Difference between revisions of "Talk:DWBA"

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(Breaking into components)
Line 124: Line 124:
  
 
We define the ratio between the channels to be:
 
We define the ratio between the channels to be:
 +
 
<math>
 
<math>
 
\begin{align}
 
\begin{align}
 
w
 
w
   & = \frac{ I_{Tc}(q_z) }{ I_{Tc}(q_z) | I_{Rc}(q_z) }
+
   & = \frac{ I_{Tc}(q_z) }{ I_{Tc}(q_z) + I_{Rc}(q_z) }
 +
\end{align}
 +
</math>
 +
 
 +
Such that one can compute the two components from:
 +
 
 +
<math>
 +
\begin{align}
 +
I_d(q_{z}) & = |Tc|^2 ( I_{Tc}(q_z) ) + |Rc|^2 ( I_{Rc}(q_z) ) \\
 +
I_d(q_{z}) & = |Tc|^2 ( I_{Tc}(q_z) ) + |Rc|^2 \left ( \frac{ I_{Tc}(q_z) - w I_{Tc}(q_z) }{w}  \right ) \\
 +
I_d(q_{z}) & = I_{Tc}(q_z) \times \left ( |Tc|^2  +  |Rc|^2 \frac{ 1}{w}  - |Rc|^2 \frac{w }{w}  \right ) \\
 +
I_{Tc}(q_z)  & = \frac{ I_d(q_{z}) }{  |Tc|^2  +  \frac{ |Rc|^2 }{w}  - |Rc|^2  } \\
 +
\end{align}
 +
</math>
 +
 
 +
and:
 +
 
 +
 
 +
<math>
 +
\begin{align}
 +
I_{Rc}(q_z) & = \frac{ I_d(q_{z}) - |Tc|^2 I_{Tc}(q_z) }{|Rc|^2}
 
\end{align}
 
\end{align}
 
</math>
 
</math>

Revision as of 12:39, 12 March 2018

DWBA Equation in thin film

Using the notation for compactness, the DWBA equation inside a thin film can be written:

Expansion

Terms

If one expands the of the DWBA, one obtains 16 terms:

Equation

The equation can thus be expanded as:

Simplification

We can rearrange to:


We can rewrite in a more compact form using the notation and :

Breaking into components

The experimental data can be broken into contributions from the transmitted channel and reflected channel :

We define the ratio between the channels to be:

Such that one can compute the two components from:

and: