Since \( S=0 \) yields always a zero tensor force contribution, for the combination of \( T=1 \) and then even \( l \) values, we get an attractive contribution $$ V_{\pi}(\mathbf{r})=-\frac{f_{\pi}^{2}}{4\pi m_{\pi}^{2}}\frac{e^{-m_\pi r}}{m_\pi r}. $$ With \( S=1 \) and \( T=0 \), \( l \) can only take even values in order to obey the anti-symmetry requirements and we get $$ V_{\pi}(\mathbf{r})= -\frac{f_{\pi}^{2}}{4\pi m_{\pi}^{2}} \left(1+( 1 + {3\over m_\pi r} + {3\over\left(m_\pi r\right))^2}) S_{12} (\hat r)\right) \frac{e^{-m_\pi r}}{m_\pi r}, $$ while for \( S=1 \) and \( T=1 \), \( l \) can only take odd values, resulting in a repulsive contribution $$ V_{\pi}(\mathbf{r})= \frac{1}{3}\frac{f_{\pi}^{2}}{4\pi m_{\pi}^{2}}\left(1+( 1 + {3\over m_\pi r} + {3\over\left(m_\pi r\right)^2}) S_{12} (\hat r)\right) \frac{e^{-m_\pi r}}{m_\pi r}. $$