Fitting Models with Structure Factors

Product models, $P@S$ models for short, multiply the structure factor $S(q)$ by the form factor $P(q)$, modulated by the effective radius of the form factor.

Many of the parameters in $P@S$ models take on specific meanings so that they can be handled correctly inside SasView:

• scale:

  The scale for $P@S$ models should usually be set to 1.0.

• volfraction:

  For hollow shapes, volfraction represents the volume fraction of material but the $S(q)$ calculation needs the volume fraction enclosed by the shape. SasView scales the user-specified volume fraction by the ratio form:shell computed from the average form volume and average shell volume returned from the $P(q)$ calculation (the original volfraction is divided by shell_volume to compute the number density, and then $P@S$ is scaled by that to get the absolute scaling on the final $I(q)$).

• radius_effective:

  If part of the $S(q)$ calculation, the value of radius_effective may be polydisperse. If it is calculated by $P(q)$, then it will be the weighted average of the effective radii computed for the polydisperse shape parameters.

• structure_factor_mode:

  If the $P@S$ model supports the $beta(q)$ correction [1] then structure_factor_mode will appear in the parameter table after the $S(q)$ parameters. This mode may be 0 for the local monodisperse approximation:

  $I = (scale / volume)$ x $P$ x $S + background$

  or 1 for the beta correction:

  $I = (scale$ x $volfraction / volume)$ x $( <FF>$ + $<F>^2 (S-1) ) + background$

  where $F$

  More options may appear here in future as more complicated operations are added.