Internal magnetic moments

The perturbation may also be an internal magnetic moment I, arising from a nuclear spin (I is here taken to include the proportionality constants between spin and moment, i.e. it includes the gAfJ-N factor from Section 8.2). 

The first derivative is the hyperfine coupling constant g (as measured by ESR), the second derivative with respect to two different nuclear spins is the NMR coupling constant, J (Planck s constant appears owing to the convention of reporting coupling constants in Hertz, and the factor of 1/2 disappears since we implicitly only consider distinct pairs of nuclei). 

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In the first, quantum mechanics can be used to calculate the NMR coupling constant between two nuclear spins in the molecular environment or the NMR shielding constant. Jensen [8] in Chapter 10 of the reference provides a comprehensive introduction to the methods for calculating these molecular properties. The NMR coupling constant, KAB, is related to the second derivative of the energy with respect to the internal magnetic moments, /u, arising from the nuclear spin of the two atoms, A and B. 

Internal Magnetic Moment 238 12.3 Enthalpy and Entropy Contributions 303... 

Because the neutron has a magnetic moment, it has a similar interaction with the clouds of impaired d or f electrons in magnetic ions and this interaction is important in studies of magnetic materials. The magnetic analogue of the atomic scattering factor is also tabulated in the International Tables [3]. Neutrons also have direct interactions with atomic nuclei, whose mass is concentrated in a volume whose radius is of the order of... 

The Stern-Gerlach experiment demonstrated that electrons have an intrinsic angular momentum in addition to their orbital angular momentum, and the unfortunate term electron spin was coined to describe this pure quantum-mechanical phenomenon. Many nuclei also possess an internal angular momentum, referred to as nuclear spin. As in classical mechanics, there is a relationship between the angular momentum and the magnetic moment. For electrons, we write... 

Observed magnetic moments, other than those in the last column, are from International Critical Tables. ... 

On the other hand, internal magnetic fields at the iron nucleus arising from the magnetic moments of unpaired valence electrons can be much stronger than any applied field and their effect can easily exceed the quadrupole interaction. For instance, Mossbauer nuclei in magnetic materials such as metals or oxides may experience fields of 30-50 T even without applied field. Similarly, the typical... 

Much of the Pt Mossbauer work performed so far has been devoted to studies of platinum metal and alloys in regard to nuclear properties (magnetic moments and lifetimes) of the excited Mossbauer states of Pt, lattice dynamics, electron density, and internal magnetic field at the nuclei of Pt atoms placed in various magnetic hosts. The observed changes in the latter two quantities, li/ (o)P and within a series of platinum alloys are particularly informative about the conduction electron delocalization and polarization. 

The shielding constant, crA, is related to a mixed second derivative of the energy with respect to an internal magnetic nuclear moment due to spin, and external magnetic field, Bext. 

Table 1.1 Conjugate pairs of variables in work terms for the fundamental equation for the internal energy U. Here/is force of elongation, Z is length in the direction of the force, <7 is surface tension, As is surface area, , is the electric potential of the phase containing species i, qi is the contribution of species i to the electric charge of a phase, E is electric field strength, p is the electric dipole moment of the system, B is magnetic field strength (magnetic flux density), and m is the magnetic moment of the system. The dots indicate scalar products of vectors.

The magnetic moments of the Ni clusters are dominated by the contribution from surface atoms.48,69 The analysis of Wan et al. indicates that the orbital and spin local moments of cluster atoms with atomic coordination 8 or larger are similar to those in the bulk (p spin 0.55 and orb 0.05 pB) 73 that is, the orbital moment is almost quenched for internal cluster atoms. In contrast, there is a large enhancement of the spin and orbital moments for atoms with coordination less than 8. This enhancement increases with the coordination deficit, and it is larger for the orbital moment. Wan et al.48 also analyzed the quantum confinement effect proposed by Fujima and Yamaguchi,56 i.e., the... 

Because the interactions measured in Mossbauer experiments are products of atomic and nuclear factors, experiments on iodine isotopes have yielded values of the change of nuclear radius between the ground state and the excited state, AR/R, quadrupole moment values Q, and magnetic moment values, fi, as well as electric field gradients and internal magnetic fields. 

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