Hi Nicolas,
Great!
I don't have the particular expression for a rod handy, but for general interest, I'll note there's a partial list of analytic shape envelopes for the reduced pair distribution function G(r) = 4 pi r ( rho(r) - rho_0 ) developed in Python here:
https://github.com/diffpy/diffpy.srfit/blob/master/src/diffpy/srfit/pdf/characteristicfunctions.py
And that Philip Chater has contributed a sphere in the PDF specific Topas user macros:
macro spherical_damping(r,rv)
{
#m_argu r
If_Prm_Eqn_Rpt(r, rv, min 1 max 1000, del = 0.01 Val;)
scale_phase_X =
IF X > 2 CeV(r,rv) THEN
0
ELSE
If(X>0.01,(Pi X^2 ((0.25 (X/CeV(r,rv))^3)-(3 X/CeV(r,rv))+4)) / (4 Pi X^2 1),1)
ENDIF;
}
and I've written the following for a sheet:
macro sheet_damping(sthick_c, sthick_v)
' damping envelope assuming sheet thickness model
' ref: Kodama et al. Acta Cryst. A 62(6) 444-454 (2006). doi: 10.1107/S0108767306034635
{
#m_argu sthick_c
If_Prm_Eqn_Rpt(sthick_c, sthick_v, min 1 max 1000, del = 0.01 Val;)
scale_phase_X =
IF X <= CeV(sthick_c, sthick_v) THEN
1 - 0.5 * X / CeV(sthick_c, sthick_v)
ELSE
0.5 * CeV(sthick_c, sthick_v) / X
ENDIF;
}
I hope these will help speed you on your way.
-Peter