Changeset 4f5afc9 in sasmodels

Timestamp:

Nov 15, 2017 6:12:11 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:

• doc/guide/magnetism/magnetism.rst (modified) (3 diffs)

doc/guide/magnetism/magnetism.rst

@@ -5 +5 @@
 
 Models which define a scattering length density parameter can be evaluated
- as magnetic models. 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.
+as magnetic models. 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 $\mathbf{M_\perp}$
 perpendicular to the scattering vector $\mathbf{Q}$ contributes to the magnetic
 scattering length.
-
 
 .. figure::
@@ -28 +27 @@
 is the Pauli spin.
 
-Assuming that incident neutrons are polarized parallel (+) and anti-parallel (-)
-to the $x'$ axis, the possible spin states after the sample are then
+Assuming that incident neutrons are polarized parallel $(+)$ and anti-parallel
+$(-)$ to the $x'$ axis, the possible spin states after the sample are then:
 
-Non spin-flip (+ +) and (- -)
+* Non spin-flip $(+ +)$ and $(- -)$
 
-Spin-flip    (+ -) and (- +)
+* Spin-flip $(+ -)$ and $(- +)$
+
+Each measurement is an incoherent mixture of these spin states based on the
+fraction of $+$ neutrons before ($u_i$) and after ($u_f$) the sample,
+with weighting:
+
+.. math::
+    -- &= ((1-u_i)(1-u_f))^{1/4} \\
+    -+ &= ((1-u_i)(u_f))^{1/4} \\
+    +- &= ((u_i)(1-u_f))^{1/4} \\
+    ++ &= ((u_i)(u_f))^{1/4}
+
+Ideally the experiment would measure the pure spin states independently and
+perform a simultaneous analysis of the four states, tying all the model
+parameters together except $u_i$ and $u_f$.
 
 .. figure::
@@ -76 +89 @@
 
 ===========   ================================================================
- M0_sld        = $D_M M_0$
- Up_theta      = $\theta_\mathrm{up}$
- 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
+ M0:sld       $D_M M_0$
+ mtheta:sld   $\theta_M$
+ mphi:sld     $\phi_M$
+ up:angle     $\theta_\mathrm{up}$
+ up:frac_i    $u_i$ = (spin up)/(spin up + spin down) *before* the sample
+ up:frac_f    $u_f$ = (spin up)/(spin up + spin down) *after* the sample
 ===========   ================================================================
 
 .. note::
-    The values of the 'Up_frac_i' and 'Up_frac_f' must be in the range 0 to 1.
+    The values of the 'up:frac_i' and 'up:frac_f' must be in the range 0 to 1.
 
 *Document History*
 
 | 2015-05-02 Steve King
-| 2017-05-08 Paul Kienzle
+| 2017-11-15 Paul Kienzle