Orbital momentum electron

Photoelectron peaks are labelled according to the quantum numbers of the level from which the electron originates. An electron coming from an orbital with main quantum number n, orbital momentum / (0, 1, 2, 3,. .. indicated as s, p, d, f,. ..) and spin momentum s (+1/2 or -1/2) is indicated as For every orbital momentum / > 0 there are two values of the total momentum j = l+Ml and j = l-Ml, each state filled with 2j + 1 electrons. Flence, most XPS peaks come in doublets and the intensity ratio of the components is (/ + 1)//. When the doublet splitting is too small to be observed, tire subscript / + s is omitted. 

A second approximation neglects coupling between the spin of an electron and its orbital momentum but assumes that coupling between orbital momenta is strong and that between spin momenta relatively weak but appreciable. This represents the opposite extreme to the 77-coupling approximation. It is known as the Russell-Saunders coupling approximation and serves as a useful basis for describing most states of most atoms and is the only one we shall consider in detail. 

The phrase total angular momentum is commonly used to refer to a number of different quantities. Here it implies orbital plus electron spin but it is also used to imply orbital plus electron spin plus nuclear spin when the symbol F is used. 

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... 

But similar calculations for the iron-group ions show marked disagreement with experiment, and many attempts were made to explain the discrepancies. The explanation is simple in many condensed systems the perturbing effect of the atoms or molecules surrounding a magnetic atom destroys the contribution of the orbital momentum to the magnetic moment, which is produced entirely by the spin moments of unpaired electrons.40... 

Secondly, correlations in the initial state can lead to experimental orbital momentum densities significantly different from the calculated Hartree-Fock ones. Figure 3 shows such a case for the outermost orbital of water, showing how electron-electron correlations enhance the density at low momentum. Since low momentum components correspond in the main to large r components in coordinate space, the importance of correlations to the chemically interesting long range part of the wave function is evident. 

Figure 2. The binding energy spectrum for valence electrons of ethyne and the corresponding measured and calculated self-consistent-field independent particle orbital momentum densities [5]. 

Figure 3.12 The motion of an electron in orbit about a nucleus generates an orbital momentum (L) adding a component to the magnetic field experienced by the electron spin (5). (Adapted with permission from Figure 2.18 of Cowan, J. A. Inorganic Biochemistry, An Introduction, 2nd ed., Wiley-VCH, New York, 1997. Copyright 1997, Wiley-VCH.)...

Photoelectron peaks are labeled according to the quantum numbers of the level from which the electron originates. An electron with orbital momentum / (0,1, 2, 3,.. 

Section III. Methods for obtaining momentum densities, both experimental and computational, are reviewed in Section IV. Only a sample of representative work on the electron momentum densities of atoms and molecules is summarized in Sections V and VI because the topic is now too vast for comprehensive coverage. Electron momentum densities in solids and other condensed phases are not considered at all. The literature on electron momentum spectroscopy and Dyson orbital momentum densities is not surveyed, either. Hartree atomic units are used throughout. 

This term is important only in that it gives a second-order contribution to the hyperfine interaction by allowing the nuclear spin and electron spin to couple indirectly through the orbital momentum. 

The quantum number / occurs in the 0(0) factor of the wave function. It may be thought of as representing the angular momentum of the electron, in units of /i/27t, because of its orbital motion, and we shall call it the orbital momentum quantum number. It may take all values 0, 1, 2,. .., / — 1, where n is the principal quantum number. Thus, in the first principal shell, there exist only wave functions with / = 0 in the second shell there are wave functions with 1 = 0 and 1 and so on. For historical reasons, letter symbols are given to orbitals according to the value of /, as shown in the following scheme ... 

Let us illustrate this method in the special case of two non-equivalent electrons ni/ir fe, described by four momenta two orbital li, I2 and two spin si, S2- Having in mind the commutativity of the addition as well as the fact that the interaction of the orbital momentum of a given electron with its own spin momentum is much stronger than that with... 

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