Magnetic properties in the nonrelativistic limit

We shall later (section 4.8) study the relativistic corrections to properties. At this point we are interested in their nrl. We shall see that for electric properties one gets the correct nrl automatically from the Schrodinger equation. The nrl of magnetic properties is more subtle. The result for a first-order magnetic property is e.g. 

Application of the turn-over rule changes this expression to (see the previous section) 

The problem is that the turn-over rule is valid only if the integrand vanishes at the boundaries. This is the case, e.g. for a homogeneous magnetic field, but not for the magnetic field created by a (point) nucleus. In the former case we get the same result as from the Pauli Hamiltonian (128) 

The term a6(0) is spherically symmetric and contributes to Bqi as du means the differential with respect to angular and spin coordinates) 

If one evaluates Boi from the original expression (132), and avoids to apply the turn-over rule, there is no need for differentiation in the distribution sense. We illustrate this for the ground state of H-like ions. 

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