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documentation:standard_operators:coulomb_repulsion [2017/02/23 17:28] – Maurits W. Haverkort | documentation:standard_operators:coulomb_repulsion [2017/02/27 11:30] – Maurits W. Haverkort | ||
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NewOperator(" | NewOperator(" | ||
</ | </ | ||
- | 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, | F^{(k)}=e^2\int_0^{\infty}\int_0^{\infty}\frac{\mathrm{Min}[r_i, | ||
\end{equation} | \end{equation} | ||
- | with $0 \leq k \leq \mathrm{Min}[2l_1, | + | with $0 \leq k \leq \mathrm{Min}[2l_1, |
+ | |||
+ | 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, | G^{(k)}=e^2\int_0^{\infty}\int_0^{\infty}\frac{\mathrm{Min}[r_i, | ||
\end{equation} | \end{equation} | ||
- | with $|l_1-l_2| \leq k \leq |l_1+l_2|$. | + | with $|l_1-l_2| \leq k \leq |l_1+l_2|$ |
### | ### | ||
Line 102: | Line 104: | ||
<code Quanty Example.Quanty> | <code Quanty Example.Quanty> | ||
NewOperator(" | NewOperator(" | ||
- | \end{lstlisting} | + | </ |
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(" | OppF0pd = NewOperator(" | ||
OppF2pd = NewOperator(" | OppF2pd = NewOperator(" |