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[49148bb]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
6Generic SANS Calculator Tool
7============================
8
9Description
10-----------
11
12This tool attempts to simulate the SANS expected from a specified
13shape/structure or scattering length density profile. The tool can
14handle both nuclear and magnetic contributions to the scattering.
15
16Theory
17------
18
19In general, a particle with a volume *V* can be described by an ensemble
20containing *N* 3-dimensional rectangular pixels where each pixel is much
21smaller than *V*.
22
23Assuming that all the pixel sizes are the same, the elastic scattering
24intensity from the particle is
25
26.. image:: gen_i.gif
27
28Equation 1.
29
30where |beta|\ :sub:`j` and *r*\ :sub:`j` are the scattering length density and
31the position of the j'th pixel respectively.
32
33The total volume *V*
34
35.. image:: v_j.gif
36
37for |beta|\ :sub:`j` |noteql|\0 where *v*\ :sub:`j` is the volume of the j'th
38pixel (or the j'th natural atomic volume (= atomic mass / (natural molar
39density * Avogadro number) for the atomic structures).
40
41*V* can be corrected by users. This correction is useful especially for an
42atomic structure (such as taken from a PDB file) to get the right normalization.
43
44*NOTE!* |beta|\ :sub:`j` *displayed in the GUI may be incorrect but this will not
45affect the scattering computation if the correction of the total volume V is made.*
46
47The scattering length density (SLD) of each pixel, where the SLD is uniform, is
48a combination of the nuclear and magnetic SLDs and depends on the spin states
49of the neutrons as follows.
50
51Magnetic Scattering
52^^^^^^^^^^^^^^^^^^^
53
54For magnetic scattering, only the magnetization component, *M*\ :sub:`perp`\ ,
55perpendicular to the scattering vector *Q* contributes to the magnetic
56scattering length.
57
58.. image:: mag_vector.bmp
59
60The magnetic scattering length density is then
61
62.. image:: dm_eq.gif
63
64where the gyromagnetic ratio |gamma| = -1.913, |mu|\ :sub:`B` is the Bohr
65magneton, *r*\ :sub:`0` is the classical radius of electron, and |sigma| is the
66Pauli spin.
67
68For a polarized neutron, the magnetic scattering is depending on the spin states.
69
70Let us consider that the incident neutrons are polarised both parallel (+) and 
71anti-parallel (-) to the x' axis (see below). The possible states after
72scattering from the sample are then
73
74*  Non-spin flips: (+ +) and (- -)
75*  Spin flips:     (+ -) and (- +)
76
77.. image:: gen_mag_pic.bmp
78
79Now let us assume that the angles of the *Q* vector and the spin-axis (x')
80to the x-axis are |phi| and |theta|\ :sub:`up` respectively (see above). Then,
81depending upon the polarization (spin) state of neutrons, the scattering
82length densities, including the nuclear scattering length density (|beta|\ :sub:`N`\ )
83are given as
84
85*  for non-spin-flips
86
87   .. image:: sld1.gif
88
89*  for spin-flips
90
91   .. image:: sld2.gif
92
93where
94
95.. image:: mxp.gif
96
97.. image:: myp.gif
98
99.. image:: mzp.gif
100
101.. image:: mqx.gif
102
103.. image:: mqy.gif
104
105Here the *M0*\ :sub:`x`\ , *M0*\ :sub:`y` and *M0*\ :sub:`z` are the x, y and z
106components of the magnetisation vector in the laboratory xyz frame.
107
108.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
109
110Using the tool
111--------------
112
113.. image:: gen_gui_help.bmp
114
115After computation the result will appear in the *Theory* box in the SasView 
116*Data Explorer* panel.
117
118*Up_frac_in* and *Up_frac_out* are the ratio
119
120   (spin up) / (spin up + spin down)
121   
122of neutrons before the sample and at the analyzer, respectively.
123
124*NOTE 1. The values of* Up_frac_in *and* Up_frac_out *must be in the range
1250.0 to 1.0. Both values are 0.5 for unpolarized neutrons.*
126
127*NOTE 2. This computation is totally based on the pixel (or atomic) data fixed
128in xyz coordinates. No angular orientational averaging is considered.*
129
130*NOTE 3. For the nuclear scattering length density, only the real component
131is taken account.*
132
133.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
134
135Using PDB/OMF or SLD files
136--------------------------
137
138The SANS Calculator tool can read some PDB, OMF or SLD files but ignores
139polarized/magnetic scattering when doing so, thus related parameters such as
140*Up_frac_in*, etc, will be ignored.
141
142The calculation for fixed orientation uses Equation 1 above resulting in a 2D
143output, whereas the scattering calculation averaged over all the orientations
144uses the Debye equation below providing a 1D output
145
146.. image:: gen_debye_eq.gif
147
148where *v*\ :sub:`j` |beta|\ :sub:`j` |equiv| *b*\ :sub:`j` is the scattering
149length of the j'th atom. The calculation output is passed to the *Data Explorer* 
150for further use.
151
152.. image:: pdb_combo.jpg
153
154.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
155
156.. note::  This help document was last changed by Steve King, 01May2015
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