Spin angular momentum, total

S, L, and J are the total spin angular momentum, total orbital angular momentum, and total angular momentum, respectively. In a Ln -doped insulator, the coordination of anions aroimd the Ln cation produces an electrostatic field having a symmetry lower than spherical. As a result, the 2J + l)-fold degeneracy of the multiplets in the free ion case is partially or completely... 

The simplest case arises when the electronic motion can be considered in temis of just one electron for example, in hydrogen or alkali metal atoms. That electron will have various values of orbital angular momentum described by a quantum number /. It also has a spin angular momentum described by a spin quantum number s of d, and a total angular momentum which is the vector sum of orbital and spin parts with... 

The simplest case is a transition in a linear molecule. In this case there is no orbital or spin angular momentum. The total angular momentum, represented by tire quantum number J, is entirely rotational angular momentum. The rotational energy levels of each state approximately fit a simple fomuila ... 

In summary, proper spin eigenfunetions must be eonstmeted from antisymmetrie (i.e., determinental) wavefunetions as demonstrated above beeause the total and total Sz remain valid symmetry operators for many-eleetron systems. Doing so results in the spin-adapted wavefunetions being expressed as eombinations of determinants with eoeffieients determined via spin angular momentum teehniques as demonstrated above. In... 

For an electron having orbital and spin angular momentum there is a quantum number j associated with the total (orbital + spin) angular momentum which is a vector quantity whose magnitude is given by... 

The component of the total (orbital plus electron spin) angular momentum along the intemuclear axis is Qfi, shown in Figure 7.16(a), where the quantum number Q is given by... 

Suppose a quantum system consists of a pair of spin- particles, and that the system is prepared in such a way that (1) the total spin angular momentum is zero (i.e. the... 

Here L, S, and J are the quantum numbers corresponding to the total orbital angular momentum of the electrons, the total spin angular momentum, and the resultant of these two. Hund predicted values of L, S, and J for the normal states of the rare-earth ions from spectroscopic rules, and calculated -values for them which are in generally excellent agreement with the experimental data for both aqueous solutions and solid salts.39 In case that the interaction between L and S is small, so that the multiplet separation corresponding to various values of J is small compared with kT, Van Vleck s formula38... 

It can also be seen from Fig. 6 that if the T+x or T x states mixed with S, this would involve concomitant electron and nuclear spin flipping in order that the total spin angular momentum be conserved, and this would ultimately produce the same polarization in c- and e-products. This point will be discussed further in Section IV. 

Now the total spin-angular momentum quantum number S is given by the number, n, of unpaired electrons times the spin angular momentum quantum number s for the electron, that is, S = nil. Substitution of this relationship into Eq. (5.11) yields an alternative form of the spin-only formula. 

The singlet function corresponds to zero total electron spin angular momentum, S = 0 the triplet functions correspond to S = 1. Operating on these functions with the spin Hamiltonian, we get ... 

Singlet and triplet states refer to those states that have a total electron spin quantum number equal to 0 and 1, respectively. The spin multiplicity calculated as 25 - - 1, where S corresponds to the spin angular momentum, corresponds to 1 and 3 for the singlet and triplet states, respectively. 

For a given total electron spin quantum number (S), the multiplicity is the number of possible orientations of the spin angular momentum for the same spatial electronic wavefunction. Thus, the multiphcity equals 25 -F 1. For... 

A rule that affects energy transfers in photochemical reactions, particularly photosensitization processes. The total electron spin (/.c., the vectorial overall spin angular momentum of the system) does not change after the electronic energy transfer between an excited molecular entity and another molecular entity. 

For an Ai-electron spin function, tlie total spin angular momentum is additive, i.e.. 

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