.. 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. .. _SANS_Calculator_Tool: 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.png Equation 1. where $\beta_j$ and $r_j$ are the scattering length density and the position of the $j^\text{th}$ pixel respectively. The total volume $V$ .. math:: V = \sum_j^N v_j for $\beta_j \ne 0$ where $v_j$ is the volume of the $j^\text{th}$ pixel (or the $j^\text{th}$ 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! $\beta_j$ 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, $M_\perp$, perpendicular to the scattering vector $Q$ contributes to the magnetic scattering length. .. image:: mag_vector.png The magnetic scattering length density is then .. image:: dm_eq.png where the gyromagnetic ratio is $\gamma = -1.913$, $\mu_B$ is the Bohr magneton, $r_0$ 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.png Now let us assume that the angles of the *Q* vector and the spin-axis (x') to the x-axis are $\phi$ and $\theta_\text{up}$ respectively (see above). Then, depending upon the polarization (spin) state of neutrons, the scattering length densities, including the nuclear scattering length density ($\beta_N$) are given as * for non-spin-flips .. image:: sld1.png * for spin-flips .. image:: sld2.png where .. image:: mxp.png .. image:: myp.png .. image:: mzp.png .. image:: mqx.png .. image:: mqy.png Here the $M0_x$, $M0_y$ and $M0_z$ are the $x$, $y$ and $z$ components of the magnetisation vector in the laboratory $xyz$ frame. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ Using the tool -------------- .. image:: gen_gui_help.png 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.png where $v_j \beta_j \equiv b_j$ is the scattering length of the $j^\text{th}$ 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