Introduction to Electric Hyperfine Interactions

The total energy of the electrostatic interaction between a nucleus with charge Ze and charges around this nucleus may be expressed in classical terms as [1], [9] in Chap. 1  

Giitlich et al., Mossbauer Spectroscopy and Transition Metal Chemistry, 

The variable p (r) denotes the nuclear charge density at a point r with coordinates r = xi,X2,x ), and V r) is the Coulomb potential set up at that point by all other charges (the Coulomb constant k = l/(47t o) is dropped in this description). The integration variable in (4.1) is the volume element dr = Ax dr2dx3. The origin of the coordinate system is chosen to coincide with the center of the nuclear charge. A more convenient expression can be obtained by expanding V r) at f = (0,0,0) in a Taylor series, that is, 

The first derivative of the potential T at r = (0,0,0), taken as negative value, represents the ekctric field E, and the second derivative represents the electric field gradient tensor V at the nucleus, 

With these notations, we obtain for the electrostatic energy 

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