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| Both sides previous revisionPrevious revision | Next revisionBoth sides next revision | ||
| documentation:standard_operators:coulomb_repulsion [2017/02/27 11:28] – 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. |
| ### | ### | ||
| Line 91: | Line 91: | ||
| 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: | The indirect term is given by the exchange integrals: | ||
| Line 97: | Line 97: | ||
| 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 $|l_1-l_2| \leq k \leq |l_1+l_2|$ in steps of 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. |
| ### | ### | ||
