Hamiltonian and hyperfine constants

Appendix 8.5. Magnetic hyperfine Hamiltonian and hyperfine constants 

In a classic paper, Frosch and Foley [117] derived an elFective Hamiltonian to describe the magnetic nuclear hyperfine interactions of a diatomic molecule in an open shell electronic state. Their Hamiltonian was expressed in the following form  

The constant b therefore contains contributions from two quite different magnetic interactions, the Fermi contact and the electron-nuclear dipolar interactions. Interpretation of the magnitudes of these constants in terms of electronic structure theory always involves the separate assessment of these different effects, so that we prefer to use an effective Hamiltonian which separates them at the outset. Consequently the effective magnetic hyperfine Hamiltonian used throughout this book is 

The orbital hyperfine constant a is the same in both (8.509) and (8.510), but the second term in (8.510) describes only the Fermi contact interaction, the constant hp being equal to the first part of b in (8.509). It is clear from a comparison of the two equations that 

The third term in equation (8.510) describes only the electron-nuclear spin dipolar interaction, with the first-rank tensor T1 (.S. C2) being constructed so that 

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