Section 4: Adding Shells to the Model¶
The solid sphere is the simplest possible scattering object, but real materials are rarely uniform. A polymer nanoparticle may have a dense core and a swollen outer layer. A lipid vesicle is a hollow sphere — an aqueous interior enclosed by a thin membrane. To describe these structures we need to add shells: concentric regions with different scattering length densities.
This section builds the shell model in three steps: a single shell around a core, then multiple shells, then the special case where the core and matrix have the same SLD — which produces a hollow sphere and connects directly to the physics of lipid vesicles.
By the end of this section you will have:
- A general multi-shell form factor function that handles any number of concentric layers
- Physical intuition for how each shell changes the scattering curve
- An understanding of why the hollow sphere model is a good first description of a vesicle
- A complete, reusable scattering toolkit built across Sections 2 and 4
All code belongs in a new notebook: chapter_04_shells.ipynb. Copy your
sphere_amplitude, sphere_form_factor, and plot_form_factor functions from
chapter_02_sphere.ipynb into the first code cell of the new notebook so that
everything is self-contained.