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documentation:standard_operators:coulomb_repulsion [2017/02/23 17:28] – Maurits W. Haverkortdocumentation:standard_operators:coulomb_repulsion [2017/02/27 12:40] – Maurits W. Haverkort
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 ===== Single shell ===== ===== Single shell =====
 +
 +{{:documentation:standard_operators:coulomb_diagram_ll.png?nolink|}}
  
 ### ###
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 NewOperator("U", NF, IndexUp, IndexDn, SlaterIntegrals) NewOperator("U", NF, IndexUp, IndexDn, SlaterIntegrals)
 </code> </code>
-whereby SlaterIntegrals represents a list of $F^{(k)}$ with $k$ running from $0$ to $2l$ in steps of $2$.+whereby SlaterIntegrals represents a list of $F^{(k)}$ with $k$ running from $0$ to $2l$ in steps of $2$, i.e. $k$ is even.
 ### ###
  
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 F^{(k)}=e^2\int_0^{\infty}\int_0^{\infty}\frac{\mathrm{Min}[r_i,r_j]^k}{\mathrm{Max}[r_i,r_j]^{k+1}}R_1[r_i]^2R_2[r_j]^2\mathrm{d}r_i\mathrm{d}r_j, F^{(k)}=e^2\int_0^{\infty}\int_0^{\infty}\frac{\mathrm{Min}[r_i,r_j]^k}{\mathrm{Max}[r_i,r_j]^{k+1}}R_1[r_i]^2R_2[r_j]^2\mathrm{d}r_i\mathrm{d}r_j,
 \end{equation} \end{equation}
-with $0 \leq k \leq \mathrm{Min}[2l_1,2l_2]$. The indirect term is given by the exchange integrals:+with $0 \leq k \leq \mathrm{Min}[2l_1,2l_2]$ in steps of 2, i.e. $k$ is even.  
 + 
 +The indirect term is given by the exchange integrals:
 \begin{equation} \begin{equation}
 G^{(k)}=e^2\int_0^{\infty}\int_0^{\infty}\frac{\mathrm{Min}[r_i,r_j]^k}{\mathrm{Max}[r_i,r_j]^{k+1}}R_1[r_i]R_1[r_j]R_2[r_i]R_2[r_j]\mathrm{d}r_i\mathrm{d}r_j, G^{(k)}=e^2\int_0^{\infty}\int_0^{\infty}\frac{\mathrm{Min}[r_i,r_j]^k}{\mathrm{Max}[r_i,r_j]^{k+1}}R_1[r_i]R_1[r_j]R_2[r_i]R_2[r_j]\mathrm{d}r_i\mathrm{d}r_j,
 \end{equation} \end{equation}
-with $|l_1-l_2| \leq k \leq |l_1+l_2|$.+with $|l_1-l_2| \leq k \leq |l_1+l_2|$ in steps of 2, i.e. $k$ is even if both $l_1$ and $l_2$ are even or odd and $k$ is odd if one of the angular momenta involved is even and the other is odd.
 ### ###
  
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 <code Quanty Example.Quanty> <code Quanty Example.Quanty>
 NewOperator("U", NF, IndexUp_1, IndexDn_1, IndexUp_2, IndexDn_2, Fk, Gk) NewOperator("U", NF, IndexUp_1, IndexDn_1, IndexUp_2, IndexDn_2, Fk, Gk)
-\end{lstlisting}+</code>
 For $l_1=1$ and $l_2=2$ one could define: For $l_1=1$ and $l_2=2$ one could define:
-\begin{lstlisting}+<code Quanty Example.Quanty>
 OppF0pd = NewOperator("U", NF, IndexUp_1, IndexDn_1, IndexUp_2, IndexDn_2, {1,0}, {0,0}) OppF0pd = NewOperator("U", NF, IndexUp_1, IndexDn_1, IndexUp_2, IndexDn_2, {1,0}, {0,0})
 OppF2pd = NewOperator("U", NF, IndexUp_1, IndexDn_1, IndexUp_2, IndexDn_2, {0,1}, {0,0}) OppF2pd = NewOperator("U", NF, IndexUp_1, IndexDn_1, IndexUp_2, IndexDn_2, {0,1}, {0,0})
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 OppG3pd = NewOperator("U", NF, IndexUp_1, IndexDn_1, IndexUp_2, IndexDn_2, {0,0}, {0,1}) OppG3pd = NewOperator("U", NF, IndexUp_1, IndexDn_1, IndexUp_2, IndexDn_2, {0,0}, {0,1})
 </code> </code>
 +###
 +
 +
 +===== General case of 4 different shells =====
 +###
 +
 ### ###
  

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