The electron pair density operator

We can verify that the electron pair density operator has the following coordinate representation: \[\begin{equation} \require{physics} \rho^c(\vb{r}_1, \vb{r}_2) = \frac{1}{2} \sum_{i \neq j}^N \delta(\vb{r}_1 - \vb{r}_i) \delta(\vb{r}_2 - \vb{r}_j) \thinspace , \end{equation}\] which probes the simultaneous presence of an electron at \(\vb{r}_1\) and another electron at \(\vb{r}_2\).