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  • src/sas/sasgui/perspectives/fitting/media/mag_help.rst

    reca66a1 r5ed76f8  
    44.. by S King, ISIS, during SasView CodeCamp-III in Feb 2015. 
    55 
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    1515 
    1616 
     
    2020-------------------------------- 
    2121 
    22 Magnetic scattering is implemented in five (2D) models  
     22Magnetic scattering is implemented in five (2D) models 
    2323 
    2424*  *sphere* 
     
    2828*  *parallelepiped* 
    2929 
    30 In general, the scattering length density (SLD, = |beta|) in each region where the 
     30In general, the scattering length density (SLD, = $\beta$) in each region where the 
    3131SLD is uniform, is a combination of the nuclear and magnetic SLDs and, for polarised 
    3232neutrons, also depends on the spin states of the neutrons. 
    3333 
    34 For magnetic scattering, only the magnetization component, *M*\ :sub:`perp`, 
    35 perpendicular to the scattering vector *Q* contributes to the the magnetic 
     34For magnetic scattering, only the magnetization component, $M_\perp$, 
     35perpendicular to the scattering vector $Q$ contributes to the the magnetic 
    3636scattering length. 
    3737 
    38 .. image:: mag_vector.bmp 
     38.. image:: mag_vector.png 
    3939 
    4040The magnetic scattering length density is then 
    4141 
    42 .. image:: dm_eq.gif 
     42.. image:: dm_eq.png 
    4343 
    44 where |gamma| = -1.913 is the gyromagnetic ratio, |mu|\ :sub:`B` is the 
    45 Bohr magneton, *r*\ :sub:`0` is the classical radius of electron, and |sigma| 
     44where $\gamma = -1.913$ is the gyromagnetic ratio, $\mu_B$ is the 
     45Bohr magneton, $r_0$ is the classical radius of electron, and $\sigma$ 
    4646is the Pauli spin. 
    4747 
     
    5353Spin-flips    (+ -) and (- +) 
    5454 
    55 .. image:: M_angles_pic.bmp 
     55.. image:: M_angles_pic.png 
    5656 
    57 If the angles of the *Q* vector and the spin-axis (*x'*) to the *x*-axis are |phi| 
    58 and |theta|\ :sub:`up`, respectively, then, depending on the spin state of the 
     57If the angles of the $Q$ vector and the spin-axis (*x'*) to the *x*-axis are $\phi$ 
     58and $\theta_\text{up}$, respectively, then, depending on the spin state of the 
    5959neutrons, the scattering length densities, including the nuclear scattering 
    60 length density (|beta|\ :sub:`N`) are 
     60length density ($\beta_N$) are 
    6161 
    62 .. image:: sld1.gif 
     62.. image:: sld1.png 
    6363 
    6464when there are no spin-flips, and 
    6565 
    66 .. image:: sld2.gif 
     66.. image:: sld2.png 
    6767 
    6868when there are, and 
    6969 
    70 .. image:: mxp.gif 
     70.. image:: mxp.png 
    7171 
    72 .. image:: myp.gif 
     72.. image:: myp.png 
    7373 
    74 .. image:: mzp.gif 
     74.. image:: mzp.png 
    7575 
    76 .. image:: mqx.gif 
     76.. image:: mqx.png 
    7777 
    78 .. image:: mqy.gif 
     78.. image:: mqy.png 
    7979 
    80 Here, *M*\ :sub:`0x`, *M*\ :sub:`0y` and *M*\ :sub:`0z` are the x, y and z components 
    81 of the magnetization vector given in the laboratory xyz frame given by 
     80Here, $M_{0x}$, $M_{0y}$ and $M_{0z}$ are the $x$, $y$ and $z$ components 
     81of the magnetization vector given in the laboratory $xyz$ frame given by 
    8282 
    83 .. image:: m0x_eq.gif 
     83.. image:: m0x_eq.png 
    8484 
    85 .. image:: m0y_eq.gif 
     85.. image:: m0y_eq.png 
    8686 
    87 .. image:: m0z_eq.gif 
     87.. image:: m0z_eq.png 
    8888 
    89 and the magnetization angles |theta|\ :sub:`M` and |phi|\ :sub:`M` are defined in 
     89and the magnetization angles $\theta_M$ and $\phi_M$ are defined in 
    9090the figure above. 
    9191 
     
    9393 
    9494===========   ================================================================ 
    95  M0_sld        = *D*\ :sub:`M` *M*\ :sub:`0` 
    96  Up_theta      = |theta|\ :sub:`up` 
    97  M_theta       = |theta|\ :sub:`M` 
    98  M_phi         = |phi|\ :sub:`M` 
     95 M0_sld        = $D_M M_0$ 
     96 Up_theta      = $\theta_\text{up}$ 
     97 M_theta       = $\theta_M$ 
     98 M_phi         = $\phi_M$ 
    9999 Up_frac_i     = (spin up)/(spin up + spin down) neutrons *before* the sample 
    100100 Up_frac_f     = (spin up)/(spin up + spin down) neutrons *after* the sample 
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