Differences

This shows you the differences between two versions of the page.

--- documentation:standard_operators:coulomb_repulsion [2017/02/27 11:24] – Maurits W. Haverkort
+++ documentation:standard_operators:coulomb_repulsion [2017/02/27 11:30] – Maurits W. Haverkort
@@ Line 71: / Line 71: @@
 NewOperator("U", NF, IndexUp, IndexDn, SlaterIntegrals)
 </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.
 ###
@@ Line 91: / Line 91: @@
 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}
-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}
 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}
-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.
 ###