PolyRectSphere

Steve Kline 20 JAN 1999

Alan Munter 08 JULY 1999, converted to Java

Calculates the form factor for a polydisperse population of spheres with uniform scattering length density. The distribution of radii is a rectangular (box) distribution. The form factor is normalized by the average particle volume such that P(q) = scale*<f*f>/Vol + bkg, where f is the single particle scattering amplitude and the < > denote an average over the size distribution.

Resolution smeared version is also provided.

Input Variables (default values):

Parameter	Variable	Value
0	Scale	1.0
1	Average Radius (Å)	60.0
2	Polydispersity (0-1)	0.12
3	Contrast (Å-2)	3.0e-6
4	Incoherent Background(cm-1)	0.000

The returned value is scaled to units of [cm^-1], absolute scale.

contrast = SLD (sphere) - SLD (solvent)

The (normalized) rectangular distribution is:

with the constraint that w <= R. Here R is the average radius specified by parameter[1] above.

R is the mean of the distribution and w is the half-width. The root mean square deviation is . The polydispersity, .

The form factor is normalized by the average volume, using

.

If the scale factor Parameter[0] is set equal to the particle volume fraction, phi, the returned value is the scattered intensity per unit volume, I(q) = phi*P(q). However, no interparticle interference effects are included in this calculation.

Parameter[0] (scale) and Parameter[3] (contrast) are multiplicative factors in the model and are perfectly correlated. Only one of these parameters should be left free during model fitting.

Kotlarchyk, M.; Chen, S.-H. J. Chem. Phys., 1983, 79, 2461.

This example dataset is produced by calculating the PolyRectSphere using 128 data points, q_min = 0.001 Å^-1, q_max = 0.7 Å^-1 and the above default parameter values.