Index: c/sas/sasgui/perspectives/calculator/media/gen_sas_help.html
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-
-Generic Scattering Calculator:
-Polarization and Magnetic Scattering
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-1. Theory
-
-In general, a particle with a volume V can be described by an ensemble containing N
-3-dimensional rectangular pixels where each pixels are much smaller than V.
-Assuming that
-all the pixel sizes are same, the elastic scattering intensity
-by the particle
-
-
-
-
-where βj and rj are the scattering
-length density and the position
-of the j'th pixel respectively. And the total volume
-
-
-
-
-for βj ≠ 0 where vj 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). The total volume V can be corrected by users.
-This correction is useful especially for an atomic structure (taken from a pdb file) to get the right
-normalization. Note that the βj displayed in GUI may be incorrect but will not
-affect the scattering computation if the correction of the total volume 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:
-
-
-For magnetic scattering, only the magnetization component, Mperp,
-perpendicular to the scattering vector Q contributes to the the magnetic
-scattering length. (Figure below).
-
-
-
-
-The magnetic scattering length density is then
-
-
-
-
-where γ = -1.913 the gyromagnetic ratio, μB is the Bohr magneton,
-r0 is the classical radius of electron,
-and σ is the Pauli spin.
-
-For polarized neutron, the magnetic scattering is depending on the spin states.
-Let's consider that the incident neutrons are polarized parallel (+)/anti-parallel
-(–) to the x' axis (See both Figures above).
-The possible out-coming states then are + and - states for both incident states.
-
- - Non-spin-flips: (+ +) and (- -)
-
- - Spin-flips: (+ -) and (- +)
-
-
-
-
-
-
-Now, let's assume that the angles of the Q vector and the spin-axis (x') from x-axis
-are φ and θup, respectively (See Figure above).
-Then, depending upon the polarization (spin) state of neutrons, the scattering length
-densities , including the nuclear scattering length density (β N) are given as, for non-spin-flips,
-
-
-
-
-
-for spin-flips,
-
-
-
-
-
-where
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-
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-Here, the M0x, M0y and M0z are the x, y and z
-components of the magnetization vector given in the xyz lab frame.
-
-
-2. GUI
-
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-
-After the computation, the result will be listed in the 'Theory' box
-in the data explorer panel on the main window.
-
-The 'Up_frac_in' and 'Up_frac_out' are the ratio, (spin up) /(spin up + spin down) neutrons
-before the sample and at the analyzer, respectively.
-
-
-*Note I: The values of 'Up_frac_in' and 'Up_frac_out' must be in the range between 0 and 1.
-For example, both values are 0.5 for unpolarized neutrons.
-
-*Note II: This computation is totally based on the pixel (or atomic) data fixed
-in the xyz coordinates. Thus no angular orientational averaging is considered.
-
-*Note III: For the nuclear scattering length density, only the real component is taken account.
-
-
-3. PDB Data
-
-This Generic scattering calculator also supports some pdb files without considering polarized/magnetic scattering
- so that the related parameters such as Up_*** will be ignored (see the Picture below). The calculation for fixed orientation uses (the first) Equation above resulting
-in a 2D output, whileas the scattering calculation averaged over all the orientations uses the Debye equation providing a 1D output:
-
-
-
-
-where vjβj ≡ bj is the scattering length of the j'th atom.
-The resultant outputs will be displayed in the DataExporer for further uses.
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