Electric quadrupole transition moment

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. 

Qjy), j is the electric quadrupole transition moment, the electric dipole magnetic dipole... 

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

The interaction between groups is thus approximated by the electrostatic interaction between point dipoles. The values of the dipoles can be either the transition moments or the permanent moments of the groups. However, for the electric dipole forbidden transitions, i,oa is zero and in this approximation we would need to use the next term involving the electric quadrupole transition... 

Furthermore, to avoid cluttering the discussion, we restrict ourselves to electric quadrupole transitions and we shall be guided by the relations between energy E, angular frequency a> and moment of inertia 0 found for classical rotations ... 

The experimental handle is then provided by the gamma ray branching ratios between Ml and E2 transitions in a rotational band built on a state with a g-factor gK- The intensities of the magnetic dipole transitions are proportional to gK — gi ), while those of the electric quadrupole transitions are proportional to the electric quadrupole moment Q, which does not tend to vary greatly between bands in a given nucleus as it is associated predominantly with the shape of the nucleus as a whole. 

An electric quadrupole transition is a y-ray transition between the hyperfine multi-plets of the nucleus in its ground and excited states. Only those nuclear states with 7 > 1 /2 have a nuclear quadrupole moment and hence show quadrupole hyper-flne splitting. Thus, it is often possible to observe a quadrupole interaction in the Mdssbauer spectrum that derives from the excited nuclear state. 

The electric quadrupole transition arises from a displacement of charge that has a quadrupolar nature. An electric quadrupole consists of four point charges with overall zero charge and zero dipole moment. It may be pictured as two dipoles arranged so that their dipole moments cancel. An electric quadrupole has even parity. Electric quadrupole transitions are much weaker than magnetic dipole and induced electric dipole transitions. At this moment no experimental evidence exists for the occurrence of quadrupole transitions in lanthanide spectra, although some authors have claimed the existence of such transitions (e.g. Chrysochoos and Evers 1973). However, the so-called hypersensitive transitions (see sect. 8) are eonsidered as pseudo-quadrupole transitions, because these transitions obey the selection rules of quadrupole transitions. 

Electric dipole transitions, that is, transitions resulting from the interaction of the radiation field with the molecular electric dipole moment, are the most common transitions encountered in planetary spectra. There are other, generally weaker, types of transitions, however. The molecule might have an electric quadrupole moment or magnetic dipole moment, both of which interact with the radiation field. In particular, electric quadrupole transitions are important in diatomic molecules of identical atoms, since these have no dipole moment Magnetic dipole transitions are rare in planetary spectra. Weak electric dipoles can also be induced in molecules during collisions with other molecules, and these are treated in Subsection 3.3.d. 

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. 

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