Transition electric 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. 

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. 

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. 

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. 

The second example is the FOTOS computation of the electric quadrupole transition Ca 4s 4s3d [49]. The 1983 prediction in Ref. [49] for... 

D.R. Beck, G.A. Nicolaides, Electric quadrupole transition probabilities for the lowest D metastable state in Ca and Sr, J. Phys. B 16 (1983) L627. 

A state-of-the-art example [28] for trapped-ion optical frequency standards is the case of a laser with a line-width of less than 25 Hz locked to a electric quadrupole transition at 282 nm in a single laser-cooled Hg ion. The inherent stability of this trap based on the radiative lifetime of the metastable upper level of this transition is calculated to be about 1,5 x 10" x[29]. This is an exceptional example - in most cases as yet, the lasers used as oscillators for optical frequency standards based on ion traps often do not have a stability which matches the spectral sharpness of the trapped ion reference resonance. 

A single Ca+ ion is cooled in a miniature radiofrequency trap (see Section 11.4.2.4) [37]. The electric quadrupole transition between the ground state and the upper level of the first metastable state of a single Ca+ ion is an attractive choice for a... 

Bands of the A - X A system of HO2 and DO2 have also been recorded (13). With oxygen alone, the b Eg - a Ag electric quadrupole transition of O2 (14) has been observed, indicating the sensitivity of the Fourier transform system in the near infrared. 

More details of this development, including the extension to the higher-order tensors containing magnetic dipole and electric quadrupole transition moments that are resonsible for optical activity phenomena, can be found elsewhere [l2.l. 

The convention 3333 2233 1133 allows to introduce the orientation axis of a molecule, i.e., the best ordered molecular axis in an anisotropic phase . The -,33 (i= 1, 2, 3) are given in their principal axes, otherwise nondiagonal elements of Ac/y (i= 1, 2, 3) are required in eqn [38]. The Ac are complicated functions of the involved electric and magnetic dipole and the electric quadrupole transition moments. The contribution of the electric dipole, magnetic dipole, and the electric quadrupole transition moments can be obtained for the transition 0> -> > directly by... 

The three diagonal elements Ae P(v) (1=1, 2, 3) are proportional to products of electric dipole times electric quadrupole transition moments. They do not contribute to the isotropic CD because the sum over the three coordinates (v) (1 = 1, 2, 3) is zero. Asu, measured for oriented guest molecules in ordered liquid crystal phases, yield spectroscopic and structural information and, has been used, especially for the check of sector and helicity rules. First numerical quantum mechanical calculations of the CD tensor coordinates Asu have been published recently. 

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