Orbital angular momentum spin-orbit coupling

Unlike a free electron, an electron in a molecule also experiences a complex interaction between spin and orbital angular momentum, spin-orbit coupling. These interactions are described in terms of a tensor, EPR spectroscopy is... 

The fine structure in purely rotational, rotational-vibrational, and electronic spectra of NH (ND) arises from the interaction of the unpaired electron spin with the orbital angular momentum (spin-orbit coupling constant A for the 11 states), from the interaction of the unpaired electron spins with each other and with the rotational angular momentum (spin-... 

As an angular momentum, spin can couple with the orbital angular momentum to yield a total angular momentum for a single particle. The corresponding... 

In L-S coupling, the total electronic angular momentum (spin and orbital) is defined by the quantum number J whose allowed values are... 

We assume that each nucleon has a pseudo-spin i and pseudo-orbital angular momentum k. These couple to form the single particle angular momenta J,J (in [j]) of the two interacting nucleons. The wavefunction of a pair of nucleons coupled to a total angular momentum L (and z component p) is then given by ... 

In addition there will often be nuclear spin angular momentum ), which is coupled to the electronic orbital and spin angular momenta these coupling cases are described... 

Lande interval rule A rule in atomic spectra stating that it the spin-orbit coupling is weak in a given multiplet, the energy differences between two successive /levels (where /is the total resultant angular momentum of the coupled electrons) are proportional to the larger of the two values of/. The rule was stated bythe German-born US physicist Alfred Lande (1888-1975) in 1923. 

As illustrated above, any p2 configuration gives rise to iD , and levels which contain nine, five, and one state respectively. The use of L and S angular momentum algebra tools allows one to identify the wavefunctions corresponding to these states. As shown in detail in Appendix G, in the event that spin-orbit coupling causes the Hamiltonian, H, not to commute with L or with S but only with their vector sum J= L +... 

Their symmetry labels can be obtained by vector coupling (see Appendix G) the spin and orbital angular momenta of the two subsystems. The orbital angular momentum coupling... 

There is appreciable coupling between the resultant orbital and resultant spin momenta. This is referred to as LS coupling and is due to spin-orbit interaction. This interaction is caused by the positive charge Ze on the nucleus and is proportional to Z". The coupling between L and S gives the total angular momentum vector J. 

Spin-orbit coupling decreases as the orbital angular momentum quantum number f increases. This is illustrated by the fact that the Pj and P3 transitions, split by only about 70 eV, are not resolved. 

The spin rule is satisfied, but the orbital angular momentum rule is not. The reaction is apparently fast at low ion energies (4) hence, if there is an important selection rule in the combination of reactants, it is seemingly the spin rule. Conservation of spin in combining reactants is probably more likely than conservation of orbital angular momentum, since the latter will be more strongly coupled to collision angular momentum. 

A term label like for example, is thus no longer strictly meaningful for it implies constant spin- and orbital angular momentum properties (5 = 1, L = 3). One consequence of spin-orbit coupling is a scrambling of the two kinds of angular momentum. So a nominal term may really more properly be described as a mixture of terms of different spin-multiplicity as, for example, in Eq. (4.10). 

The angular momenta of atoms are described by the quantum numbers L, S or J. When spin-orbit coupling is important, it is the total angular momentum J which is a constant of the system. A group of atomic wavefunctions with a common J value - akin to a term, as described in Section 3.6 - comprise (27 -i- 1) members with Mj... 

---