Electric dipole operator ($\mathbf{d}={\sum }_a{q}_a{\mathbf{r}}_a$)

The electric dipole operator is the charge-weighted position operator of a system. It is odd under parity and transforms as a rank-one spherical tensor operator. In the nonrelativistic electric-dipole approximation it acts on spatial coordinates without directly changing spin, explaining the parity, angular-momentum and approximate spin selection rules.