition has an advantage over two-photon Doppler free transitions because ac Stark shifts are negligible. 

There are two other fairly common causes of apparent breakdown of the electronic selection rules. First, collisions with other atoms or molecules, or the presence of electric or magnetic fields, may invalidate selection rules based on state descriptions of the unperturbed species. Secondly, although the transition may be forbidden for an electric-dipole interaction, it may be permitted for the (much weaker) magnetic-dipole or electric-quadrupole transitions. 

According to Jorgensen and Judd, hypersensitivity may occur due to pseudoquadrupole transitions [66]. Consequently an ion embedded in an inhomogeneous dielectric would exhibit hypersensitive behavior. These normally weak electric quadrupole transitions are probably intensified and become hypersensitive transitions. Hypersensitivity can also occur in symmetries of spherical harmonics (Ymk, with k = 1) which form totally symmetrical representations. Thus this permits their inclusion in the crystal field potential. 

A very exceptional case of energy migration in a Eu compound was recently reported by Bettinelli et al. (193). These authors studied Cs2NaEuCl6 in which the Eu " ion occupies a site with perfect octahedral symmetry in which the pure electronic transitions are completely forbidden as electric-dipole transitions. Nevertheless the very forbidden Fo- Do transition was observed in the excitation spectra. The electronic origin is weak, but sharp and clear, and is accompanied by much stronger vibronic transitions. This suggests that the authors have observed here one of the rare examples of an electric quadrupole transition. 

Forbidden pure rotational transitions of H3, following the selection rules Ak = +3, occur in the wide region from millimetre wave to mid-infrared.These transitions are caused by centrifugal distortions of the symmetric structure. No laboratory observation of them has been reported so far. These transitions are much weaker than the usual dipole-allowed rotational transitions in polar molecules, and their spontaneous emission rates range from ca. 10" s" to ca. 10" s". Nevertheless, such weak transitions may be observable in low-density regions just like the Hj quadrupole transitions. Also, the spontaneous emission lifetimes are short compared with the collisional time in low-density areas, making the forbidden rotational transitions important processes for cooling the rotational temperature of Hj. ... 

Symmetry arguments show that parity-odd, time-even molecular properties which have a non-vanishing isotropic part underlie chirality specific experiments in liquids. In linear optics it is the isotropic part of the optical rotation tensor, G, that gives rise to optical rotation and vibrational optical activity. Pseudoscalars can also arise in nonlinear optics. Similar to tlie optical rotation tensor, the odd-order susceptibilities require magnetic-dipole (electric-quadrupole) transitions to be chirally sensitive. 

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