Magnetic quantized

The expression (1.5) for the resonant scattering length can be expanded in powers of the unit vector m that defines the magnetic quantization axis of the atom in the sample. The resonant scattering length for an electric dipole transition (L= I) gets the form [42]... 

Like the curl condition is reminiscent of the Yang-Mills field, the quantization just mentioned is reminiscent of a study by Wu and Yang [76] for the quantization of Dirac s magnetic monopole [77-78]. As will be shown, the present quantization conditions just like the Wu and Yang conditions result from a phase factor, namely, the exponential of a phase and not just from a phase. 

In other words, the quantization that was encountered for the non-adiabatic coupling terms is associated with the quantization of the intensity of the magnetic field along the seam. Moreover, Eq. (154) reveals another feature, namely, that there are fields for which n is an odd integer, namely, conical intersections and there are fields for which is an even integer, namely, parabolical intersections. 

An effect of space quantization of orbital angular momentum may be observed if a magnetic field is introduced along what we now identify as the z axis. The orbital angular momentum vector P, of magnitude Pi, may take up only certain orientations such that the component (Pi) along the z axis is given by... 

All possible alignments between the dipole and the magnetic induction are allowed, and the energies are continuous there is no hint of quantization. 

Stem-Gerlach experiment The demonstration of the quantization of electron spin by passing a beam of atoms through a magnetic field, stick structure See line structure. stock solution A solution stored in concentrated form, stoichiometric coefficients The numbers multiplying chemical formulas in a chemical equation. 

The calculated energy of interaction of an atomic moment and the Weiss field (0.26 uncoupled conduction electrons per atom) for magnetic saturation is 0.135 ev, or 3070 cal. mole-1. According to the Weiss theory the Curie temperature is equal to this energy of interaction divided by 3k, where k is Boltzmann s constant. The effect of spatial quantization of the atomic moment, with spin quantum number S, is to introduce the factor (S + 1)/S that is, the Curie temperature is equal to nt S + l)/3Sk. For iron, with 5 = 1, the predicted value for the Curie constant is 1350°K, in rough agreement with the experimental value, 1043°K. 

Some years later a more thorough discussion of the motion of pairs of electrons in a metal was given by Cooper,7 as well as by Abrikosov8 and Gor kov,9 who emphasized that the effective charge in superconductivity is 2e, rather than e. The quantization of flux in units hc/2e in superconducting metals has been verified by direct experimental measurement of the magnetic moments induced in thin films.10 Cooper s discussion of the motion of electron pairs in interaction with phonons led to the development of the Bardeen-Cooper-Schrieffer (BCS) theory, which has introduced great clarification in the field of superconductivity.2... 

Among atomic orbitals, s orbitals are spherical and have no directionality. Other orbitals are nonspherical, so, in addition to having shape, every orbital points in some direction. Like energy and orbital shape, orbital direction is quantized. Unlike footballs, p, d, and f orbitals have restricted numbers of possible orientations. The magnetic quantum number (fflj) indexes these restrictions. 

As mentioned in Section Wl, an electron has magnetism associated with a property called spin. Magnetism is directional, so the spin of an electron is directional, too. Like orbital orientation, spin orientation is quantized Electron spin has only two possible orientations, up or down. The spin orientation quantum number )... 

The value of is given by the component of the EFG tensor along the main quantization axis. Therefore, in this example where the EFG is axial (77 = 0) with the main component the quadrupole shift is eQVzJ - This is just half the quadrupole splitting that would be observed in an unperturbed quadrupole spectrum without a magnetic field at the nucleus. 

Here, the magnetic perturbation is projected onto the quantization axes of Hq as the major interaction. 

When a magnetic field is applied to an electron or nuclear spin, the spin quantization axis is defined by the field direction. Spin magnetic moments... 

When we include the Zeeman interaction term, gpBB-S, in the spin Hamiltonian a complication arises. We have been accustomed to evaluating the dot product by simply taking the direction of the magnetic field to define the z-axis (the axis of quantization). When we have a strong dipolar interaction, the... 

Now consider what happens when the field is applied perpendicular to the symmetry axis. The large value of D ensures that z will continue to be the quantization axis. We ought to solve a 6 x 6 secular equation, but we can get a reasonable approximation more easily. Since D is big, the 5/2 and 3/2 levels are well separated from the 1/2 levels before application of the magnetic field. Thus mixing of 3/2) with 11/2) will be much less important than mixing of 11/2) with —1/2). Thus we can solve just the middle 2x2 block for the energies of ms= 1/2 levels ... 

The significance of the terms in the g tensor can best be illustrated by means of a simple example. Let us redefine our coordinates such that the spin is quantized along the z axis. The magnetic field vector is now at some different position in space as shown in Fig. 11. Expanding the Hamiltonian in Eq. (1C) gives,... 

Magnets producing fields more than 50 T are used to apply quantizing fields for experiments on electrons in metals and in semiconductors. 

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