Difference between revisions of "Talk:DWBA"

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(Expansion)
(Expansion)
Line 158: Line 158:
  
 
     & \begin{align}
 
     & \begin{align}
         = \,\, &  |T_i T_f|^2 | F_{+1} |^2 && + |T_i|^2 T_f R_f F_{+1}F_{-2}^* \\
+
         = \,\, &  |T_i T_f|^2 | F_{+1} |^2 && + |T_i|^2 T_f R_f^* F_{+1}F_{-2}^* \\
           & && + T_i R_i |T_f|^2 F_{+1}F_{+2}^* + T_i R_i T_f R_f F_{+1} F_{-1}^*  \\
+
           & && + T_i R_i^* |T_f|^2 F_{+1}F_{+2}^* + T_i R_i^* T_f R_f^* F_{+1} F_{-1}^*  \\
  
           & + |T_i R_f|^2 | F_{-2} |^2 && + |T_i|^2T_fR_f F_{+1}^* F_{-2} \\
+
           & + |T_i R_f|^2 | F_{-2} |^2 && + |T_i|^2T_f^*R_f F_{+1}^* F_{-2} \\
           & && + T_i R_i T_f R_f F_{+2}^*F_{-2} + T_i R_i |R_f|^2 F_{-1}^* F_{-2}  \\
+
           & && + T_i R_i^* T_f^* R_f F_{+2}^*F_{-2} + T_i R_i^* |R_f|^2 F_{-1}^* F_{-2}  \\
  
           & + |R_i T_f|^2 | F_{+2} |^2 && + T_i R_i |T_f|^2 F_{+1}^* F_{+2} \\
+
           & + |R_i T_f|^2 | F_{+2} |^2 && + T_i^* R_i |T_f|^2 F_{+1}^* F_{+2} \\
           & && + T_i R_i T_f R_f F_{+2}^*F_{-2} + |R_i|^2 T_f R_f F_{-1}^* F_{+2}  \\
+
           & && + T_i^* R_i T_f R_f^* F_{+2}^*F_{-2} + |R_i|^2 T_f R_f^* F_{-1}^* F_{+2}  \\
  
           & + |R_i R_f|^2 | F_{-1} |^2 && + T_i R_i T_f R_f F_{+1}^* F_{-1} \\
+
           & + |R_i R_f|^2 | F_{-1} |^2 && + T_i^* R_i T_f^* R_f F_{+1}^* F_{-1} \\
           & && + T_i R_i |R_f|^2 F_{-1}F_{-2}^* + |R_i|^2 T_f R_f F_{-1} F_{+2}^*  \\
+
           & && + T_i^* R_i |R_f|^2 F_{-1}F_{-2}^* + |R_i|^2 T_f^* R_f F_{-1} F_{+2}^*  \\
  
 
         \end{align} \\
 
         \end{align} \\

Revision as of 09:15, 13 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:




Equation

We take advantage of a more compact form using the notation and . The DWBA equation can thus be expanded as:

Simplification

We can rearrange to:

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: