Changeset 4f5afc9 in sasmodels


Ignore:
Timestamp:
Nov 15, 2017 4:12:11 PM (7 years ago)
Author:
Paul Kienzle <pkienzle@…>
Branches:
master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
ac60a39
Parents:
1e867a4
Message:

magnetism: add docs about spin state weighting in final calc

File:
1 edited

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  • doc/guide/magnetism/magnetism.rst

    r2c108a3 r4f5afc9  
    55 
    66Models which define a scattering length density parameter can be evaluated 
    7  as magnetic models. In general, the scattering length density (SLD = 
    8  $\beta$) in each region where the SLD is uniform, is a combination of the 
    9  nuclear and magnetic SLDs and, for polarised neutrons, also depends on the 
    10  spin states of the neutrons. 
     7as magnetic models. In general, the scattering length density (SLD = 
     8$\beta$) in each region where the SLD is uniform, is a combination of the 
     9nuclear and magnetic SLDs and, for polarised neutrons, also depends on the 
     10spin states of the neutrons. 
    1111 
    1212For magnetic scattering, only the magnetization component $\mathbf{M_\perp}$ 
    1313perpendicular to the scattering vector $\mathbf{Q}$ contributes to the magnetic 
    1414scattering length. 
    15  
    1615 
    1716.. figure:: 
     
    2827is the Pauli spin. 
    2928 
    30 Assuming that incident neutrons are polarized parallel (+) and anti-parallel (-) 
    31 to the $x'$ axis, the possible spin states after the sample are then 
     29Assuming that incident neutrons are polarized parallel $(+)$ and anti-parallel 
     30$(-)$ to the $x'$ axis, the possible spin states after the sample are then: 
    3231 
    33 Non spin-flip (+ +) and (- -) 
     32* Non spin-flip $(+ +)$ and $(- -)$ 
    3433 
    35 Spin-flip    (+ -) and (- +) 
     34* Spin-flip $(+ -)$ and $(- +)$ 
     35 
     36Each measurement is an incoherent mixture of these spin states based on the 
     37fraction of $+$ neutrons before ($u_i$) and after ($u_f$) the sample, 
     38with weighting: 
     39 
     40.. math:: 
     41    -- &= ((1-u_i)(1-u_f))^{1/4} \\ 
     42    -+ &= ((1-u_i)(u_f))^{1/4} \\ 
     43    +- &= ((u_i)(1-u_f))^{1/4} \\ 
     44    ++ &= ((u_i)(u_f))^{1/4} 
     45 
     46Ideally the experiment would measure the pure spin states independently and 
     47perform a simultaneous analysis of the four states, tying all the model 
     48parameters together except $u_i$ and $u_f$. 
    3649 
    3750.. figure:: 
     
    7689 
    7790===========   ================================================================ 
    78  M0_sld        = $D_M M_0$ 
    79  Up_theta      = $\theta_\mathrm{up}$ 
    80  M_theta       = $\theta_M$ 
    81  M_phi         = $\phi_M$ 
    82  Up_frac_i     = (spin up)/(spin up + spin down) neutrons *before* the sample 
    83  Up_frac_f     = (spin up)/(spin up + spin down) neutrons *after* the sample 
     91 M0:sld      $D_M M_0$ 
     92 mtheta:sld   $\theta_M$ 
     93 mphi:sld     $\phi_M$ 
     94 up:angle     $\theta_\mathrm{up}$ 
     95 up:frac_i    $u_i$ = (spin up)/(spin up + spin down) *before* the sample 
     96 up:frac_f    $u_f$ = (spin up)/(spin up + spin down) *after* the sample 
    8497===========   ================================================================ 
    8598 
    8699.. note:: 
    87     The values of the 'Up_frac_i' and 'Up_frac_f' must be in the range 0 to 1. 
     100    The values of the 'up:frac_i' and 'up:frac_f' must be in the range 0 to 1. 
    88101 
    89102*Document History* 
    90103 
    91104| 2015-05-02 Steve King 
    92 | 2017-05-08 Paul Kienzle 
     105| 2017-11-15 Paul Kienzle 
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