BornAgain
≻ 20
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ Sphere
BornAgain
≻ 20
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ Sphere
A full sphere.
Sphere(R)
Parameters:
As for any other Form factor.
Class Sphere inherits from the interface class IFormFactor .
Form factor is computed as
$$ F(\mathbf{q})=4\pi R^3 \exp(iq_z R) \dfrac{\sin(qR) - qR \cos(qR)}{(qR)^3} , $$ with the notation $$ q := \sqrt{q_x^2 + q_y^2+ q_z^2}. $$
Volume has been validated against $$ V=\dfrac{4\pi}{3} R^3. $$
More general:
Scattering by uncorrelated spheres for horizontal incidence:
Generated by Examples/ff/Sphere.py , Examples/fq/Sphere.py .
This form factor is well known; it goes back to Lord Rayleigh. In IsGISAXS, it has been implemented as form factor “Full sphere” [manual, Eq. 2.35; Renaud 2009, Eq. 226]. In BornAgain, named “FullSphere” up to version 1.19.