MODEL

Ellipsoid

AUTHOR/MODIFICATION

Steve Kline 20 JAN 1999

Alan Munter 08 JULY 1999, converted to Java

APPROVED FOR DISTRIBUTION

DESCRIPTION

Calculates the form factor for a monodisperse ellipsoid (ellipsoid
of revolution) with uniform scattering length density. The form factor
is normalized by the particle volume such that P(*q*) =
scale*<*f***f*>/Vol + bkg, where f is the scattering
amplitude and the < > denote an average over all possible
orientations of the ellipsoid.

Resolution smeared version is also provided.

VARIABLES

Input Variables (default values):

Parameter | Variable | Value |
---|---|---|

0 | Scale | 1.0 |

1 | R_{a} (rotation axis) (Å) | 20.0 |

2 | R_{b} (Å) | 400.0 |

3 | Contrast (Å^{-2}) | 3.0e-6 |

4 | Incoherent Background (cm^{-1}) | 0.0 |

**USAGE** **NOTES**

The function calculated is:

and

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

The ellipse is rotated about the axis of R_{a} to define the ellipsoid.
If (as shown below) the R_{b} >R_{a}, the object is
an oblate ellipsoid (disk-like). If R_{b} < R_{a},
then the object is a prolate ellipsoid (needle-like). If the two radii
are equal, then the ellipsoid is a sphere.

If the object is an oblate ellipsoid (disk-like), it displays a
limiting power-law slope of *q*^{-2} at low *q*.

A prolate ellipsoid (needle-like), displays a limiting power-law
slope of *q*^{-1} at low *q*.

Parameter[0] (scale) and Parameter[3] (contrast) are both multiplicative factors in the model and are perfectly correlated. One or both of these parameters must be held fixed during model fitting.

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.

REFERENCE

Feigin, L. A, and D. I. Svergun, "Structure Analysis by Small-Angle X-Ray and Neutron Scattering", Plenum Press, New York, (1987).

TEST DATASET

This example dataset is produced by calculating the Ellipsoid using
128 data points, *q*_{min} = 0.001 Å^{-1},
*q*_{max} = 0.7 Å^{-1} and the above default
parameter values.