Spin angular moment

For example, the singlet-triplet transitions in ethylenic compounds generally have tmax <3C 1. The fact that spin-forbidden transitions can be observed at all shows that the transition moment, f electric dipole operator. This operator also contains small terms such as quadrupole operators and spin-orbit operators. The latter is the part of any dynamical operator which couples orbital and spin angular moments this term is responsible for the appearance of weak triplet — singlet absorption spectra. 

For a solid to interact with a magnetic field intensity, it must possess a net magnetic moment which, as discussed momentarily, is related to the angular momentum of the electrons, as a result of either their revolution around the nucleus and/or their revolution around themselves. The former gives rise to an orbital angular moment whereas the latter is the spin angular moment /ij. The sum of these two contributions is the total angular moment of an atom or ion, /ijon-... 

For a single-particle, nucleon or electron, the orbital and spin angular moments add vectoiially to form a resultant vector (Fig. 11.4(b)),... 

The angular momentum of the spinning charge can be described in terms of spin numbers, having the values of 0, 1/2, 1, 3/2, etc., where 0 denotes no spin like in i 0,32s, etc. For these elements, NMR experiments cannot be conducted since there is no spin angular moment and thus no magnetic moment to be analyzed. Several nuclei, however, such as H, h, i9p sip... 

An additional phenomenon is that electrons show a strong tendency to occupy as many states with the same spin as possible. Cr and Mn, for instance, both have five electrons with spin j in the 3d orbital. Electrons tend to occupy states with maximum spin angular moment, or at least with maximum total angular moment. In free atoms, the occupancy of states can be determined by Hand s rules (Hund, 1927 Condon Shortley, 1935) ... 

It is convenient to use a resultant effective spin when the S = V2 subunits are identical. It is then assumed that the complex can be treated as a species with S = 1 or 0. The mathematical procedure given in several text-books [20, 27, 35] to obtain the s under those conditions is technical and is not reproduced here. An expression for the exchange interaction can, however, easily be calculated using the relation for the addition of the spin angular moment vectors in quantum mechanics ... 

The iV-electron operator fh RGo) is called the orbital magnetic dipole operator, kiRoo) is the orbital angular momentum operator of electron i with respect to the gauge origin Rqo and Sj is the spin angular momentum operator of electron i. The total orbital and spin angular moment operators of all N electrons are... 

The nuclear contribution Bintemai is called the Fermi contact interaction. Mjj is the quantum number for the z component of the nuclear spin angular moment of nucleus number j and the constant aj is called the coupling constant for that nucleus. The coupling constants for nuclei in many molecules have values near 1 gauss (1 x 10 T), but the coupling constant is appreciably nonzero only if the electron approaches closely to the nucleus. If an unpaired electron occupies an orbital that has a nodal surface at... 

In this chapter, we will be mainly concerned with the magnetism originating Irom the spin angular moments of localized electrons. The magnetic moment p of a chemical entity is associated with the total angular momentum / and is given by... 

The z-component of the spin angular momentum vector / takes values / = /,/ -1,...,-/. Spin angular moments give rise to magnetic moments. The magnetic moment p is directly proportional to the spin fl = Y -S, where y is the magnetogyric ratio measured in rads T , which is a property of the nucleus. 

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