\frac{0}{0}\sum_{s_0} \int \textrm{d}r_0 \varphi^{\dagger}_{\alpha_0}(r_0,s_0)  \varphi_{\alpha_0}(r_0,s_0) \sum_{s_0} \int \textrm{d}r_0 \varphi^{\dagger}_{\alpha_0}(r_0,s_0) \varphi_{\alpha_0}(r_0,s_0) \