Difference between revisions of "Talk:DWBA"

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(Expansion)
(Expansion)
Line 12: Line 12:
 
</math>
 
</math>
  
==Expansion==
+
==Expansion (incorrect)==
 
'''WARNING: This incorrectly ignores the complex components.'''
 
'''WARNING: This incorrectly ignores the complex components.'''
 
===Terms===
 
===Terms===
Line 111: Line 111:
 
           + 2 \times R_i^2T_fR_f F_{-1}F_{+2}
 
           + 2 \times R_i^2T_fR_f F_{-1}F_{+2}
 
\end{align}
 
\end{align}
 +
</math>
 +
 +
==Expansion==
 +
 +
===Terms===
 +
If one expands the <math>|...|^2</math> of the DWBA, one obtains 16 terms:
 +
 +
<math>
 +
 +
\begin{matrix}
 +
          &  (T_i^* T_f^*)    &  (T_i^* R_f^*)      &  (R_i^* T_f^*)    &  (R_i^* R_f^*)    \\
 +
(T_i T_f)  &  T_i T_i^* T_f T_f^*    &  T_i^2 T_f R_f  & T_iR_iT_f^2    &  T_iR_iT_fR_f  \\
 +
(T_i R_f)  &  T_i^2T_fR_f  &  T_i^2R_f^2    &  T_iR_iT_fR_f  &  T_iR_iR_f^2  \\
 +
(R_i T_f)  &  T_iR_iT_f^2  &  T_iR_iT_fR_f  &  R_i^2T_f^2    &  R_i^2T_fR_f  \\
 +
(R_i R_f)  &  T_iR_iT_fR_f  &  T_iR_iR_f^2    &  R_i^2T_fR_f  &  R_i^2R_f^2    \\
 +
\end{matrix}
 +
 
</math>
 
</math>
  

Revision as of 18:31, 12 March 2018

DWBA Equation in thin film

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

Expansion (incorrect)

WARNING: This incorrectly ignores the complex components.

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 :

Expansion

Terms

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

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: