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documentation:standard_operators:coulomb_repulsion [2017/02/27 11:24] – Maurits W. Haverkortdocumentation:standard_operators:coulomb_repulsion [2017/02/27 11:28] – Maurits W. Haverkort
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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.  
 + 
 +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.
 ### ###
  

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