Without multipole expansion the Hamiltonian (charge-charge) takes the following form \frac{1}{|\Vec{r}_e-\Vec{r}_n|}. In such a case, I would not know what to adopt as the first correction to the Hamiltonian \hat{H}_0, term |\Vec{r}_e-\Vec{r}_n| is the distance of a given nucleon from a given electron and does not give us collective information about the system.