Nuclear spin-orbit interaction

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. 

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... 

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... 

Blume and Watson33 showed in 1962 that only parts of the two-electron spin-orbit interaction may be expressed in the form [122]. According to these authors, the neglect of the remaining terms leads to a dependence of the effective nuclear charge from a particular state. For dn configurations, for example, they found that Zf can vary by as much as 20%.34... 

Apart from the selection rules for the electronic coupling matrix element, spin-forbidden and spin-allowed nonradiative transitions are treated completely analogously. Nonradiative transitions caused by spin-orbit interaction are mostly calculated in the basis of pure spin Born-Oppenheimer states. With respect to spin-orbit coupling, this implies a diabatic behavior, meaning that curve crossings may occur in this approach. The nuclear Schrodinger equation is first solved separately for each electronic state, and the rovibronic states are spin-orbit coupled then in a second step. 

The first three terms are present for both para- and ortho-H2 they represent the electron spin-rotation, electron spin-spin dipolar and spin orbit interactions respectively. The fourth term in (8.187) represents the magnetic hyperfine interactions, which we will come to a little later. We deal first, however, with the terms that do not involve nuclear spin interactions. 

The effective Hamiltonian contained terms for both nuclei describing the orbital hy-perfine interaction, the electric quadrupole interaction and the nuclear spin-rotation interaction ... 

For heavy elements, all of the above non-relativistic methods become increasingly in error with increasing nuclear charge. Dirac 47) developed a relativistic Hamiltonian that is exact for a one-electron atom. It includes relativistic mass-velocity effects, an effect named after Darwin, and the very important interaction that arises between the magnetic moments of spin and orbital motion of the electron (called spin-orbit interaction). A completely correct form of the relativistic Hamiltonian for a many-electron atom has not yet been found. However, excellent results can be obtained by simply adding an electrostatic interaction potential of the form used in the non-relativistic method. This relativistic Hamiltonian has the form... 

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