Differences
This shows you the differences between two versions of the page.
Both sides previous revisionPrevious revisionNext revision | Previous revisionNext revisionBoth sides next revision | ||
documentation:standard_operators:coulomb_repulsion [2017/02/27 11:24] – Maurits W. Haverkort | documentation:standard_operators:coulomb_repulsion [2017/02/27 12:42] – Maurits W. Haverkort | ||
---|---|---|---|
Line 71: | Line 71: | ||
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. |
### | ### | ||
Line 85: | Line 85: | ||
===== Two shells, shell occupation conserving ===== | ===== Two shells, shell occupation conserving ===== | ||
+ | |||
+ | {{: | ||
### | ### | ||
Line 91: | Line 93: | ||
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 111: | Line 115: | ||
OppG3pd = NewOperator(" | OppG3pd = NewOperator(" | ||
</ | </ | ||
+ | ### | ||
+ | |||
+ | ===== General case of 4 different shells ===== | ||
+ | |||
+ | {{: | ||
+ | |||
+ | ### | ||
+ | |||
### | ### | ||