.. sas_calculator_help.rst .. This is a port of the original SasView html help file to ReSTructured text .. by S King, ISIS, during SasView CodeCamp-III in Feb 2015. Generic SANS Calculator Tool ============================ Description ----------- This tool attempts to simulate the SANS expected from a specified shape/structure or scattering length density profile. The tool can handle both nuclear and magnetic contributions to the scattering. Theory ------ In general, a particle with a volume *V* can be described by an ensemble containing *N* 3-dimensional rectangular pixels where each pixel is much smaller than *V*. Assuming that all the pixel sizes are the same, the elastic scattering intensity from the particle is .. image:: gen_i.gif Equation 1. where |beta|\ :sub:`j` and *r*\ :sub:`j` are the scattering length density and the position of the j'th pixel respectively. The total volume *V* .. image:: v_j.gif for |beta|\ :sub:`j` |noteql|\0 where *v*\ :sub:`j` is the volume of the j'th pixel (or the j'th natural atomic volume (= atomic mass / (natural molar density * Avogadro number) for the atomic structures). *V* can be corrected by users. This correction is useful especially for an atomic structure (such as taken from a PDB file) to get the right normalization. *NOTE!* |beta|\ :sub:`j` *displayed in the GUI may be incorrect but this will not affect the scattering computation if the correction of the total volume V is made.* The scattering length density (SLD) of each pixel, where the SLD is uniform, is a combination of the nuclear and magnetic SLDs and depends on the spin states of the neutrons as follows. Magnetic Scattering ^^^^^^^^^^^^^^^^^^^ For magnetic scattering, only the magnetization component, *M*\ :sub:`perp`\ , perpendicular to the scattering vector *Q* contributes to the magnetic scattering length. .. image:: mag_vector.bmp The magnetic scattering length density is then .. image:: dm_eq.gif where the gyromagnetic ratio |gamma| = -1.913, |mu|\ :sub:`B` is the Bohr magneton, *r*\ :sub:`0` is the classical radius of electron, and |sigma| is the Pauli spin. For a polarized neutron, the magnetic scattering is depending on the spin states. Let us consider that the incident neutrons are polarised both parallel (+) and anti-parallel (-) to the x' axis (see below). The possible states after scattering from the sample are then * Non-spin flips: (+ +) and (- -) * Spin flips: (+ -) and (- +) .. image:: gen_mag_pic.bmp Now let us assume that the angles of the *Q* vector and the spin-axis (x') to the x-axis are |phi| and |theta|\ :sub:`up` respectively (see above). Then, depending upon the polarization (spin) state of neutrons, the scattering length densities, including the nuclear scattering length density (|beta|\ :sub:`N`\ ) are given as * for non-spin-flips .. image:: sld1.gif * for spin-flips .. image:: sld2.gif where .. image:: mxp.gif .. image:: myp.gif .. image:: mzp.gif .. image:: mqx.gif .. image:: mqy.gif Here the *M0*\ :sub:`x`\ , *M0*\ :sub:`y` and *M0*\ :sub:`z` are the x, y and z components of the magnetisation vector in the laboratory xyz frame. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ Using the tool -------------- .. image:: gen_gui_help.bmp After computation the result will appear in the *Theory* box in the SasView *Data Explorer* panel. *Up_frac_in* and *Up_frac_out* are the ratio (spin up) / (spin up + spin down) of neutrons before the sample and at the analyzer, respectively. *NOTE 1. The values of* Up_frac_in *and* Up_frac_out *must be in the range 0.0 to 1.0. Both values are 0.5 for unpolarized neutrons.* *NOTE 2. This computation is totally based on the pixel (or atomic) data fixed in xyz coordinates. No angular orientational averaging is considered.* *NOTE 3. For the nuclear scattering length density, only the real component is taken account.* .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ Using PDB/OMF or SLD files -------------------------- The SANS Calculator tool can read some PDB, OMF or SLD files but ignores polarized/magnetic scattering when doing so, thus related parameters such as *Up_frac_in*, etc, will be ignored. The calculation for fixed orientation uses Equation 1 above resulting in a 2D output, whereas the scattering calculation averaged over all the orientations uses the Debye equation below providing a 1D output .. image:: gen_debye_eq.gif where *v*\ :sub:`j` |beta|\ :sub:`j` |equiv| *b*\ :sub:`j` is the scattering length of the j'th atom. The calculation output is passed to the *Data Explorer* for further use. .. image:: pdb_combo.jpg .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ .. note:: This help document was last changed by Steve King, 01May2015