Nuclear-orbit interaction

The simplest system exliibiting a nuclear hyperfme interaction is the hydrogen atom with a coupling constant of 1420 MHz. If different isotopes of the same element exhibit hyperfme couplings, their ratio is detemiined by the ratio of the nuclear g-values. Small deviations from this ratio may occur for the Femii contact interaction, since the electron spin probes the inner stmcture of the nucleus if it is in an s orbital. However, this so-called hyperfme anomaly is usually smaller than 1 %. 

In this section, the spin-orbit interaction is treated in the Breit-Pauli [13,24—26] approximation and incoi porated into the Hamiltonian using quasidegenerate perturbation theory [27]. This approach, which is described in [8], is commonly used in nuclear dynamics and is adequate for molecules containing only atoms with atomic numbers no larger than that of Kr. 

When the molecule is not in a S state there is an interaction between the rotation of the molecule and S and/or L, and the details of coupling the angular momenta are involved. Most nonsinglet molecules with electronic orbital angular momentum A = 0 obey Hund s case (b) coupling. In Case (b), the electronic orbital angular momentum combines with the nuclear orbital angular... 

Here and H describe radicals A and B of the radical pair and He the interaction of their electrons. The other terms in equation (15) are H g, the spin orbit coupling term, H g and Hgj, representing the interaction of the externally applied magnetic field with the electron spin and nuclear spin, respectively Hgg is the electron spin-spin interaction and Hgi the electron-nuclear hyperfine interaction. 

An indirect mode of anisotropic hyperfine interaction arises as a result of strong spin-orbit interaction (174)- Nuclear and electron spin magnetic moments are coupled to each other because both are coupled to the orbital magnetic moment. The Hamiltonian is... 

Show that the zero-order energies E() of nuclear energy states with quantum numbers l, s, where s = 1/2, are shifted respectively by the spin-orbit interaction —al.s to... 

The dipolar parts of the analyzed hfs tensors have been compared with calculated values obtained from first order expressions of the electron-nuclear dipole interaction (5.3)57. The coefficients of the atomic orbitals used in this computation, which considers all two- and three-center contributions, are obtained from an extended Huckel calculation (ethyl groups replaced by protons). It has been found that almost 100% of the unpaired electron is located on the CuS4 fragment so that the replacement of the ethyl groups by protons is of minor importance for the calculation of the atomic orbital coefficients. The experimental and theoretical hfs data, summarized in Table 8, are found to... 

It was noted that for 78b and 79b, 7hf and 7cf are dependent on the molecular conformation, but this is not the case with 7nf. which is independent of the conformation. It is well known that the internuclear couplings are electron coupled interactions for which there are three possible mechanisms (1) the nuclear moments interact with the electronic currents produced by the orbiting electrons (2) there is a dipolar interaction between the nuclear and electronic magnetic moments (3) there is an interaction between the nuclear moments and the electronic spins in i-orbitals, the so-called Fermi contact term. ... 

Finally, spin-orbit interaction has often been considered as the cause of states of mixed permutational symmetry. There are, however, a variety of other spin interactions which may accomplish such mixing electron spin-electron spin, electron spin-nuclear spin, spin-other-orbit, and spin rotation interactions. That other such spin interactions may enhance spin-forbidden processes in organic molecules is frequently ignored, though they may be of importance.66,136... 

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