Field Theory of ESR

The general Hamiltonian including magnetic as well as electric interactions can be written 

LS Spin-Orbit Interaction. When a charge moves in an electric field, the theory of special relativity tells us that part of the electric field appears as a magnetic field to the electron. The magnetic moment of the electron interacts with this magnetic field giving rise to what is known as the spin-orbit interaction. From Dirac s theory of the electron, it can be shown (/) that this interaction takes the form 

3Hfz Zeeman Interaction. The interaction of the magnetic field and 

This is just the interaction between two electron magnetic dipoles a distance tjk apart. 

8(rik) is the Dirac delta function which, when integrated with the wave function, gives the value of the wave function at rik = 0. The two terms in Eq. (15) are in reality two limiting forms of the same interaction. The first term is the ordinary dipole-dipole interaction for two dipoles that are not too close to each other. It is the proper form of M S1 to be applied to p, d, and / electrons which are not found near the nucleus. For s electrons, which have a finite probability of being at the nucleus, the first term is clearly inappropriate, since it gives zero contribution at large values of rik and does not hold for small values of rik. From Dirac s relativistic theory of the electron, it is found (4) that the second term in Eq. (15) is the correct form for Si when the electron is close to the nucleus. Thus the contribution toJT S] from s electrons is proportional to the wave function squared at the site of the nucleus and the second term in Eq. (15) is often called the contact term in the hyperfine interaction. 

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