Atoms electronic angular momentum

The first application of quantum theory to a problem in chemistry was to account for the emission spectrum of hydrogen and at the same time explain the stability of the nuclear atom, which seemed to require accelerated electrons in orbital motion. This planetary model is rendered unstable by continuous radiation of energy. The Bohr postulate that electronic angular momentum should be quantized in order to stabilize unique orbits solved both problems in principle. The Bohr condition requires that... 

Thus, each atom experiences a force which is proportional to the z-component of its electronic angular momentum. By measuring the deflection of the beam Fz can be calculated. 

Fig. 10. Hybridized model densities of states for UN. The full rectangles are the original unhybridized densities of states (see Fig. 48). The broken rectangles are the additional projected densities of states due to hybridization. In a vertical line are the contributions to the local atomic and angular momentum projected densities of states. The electron transfer, in terms of the fractional occupancy (F) of the unhybridized f-band, is shown...

E are the projections of the electron orbital angular momentum on the molecular axis and the subscript is the projection of the total electron angular momentum on the molecular axis directed from the heavy atom to fluorine. It is convenient to describe the spin-rotational spectrum of the ground electronic state in terms of the effective spin-rotational Hamiltonian following [90, 117] ... 

We now consider many-electron atoms. We will assume Russell-Saunders coupling, so that an atomic state can be characterized by total electronic orbital and spin angular-momentum quantum numbers L and S, and total electronic angular-momentum quantum numbers J and Mj. (See Section 1.17.) The electric-dipole selection rules for L, J, and Mj can be shown to be (Bethe and Jackiw, p. 224)... 

As co) increases, the experimental scattering lobe is no longer symmetric to Zcol but turns its symmetry axis essentially into the direction of the momentum-transfer vector K=kout—kjn as indicated by 9 in Fig. 32. In Born s approximation the lobe would be exactly symmetric to K. This reflects the fact that electronic angular momentum of the atom is transferred into linear momentum of the scattered electron. 

Insufficient experimental data is available to demonstrate either the occurrence or lack of selection rules. In Table 15, some of the fastest reactions do correspond to transitions allowed for both atoms. Singlet helium transfers to Ne at a rate consistent with the data in Fig. 26, whereas triplet helium transfers comparatively slowly neither of the He transitions is allowed. However, there appear to be other cases, discussed earlier, where a forbidden transition is preferred to an allowed transition. Stepp and Anderson146 have suggested that there is partial conservation of electronic angular momentum accompanying energy transfer between atoms, and interpreted experiments on mercury fluorescence by means of the steps... 

Okunevich, A.I. (1981). Excited-state collisional relaxation by optical orientation of atoms with arbitrary electronic angular momentum,... 

A spectroscopic or Russell-Saunders state is designated rL, where r is the electron spin multiplicity and L is the total atomic orbital angular momentum... 

The sound part of Bohr s atomic model, and its successors, appears to be the assumed quantization of electronic angular momentum and energy, as well as atomic size. Had Bohr gone one step further the proposed quantiza-... 

One of the benefits that quantum theory has for chemistry is an improved understanding of elemental periodicity, spectroscopy and statistical thermodynamics topics which can be developed without reference to the nature of electrons, atoms or molecules. The success of these applications depend on approximations to model many-electron atoms on the hydrogen solution and the recognition of spin as a further component of electronic angular momentum, subject to the secondary condition known as (Pauli s) exclusion principle. 

The alternative derivation of atomic periodicity, based on the distribution of prime numbers and elementary number theory, makes firm statements on all of these unresolved issues. The number spiral predicts periodicities of 8 and 24 for all elements and nuclides respectively limits their maximum numbers, in terms of triangular numbers, to 100 and 300 respectively characterizes electronic angular-momentum sub-levels by the difference between successive square numbers (21 +1) and electron pairs per energy level by the square numbers themselves. In this way the transition series fit in naturally with the periodicity of 8. The multiplicity of 2, which is associated with electron spin, is implicit in these periodicity numbers. 

The origin of this magnetic moment was not clear in 1922. In its electronic ground state, a silver atom does not possess a spatial angular momentum, and the concept of an intrinsic electronic angular momentum (the electron spin) was yet to be created. In 1925, Goudsmit and Uhlenbeck introduced a fourth (spin) electron degree of freedom—in addition to the three spatial coordinates (x, y, z)—as a model to ease the explanation of the anomalous Zeeman effect.3,4... 

Spin-orbit coupling arises naturally in Dirac theory, which is a fully relativistic one-particle theory for spin j systems.11 In one-electron atoms, spin s and orbital angular momentum l of the electron are not separately conserved they are coupled and only the resulting total electronic angular momentum j is a good quantum number. 

Well-known realizations of the generators of this Lie algebra are given by the three components of the orbital angular momentum vector L = r x p, the three components of the spin S = a realized in terms of the Pauli spin matrices (Schiff, 1968), or the total one-electron angular momentum J = L + S. The components of each of these vector operators satisfy the defining commutation relations Eq. (4) if we use atomic units. We should also note that the vector cross-product example mentioned earlier also satisfies Eq. (4) if we define E = iey, j = 1, 2, 3. 

There are at present several distinct approaches to the treatment of collisional reorientation of electronic angular momentum j of an atom. We shall discuss these by comparing them with known exact results which,... 

In photoelectron diffraction experiments monoenergetic photons excite electrons from a particular atomic core level. Angular momentum is conserved, so the emitted electron wave-function is a spherical wave centered on the source atom, with angular momentum components / 1, where / is the angular momentum of the core level. If the incident photon beam is polarized, the orientation of the emitted electron wave-function can be controlled. These electrons then propagate through the surface and are detected and analyzed as in LEED experiments. A synchrotron x-ray source normally produces the intense beams of variable energy polarized photons needed for photoelectron diffraction. 

Two components contribute to the total angular momentum F of the atom, the nuclear angular momentum (spin) I and the electronic angular momentum J, so that... 

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