We can then use this trick to obtain $$ \begin{equation} R(k,k') = V(k,k') +\frac{2}{\pi} \int_0^{\infty}dq \frac{q^2V(k,q)R(q,k')-k_0^2V(k,k_0)R(k_0,k') } {(k_0^2-q^2)/m}. \tag{19} \end{equation} $$ This is the equation to solve numerically in order to calculate the phase shifts. We are interested in obtaining \( R(k_0,k_0) \).