and equation (6) reduces to $$ \begin{equation} V_{lm, l'm'}(k,k') = \frac{2}{\pi}i^{l' -l}\int_0^\infty drr^2j_l(kr) V_{lm,l'm'}(r) j_{l'}(k'r) \tag{9} \end{equation} $$ where $$ \begin{equation} V_{lm, l'm'}(r) = \int d{\hat{r}}Y_{lm}^*(\hat{r})V(\mathbf{r})Y_{l'm'}(\hat{r}), \tag{10} \end{equation} $$