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1.. sas_calculator_help.rst
2
3.. This is a port of the original SasView html help file to ReSTructured text
4.. by S King, ISIS, during SasView CodeCamp-III in Feb 2015.
5
6.. |beta| unicode:: U+03B2
7.. |gamma| unicode:: U+03B3
8.. |theta| unicode:: U+03B8
9.. |mu| unicode:: U+03BC
10.. |sigma| unicode:: U+03C3
11.. |phi| unicode:: U+03C6
12
13.. |equiv| unicode:: U+2261
14.. |noteql| unicode:: U+2260
15
16Generic SANS Calculator Tool
17============================
18
19Description
20-----------
21
22This tool attempts to simulate the SANS expected from a specified
23shape/structure or scattering length density profile. The tool can
24handle both nuclear and magnetic contributions to the scattering.
25
26Theory
27------
28
29In general, a particle with a volume *V* can be described by an ensemble
30containing *N* 3-dimensional rectangular pixels where each pixel is much
31smaller than *V*.
32
33Assuming that all the pixel sizes are the same, the elastic scattering
34intensity from the particle is
35
36.. image:: gen_i.gif
37
38Equation 1.
39
40where |beta|\ :sub:`j` and *r*\ :sub:`j` are the scattering length density and
41the position of the j'th pixel respectively.
42
43The total volume *V*
44
45.. image:: v_j.gif
46
47for |beta|\ :sub:`j` |noteql|\0 where *v*\ :sub:`j` is the volume of the j'th
48pixel (or the j'th natural atomic volume (= atomic mass / (natural molar
49density * Avogadro number) for the atomic structures).
50
51*V* can be corrected by users. This correction is useful especially for an
52atomic structure (such as taken from a PDB file) to get the right normalization.
53
54*NOTE!* |beta|\ :sub:`j` *displayed in the GUI may be incorrect but this will not
55affect the scattering computation if the correction of the total volume V is made.*
56
57The scattering length density (SLD) of each pixel, where the SLD is uniform, is
58a combination of the nuclear and magnetic SLDs and depends on the spin states
59of the neutrons as follows.
60
61Magnetic Scattering
62^^^^^^^^^^^^^^^^^^^
63
64For magnetic scattering, only the magnetization component, *M*\ :sub:`perp`\ ,
65perpendicular to the scattering vector *Q* contributes to the magnetic
66scattering length.
67
68.. image:: mag_vector.bmp
69
70The magnetic scattering length density is then
71
72.. image:: dm_eq.gif
73
74where the gyromagnetic ratio |gamma| = -1.913, |mu|\ :sub:`B` is the Bohr
75magneton, *r*\ :sub:`0` is the classical radius of electron, and |sigma| is the
76Pauli spin.
77
78For a polarized neutron, the magnetic scattering is depending on the spin states.
79
80Let us consider that the incident neutrons are polarised both parallel (+) and 
81anti-parallel (-) to the x' axis (see below). The possible states after
82scattering from the sample are then
83
84*  Non-spin flips: (+ +) and (- -)
85*  Spin flips:     (+ -) and (- +)
86
87.. image:: gen_mag_pic.bmp
88
89Now let us assume that the angles of the *Q* vector and the spin-axis (x')
90to the x-axis are |phi| and |theta|\ :sub:`up` respectively (see above). Then,
91depending upon the polarization (spin) state of neutrons, the scattering
92length densities, including the nuclear scattering length density (|beta|\ :sub:`N`\ )
93are given as
94
95*  for non-spin-flips
96
97   .. image:: sld1.gif
98
99*  for spin-flips
100
101   .. image:: sld2.gif
102
103where
104
105.. image:: mxp.gif
106
107.. image:: myp.gif
108
109.. image:: mzp.gif
110
111.. image:: mqx.gif
112
113.. image:: mqy.gif
114
115Here the *M0*\ :sub:`x`\ , *M0*\ :sub:`y` and *M0*\ :sub:`z` are the x, y and z
116components of the magnetisation vector in the laboratory xyz frame.
117
118.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
119
120Using the tool
121--------------
122
123.. image:: gen_gui_help.bmp
124
125After computation the result will appear in the *Theory* box in the SasView 
126*Data Explorer* panel.
127
128*Up_frac_in* and *Up_frac_out* are the ratio
129
130   (spin up) / (spin up + spin down)
131   
132of neutrons before the sample and at the analyzer, respectively.
133
134*NOTE 1. The values of* Up_frac_in *and* Up_frac_out *must be in the range
1350.0 to 1.0. Both values are 0.5 for unpolarized neutrons.*
136
137*NOTE 2. This computation is totally based on the pixel (or atomic) data fixed
138in xyz coordinates. No angular orientational averaging is considered.*
139
140*NOTE 3. For the nuclear scattering length density, only the real component
141is taken account.*
142
143.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
144
145Using PDB/OMF or SLD files
146--------------------------
147
148The SANS Calculator tool can read some PDB, OMF or SLD files but ignores
149polarized/magnetic scattering when doing so, thus related parameters such as
150*Up_frac_in*, etc, will be ignored.
151
152The calculation for fixed orientation uses Equation 1 above resulting in a 2D
153output, whereas the scattering calculation averaged over all the orientations
154uses the Debye equation below providing a 1D output
155
156.. image:: gen_debye_eq.gif
157
158where *v*\ :sub:`j` |beta|\ :sub:`j` |equiv| *b*\ :sub:`j` is the scattering
159length of the j'th atom. The calculation output is passed to the *Data Explorer*
160for further use.
161
162.. image:: pdb_combo.jpg
163
164.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
165
166.. note::  This help document was last changed by Steve King, 01May2015
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