Derivation of nuclear spin interactions from the Breit equation

Derivation of nuclear spin interactions from the Breit equation 

It is possible to obtain the nuclear spin magnetic interaction terms by starting from the Breit equation. We recall that the Breit Hamiltonian describes the interaction of two electrons of spin 1 /2, each of which may be separately represented by a Dirac Hamiltonian  

In chapter 3 we showed how the relativistic Breit Hamiltonian can be reduced to non-relativistic form by means of a Foldy Wouthysen transformation. We obtained equations (3.244) and (3.245) which represent the non-relativistic Hamiltonian for two particles of masses m, and nij and electrostatic charges and —ej and from this Hamiltonian we were able to derive the interelectronic interactions. We could, however, consider using (3.244) and (3.245) as the Hamiltonian for an electron of charge —e, = — e and mass m, = m, and a nucleus of mass nij = Ma and charge —ej = + 7. e. As before, we make the assumption that the nucleus has spin 1 /2, behaves like a Dirac particle and has an anomalous magnetic moment compared with that given by the Dirac theory. Consequently we may rewrite (3.245) by making the replacements 

Confining attention to those terms in (3.245) which contain cy and which are of order Mu 1 we obtain expressions for the electron-nuclear interactions which are 

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