Changeset 4f5afc9 in sasmodels
 Timestamp:
 Nov 15, 2017 6:12:11 PM (6 years ago)
 Branches:
 master, core_shell_microgels, magnetic_model, ticket1257vesicleproduct, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
 Children:
 ac60a39
 Parents:
 1e867a4
 File:

 1 edited
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doc/guide/magnetism/magnetism.rst
r2c108a3 r4f5afc9 5 5 6 6 Models which define a scattering length density parameter can be evaluated 7 8 9 10 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. 11 11 12 12 For magnetic scattering, only the magnetization component $\mathbf{M_\perp}$ 13 13 perpendicular to the scattering vector $\mathbf{Q}$ contributes to the magnetic 14 14 scattering length. 15 16 15 17 16 .. figure:: … … 28 27 is the Pauli spin. 29 28 30 Assuming that incident neutrons are polarized parallel (+) and antiparallel ()31 to the $x'$ axis, the possible spin states after the sample are then 29 Assuming that incident neutrons are polarized parallel $(+)$ and antiparallel 30 $()$ to the $x'$ axis, the possible spin states after the sample are then: 32 31 33 Non spinflip (+ +) and ( ) 32 * Non spinflip $(+ +)$ and $( )$ 34 33 35 Spinflip (+ ) and ( +) 34 * Spinflip $(+ )$ and $( +)$ 35 36 Each measurement is an incoherent mixture of these spin states based on the 37 fraction of $+$ neutrons before ($u_i$) and after ($u_f$) the sample, 38 with weighting: 39 40 .. math:: 41  &= ((1u_i)(1u_f))^{1/4} \\ 42 + &= ((1u_i)(u_f))^{1/4} \\ 43 + &= ((u_i)(1u_f))^{1/4} \\ 44 ++ &= ((u_i)(u_f))^{1/4} 45 46 Ideally the experiment would measure the pure spin states independently and 47 perform a simultaneous analysis of the four states, tying all the model 48 parameters together except $u_i$ and $u_f$. 36 49 37 50 .. figure:: … … 76 89 77 90 =========== ================================================================ 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 sample83 Up_frac_f = (spin up)/(spin up + spin down) neutrons*after* the sample91 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 84 97 =========== ================================================================ 85 98 86 99 .. 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. 88 101 89 102 *Document History* 90 103 91 104  20150502 Steve King 92  2017 0508Paul Kienzle105  20171115 Paul Kienzle
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