Is the Fermi field contact and isotropic?
  It is shown that the contribution to the induction which at an internal point of a spin density distribution is mathematically described as a local is virtually caused by the summing-up of the fields created by all elements of this distribution. Therefore, the proportionality coefficient between this contact (Fermi) field and magnetic moment density at the point of observation is equal to 8pi/3 only for spherically symmetrical s-shells. If the symmetry of spin density distribution lowers, the value of this coefficient becomes dependent on the spin direction. As a sequence, in low-symmetry crystals and molecules additional anisotropic contributions to the hyperfine field emerge. 
E. V. Rosenfeld