The connection between the momentum- and position space angular momentum projected potentials are then given, $$ V_{lm, l'm'}(k,k')=\frac{2}{\pi}i^{l'-l}\int_0^\infty drr^2 \int_0^\infty dr'{r'}^2j_l(kr) V_{lm,l'm'}(r,r') j_{l'}(k'r') \tag{6} $$ which is known as a double Fourier-Bessel transform. The position space angular momentum projected potential is given by $$ V_{lm, l'm'}(r,r') = \int d{\hat{r}} \int d{\hat{r}'}Y_{lm}^*(\hat{r})V(\mathbf{r}, \mathbf{r'})Y_{l'm'}(\hat{r}'). \tag{7} $$