Electric and Magnetic Moments

Parity, as used in nuclear science, refers to the symmetry properties of the wave function for a particle or a system of particles. If the wave function that specifies the state of the system is Tir,. v) where r represents the position coordinates of the system (x, y, z) and s represents the spin orientation, then (r,. v) is said to have positive or even parity when 

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ELECTRIC AND MAGNETIC MOMENTS 2.10.1 Magnetic Dipole Moment... 

Apart from electric and magnetic dipole transitions, time-dependent interactions involving higher-pole electric and magnetic moments can, in principle, occur. However, no examples of such transitions appear in this book they are of academic rather than practical interest. 

The electric and magnetic moments, <01// a> and , are based on the linear and angular momentum of electrons involved in the transition. The angular momentum corresponds to the rotational motion of an electron, while the linear momentum corresponds to the linear motion of the electron. If the electric and magnetic moment vectors, <01// a> and , are parallel to each other in one enantiomer, they should be antiparallel in the other enantiomer. Therefore, the rotational strength R, OR [a]A, and CD spectra of enantiomers are opposite in sign but of equal intensity. The problem of how to determine the ACs of... 

The time-independent electric and magnetic moments of the molecule in the presence of the external fields, using definitions (4) and (5) for the operators, are... 

The alternatives are known—to predict a value of the electric or magnetic field of a non-elementary object we have to know not only its charge and mass, but also all details of the distribution of its electric and magnetic moments (and a number of parameters beyond that). Those details should be also measured. So we need an infinite number of the parameters. 

Conspicuous by its absence is a term containing the interaction between electric and magnetic moments in different members of the degenerate set. The dot product of the terms in (IIIB-18f, 20e, 20j) which would lead to this result identically cancel. We see that interaction between degenerate groups does not contribute to the rotational strength of a polymer. 

This equation is identical in form to (IIIB-22) with the static field terms omitted. However, the electric and magnetic moments here refer to the groups in the static field of the polymer. Also, the frequencies refer to the groups as they exist in the polymer. In practice the frequencies we use in either (IIIB-22) or (32) will be a matter of experimental convenience. Equation (IIIB-32) was originally derived by Kirkwood in 1937, although he did not explicitly consider degenerate states at that time. Moffitt, Fitts, and Kirkwood (1957) did consider degenerate states, but their treatment differs from ours in certain respects which will be discussed later. 

The lanthanide ion serves as a probe of its environment in the host crystal, providing information on the site symmetry, and on the crystalline electric field (CEF) components and the CEF levels of the ion. In addition, the hyperfine interaction with the lanthanide nucleus or with the nuclei of other atoms (transferred hyperfine interaction) provides information on the electronic wave functions of both lanthanide and non-lanthanide ions. Unlike NMR and the Mossbauer effect which utilize the invariant electric and magnetic moment properties of nuclei as probes, these properties of magnetic ions are in general not invariant, but are themselves conditioned by the ionic environment. In the case of the lanthanides however, since these properties reside in the incomplete 4f shell, which is relatively well screened from the ionic environment by the filled 5s and 5p shells, they are not so strongly affected as in the case of the magnetic 3d ions, for example. 

Rotational effects (fine structure) are also seen in high resolution electronic and vibrational spectra additional structure due to the interaction of electrons with nuclear electric and magnetic moments may also be observed and is called hyperfine structure. The simplest rotational spectra are associated with diatomic molecules with no electronic orbital or spin angular momentum (i.e. singlet sigma states) and these are considered first. 

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