Subject: Field gradients

From: Anthony Stone <[email-masked]>
Date: Tue, 7 Dec 1993 09:46:09 +0000 (GMT)

Perhaps it is worth spelling out the fact that the field gradient tensor is
not normally traceless, because its trace is

   F_xx + F_yy + F_zz = F_kk = - (del squared)V = (rho/epsilon_0),

by Poisson's equation, where rho is the charge density. The `field gradient'
tensor that occurs in the interaction with nuclear quadrupole moments is the
same thing with the trace subtracted out:

   F'_ij = F_ij - (1/3)F_kk delta_ij.

So the `field gradient' eq is in fact

   eq = F'_zz = F_zz - (1/3)(F_xx+F_yy+F_zz)

(in principal axes), not just F_zz.

Most of the textbooks fudge this in various ways, sometimes by just asserting
that (del squared)V = 0 `because of Laplace's equation'. Naturally this leads
to problems when people discover that it isn't so.

Anthony Stone
University Chemical Laboratory,         Internet: [email-masked]
Lensfield Road,                         Phone:    +44 223 336375
Cambridge CB2 1EW                       Fax:      +44 223 336362