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The following tables give the coefficients of an analytic approximation
to the
integrals for the d electrons in ions of the
3d
and 4d series, and the f electrons of some
rare earth and
actinide ions. The
approximation has the form
![\begin{displaymath}\langle j_0(s)\rangle = A \exp(-as^2) + B \exp(-bs^2) + C \exp(-cs^2) + D
\end{displaymath}](ffactimg10.gif) |
(7) |
For these expansions
in units of Å-1.
The integrals
with
are zero when s=0 and have been
fitted with the form
![\begin{displaymath}\langle j_0(s)\rangle = \left(A\exp(-as^2) + B\exp(-bs^2) +
C\exp(-cs^2) + D\right)s^2
\end{displaymath}](ffactimg14.gif) |
(8) |
The second set of tables give the coefficients obtained for
<j2> for 3d, and 4d transition metals,
htmlrefrare earthsrej2 and actinides,
<j4> for htmlref3d3dj4, and 4d transition metals,
rare earths and actinides,
and <j6> for rare earths and actinides.
For the transition metal series the fits were made with
form factor integrals calculated from Hartree-Fock wave-functions [2].
For
the rare-earth and actinide series the fits were with
Dirac-Fock form factors [3,4]. In the tables the number
following the atom symbol indicates the ionisation state of the atom.
Thus the coefficients following Fe0 are for a neutral iron atom and
those following Fe2 are for Fe2+.
Next: Tables of Form Factors
Up: Magnetic Form Factors
Previous: Definition of form factors
P.J. Brown - Institut Laue Langevin, Grenoble, FRANCE. e-mail: brown@ill.fr