Orbital angular momentum of electron

The two-electron terms arise from the magnetic interaction of the spin of electron k with the orbital angular momentum of electron /. It should be noted that Hso is a two-electron operator in the electronic coordinate space, but is a one-electron operator in spin space. can be written in determinantal form analogous... 

This term involves the interaction of the spin of electron j with the orbital angular momentum of electron i around electron j, and is called the spin ther rbit interaction. 

The magnetic dipole moment is proportional to the angular momentum, the coefficient of proportionality being the magnetogyric ratio ye = e/2nje. The orbital angular momentum of electron i is defined as... 

We saw in Section 1.3.2 and in Figure 1.5 how the orbital angular momentum of an electron can be represented by a vector, the direction of which is determined by the right-hand screw mle. 

Just as the value of n can be used to calculate the energy of an electron, the value of / can be used to calculate another physical property. As its name suggests, / tells us the orbital angular momentum of the electron, a measure of the rate at which the electron circulates round the nucleus ... 

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... 

Despite this similarity with chemical shift, the Knight shift is grouped with the electron hyperfine term in (lb) to reflect the fact that both terms arise from the influence of the spin or orbital angular momentum of unpaired electrons. The distinction between the two is that for the electron hyperfine term the electron spin (or hole, as the absence of an electron can be described, e.g., in the case of d9 Cu++) is localized on a paramagnetic defect such as a deep-level transition metal ion. 

Orbital angular momentum of an electron in an atom can be measured by the same type of Stern-Gerlach experiment described before for the measurement of electron spin. In this case it will be assumed to use a metal such as magnesium whose atoms have a total electron spin of zero. The magnetic moment... 

Three quantum numbers had been proposed, based on spectral lines and inferences about electron energy levels a principal quantum number to specify energy level of the atom an azimuthal quantum number to specify the angular momentum of electrons moving elliptically and an inner or magnetic quantum number to express the orientation of the plane of the electron s orbit in a magnetic field. 20... 

The result of this lower symmetry of the environment is the quenching of the orbital angular momentum of the electron the orbital angular momentum is no longer a good quantum number and has an average value of zero. Some contribution of the orbital motion however remains, and this causes a positive or negative deviation of the g-factor from the free spin value of 2.0023. 

Here, the relevant angular momentum vectors and quantum numbers are L (7), the total orbital angular momentum of the atom, obtained as the vector coupling of those corresponding to the core and to the outer electron(s), S (S), the total spin, and J (7), the total angular momentum for a given atomic level [8] ... 

The resonance width Ts is expressed by the Wigner s threshold rule. In the case of isolated O2, the resonance state O2 (X ITg, v = 4) can couple with only one electronic partial wave with an angular momentum 1 = 2. In the case of vdW molecules, intermolecular interaction may couple with additional partial waves such as p-wave and s-wave with low energy. If a third-body molecule distorts the orbital of O2 (X ITg), new attachment channels can open with lower angular momentum of electrons and the resonance width may increase. 

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