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sasview/docs/sphinxdocs/source/user/sasgui/perspectives/fitting/mag_help.rst
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Polarisation/Magnetic Scattering
Magnetic scattering is implemented in five (2D) models
 SphereModel
 CoreShellModel
 CoreMultiShellModel
 CylinderModel
 ParallelepipedModel
In general, the scattering length density (SLD, = beta) in each region where the SLD is uniform, is a combination of the nuclear and magnetic SLDs and, for polarised neutrons, also depends on the spin states of the neutrons.
For magnetic scattering, only the magnetization component, M_{perp}, perpendicular to the scattering vector Q contributes to the the magnetic scattering length.
The magnetic scattering length density is then
where gamma = 1.913 is the gyromagnetic ratio, mu_{B} is the Bohr magneton, r_{0} is the classical radius of electron, and sigma is the Pauli spin.
Assuming that incident neutrons are polarized parallel (+) and antiparallel () to the x' axis, the possible spin states after the sample are then
No spinflips (+ +) and ( )
Spinflips (+ ) and ( +)
If the angles of the Q vector and the spinaxis (x') to the xaxis are phi and theta_{up}, respectively, then, depending on the spin state of the neutrons, the scattering length densities, including the nuclear scattering length density (beta_{N}) are
when there are no spinflips, and
when there are, and
Here, M_{0x}, M_{0y} and M_{0z} are the x, y and z components of the magnetization vector given in the laboratory xyz frame given by
and the magnetization angles theta_{M} and phi_{M} are defined in the figure above.
The user input parameters are:
M0_sld  = D_{M} M_{0} 
Up_theta  = theta_{up} 
M_theta  = theta_{M} 
M_phi  = phi_{M} 
Up_frac_i  = (spin up)/(spin up + spin down) neutrons before the sample 
Up_frac_f  = (spin up)/(spin up + spin down) neutrons after the sample 
Note: The values of the 'Up_frac_i' and 'Up_frac_f' must be in the range 0 to 1.
Note
This help document was last changed by Steve King, 02May2015