# source:sasmodels/sasmodels/models/core_shell_sphere.py@a34b811

ticket-1257-vesicle-productticket_1156ticket_822_more_unit_tests
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1r"""
2.. _core_shell_sphere:
3
4This model provides the form factor, $P(q)$, for a spherical particle with
5a core-shell structure. The form factor is normalized by the particle volume.
6
7For information about polarised and magnetic scattering, see
8the :ref:magnetism documentation.
9
10Definition
11----------
12
13The 1D scattering intensity is calculated in the following way (Guinier, 1955)
14
15.. math::
16
17    P(q) = \frac{\text{scale}}{V} F^2(q) + \text{background}
18
19where
20
21.. math::
22
23    F(q) = \frac{3}{V_s}\left[
24       V_c(\rho_c-\rho_s)\frac{\sin(qr_c)-qr_c\cos(qr_c)}{(qr_c)^3} +
25       V_s(\rho_s-\rho_\text{solv})\frac{\sin(qr_s)-qr_s\cos(qr_s)}{(qr_s)^3}
26       \right]
27
28where $V_s$ is the volume of the whole particle, $V_c$ is the volume of the
29core, $r_s$ = $radius$ + $thickness$ is the radius of the particle, $r_c$
30is the radius of the core, $\rho_c$ is the scattering length density of the
31core, $\rho_s$ is the scattering length density of the shell,
32$\rho_\text{solv}$, is the scattering length density of the solvent.
33
34The 2D scattering intensity is the same as $P(q)$ above, regardless of the
35orientation of the $q$ vector.
36
37NB: The outer most radius (ie, = radius + thickness) is used as the
38effective radius for $S(Q)$ when $P(Q) \cdot S(Q)$ is applied.
39
40Validation
41----------
42
43Validation of our code was done by comparing the output of the 1D model to
44the output of the software provided by NIST (Kline, 2006). Figure 1 shows a
45comparison of the output of our model and the output of the NIST software.
46
47References
48----------
49
50.. [#] A Guinier and G Fournet, *Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, (1955)
51
52Source
53------
54
55core_shell_sphere.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/core_shell_sphere.py>_
56
57core_shell_sphere.c <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/core_shell_sphere.c>_
58
59Authorship and Verification
60----------------------------
61
62* **Author:**
64* **Last Reviewed by:**
65* **Source added by :** Steve King **Date:** March 25, 2019
66"""
67
68import numpy as np
69from numpy import pi, inf
70
71name = "core_shell_sphere"
72title = "Form factor for a monodisperse spherical particle with particle with a core-shell structure."
73description = """
75            + V_s (sld_shell-sld_solvent) 3 (sin(q*r_s)-q*r_s*cos(q*r_s))/(q*r_s)^3]
76
77            V_s: Volume of the sphere shell
78            V_c: Volume of the sphere core
80"""
81category = "shape:sphere"
82
84#             ["name", "units", default, [lower, upper], "type","description"],
86              ["thickness",   "Ang",        10.0, [0, inf],    "volume", "Sphere shell thickness"],
87              ["sld_core",    "1e-6/Ang^2", 1.0,  [-inf, inf], "sld",    "core scattering length density"],
88              ["sld_shell",   "1e-6/Ang^2", 2.0,  [-inf, inf], "sld",    "shell scattering length density"],
89              ["sld_solvent", "1e-6/Ang^2", 3.0,  [-inf, inf], "sld",    "Solvent scattering length density"]]
91
92source = ["lib/sas_3j1x_x.c", "lib/core_shell.c", "core_shell_sphere.c"]
93have_Fq = True
95
96demo = dict(scale=1, background=0, radius=60, thickness=10,
97            sld_core=1.0, sld_shell=2.0, sld_solvent=0.0)
98
99def random():
100    """Return a random parameter set for the model."""
102    # Use a distribution with a preference for thin shell or thin core
103    # Avoid core,shell radii < 1
106    pars = dict(