# Changeset 6debc16 in sasview

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Timestamp:
Nov 28, 2017 9:21:33 AM (5 years ago)
Branches:
Children:
45bfe3f1
Parents:
0fc5a03 (diff), 1b67f3e (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
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git-author:
Steve K <smk78@…> (11/28/17 09:21:33)
git-committer:
Message:

Merge pull request #125 from SasView?/docs

translate equation images back into latex for sas_calculator_help

Files:
11 deleted
2 edited

### Legend:

Unmodified
 r5ed76f8 intensity from the particle is .. image:: gen_i.png .. math:: I(\vec Q) = \frac{1}{V}\left| \sum_j^N v_j \beta_j \exp(i\vec Q \cdot \vec r_j)\right|^2 Equation 1. atomic structure (such as taken from a PDB file) to get the right normalization. *NOTE! $\beta_j$ displayed in the GUI may be incorrect but this will not *NOTE!* $\beta_j$ *displayed in the GUI may be incorrect but this will not affect the scattering computation if the correction of the total volume V is made.* ^^^^^^^^^^^^^^^^^^^ For magnetic scattering, only the magnetization component, $M_\perp$, perpendicular to the scattering vector $Q$ contributes to the magnetic For magnetic scattering, only the magnetization component, $\mathbf{M}_\perp$, perpendicular to the scattering vector $\vec Q$ contributes to the magnetic scattering length. The magnetic scattering length density is then .. image:: dm_eq.png .. math:: \beta_M = \frac{\gamma r_0}{2 \mu_B}\sigma \cdot \mathbf{M}_\perp = D_M\sigma \cdot \mathbf{M}_\perp where the gyromagnetic ratio is $\gamma = -1.913$, $\mu_B$ is the Bohr .. image:: gen_mag_pic.png Now let us assume that the angles of the *Q* vector and the spin-axis (x') to the x-axis are $\phi$ and $\theta_\text{up}$ respectively (see above). Then, Now let us assume that the angles of the $\vec Q$ vector and the spin-axis ($x'$) to the $x$-axis are $\phi$ and $\theta_\text{up}$ respectively (see above). Then, depending upon the polarization (spin) state of neutrons, the scattering length densities, including the nuclear scattering length density ($\beta_N$) *  for non-spin-flips .. image:: sld1.png .. math:: \beta_{\pm\pm} = \beta_N \mp D_M M_{\perp x'} *  for spin-flips .. image:: sld2.png .. math:: \beta_{\pm\mp} = - D_M(M_{\perp y'} \pm i M_{\perp z'}) where .. image:: mxp.png .. math:: .. image:: myp.png M_{\perp x'} &= M_{0q_x}\cos\theta_\text{up} + M_{0q_y}\sin\theta_\text{up} \\ M_{\perp y'} &= M_{0q_y}\cos\theta_\text{up} - M_{0q_x}\sin\theta_\text{up} \\ M_{\perp z'} &= M_{0z} \\ M_{0q_x} &= (M_{0x}\cos\phi - M_{0y}\sin\phi)\cos\phi \\ M_{0q_y} &= (M_{0y}\sin\phi - M_{0y}\cos\phi)\sin\phi .. image:: mzp.png .. image:: mqx.png .. image:: mqy.png Here the $M0_x$, $M0_y$ and $M0_z$ are the $x$, $y$ and $z$ components of the magnetisation vector in the laboratory $xyz$ frame. Here the $M_{0x}$, $M_{0y}$ and $M_{0z}$ are the $x$, $y$ and $z$ components of the magnetisation vector in the laboratory $x$-$y$-$z$ frame. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ uses the Debye equation below providing a 1D output .. image:: gen_debye_eq.png .. math:: I(|\vec Q|) = \frac{1}{V}\sum_j^N v_j\beta_j \sum_k^N v_k \beta_k \frac{\sin(|\vec Q||\vec r_j - \vec r_k|)}{|\vec Q||\vec r_j - \vec r_k|} where $v_j \beta_j \equiv b_j$ is the scattering