Field-independent magnetic moment

Here (r - Rc) (r - Rq) is the dot product times a unit matrix (i.e. (r — Rg) (r — Rg)I) and (r - RG)(r — Rg) is a 3x3 matrix containing the products of the x,y,z components, analogous to the quadrupole moment, eq. (10.4). Note that both the L and P operators are gauge dependent. When field-independent basis functions are used the first-order property, the HF magnetic dipole moment, is given as the expectation value over the unperturbed wave funetion (for a singlet state) eqs. (10.18)/(10.23). 

If all the magnetic moments p were independent, their equations of motion in the field H0 would be... 

The chemical shift generally is much less important in esr spectroscopy than in nmr. One reason is that the lifetimes of the electrons in the +V2 and —V2 states generally are very short (10 fi sec or less) so esr lines are quite broad by comparison with nmr lines (see Section 27-1). Esr chemical shifts usually are measured in terms of g factors, which, like nmr 8 values, are field-independent. The resonance frequency is given by v = gix0Hulh, in which jjL0 is the magnetic moment of the electron. 

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