Using spherical harmonics for the charged interaction of particles

Question

I am currently inversitgating a system consists of positive and negative point particles satisfying charge neutrality condition. They have a unit charge +1 and -1. In most case, we deal with coulomb interaction potential energy as

$$U = \sum\limits_{i,j} \frac{q_{i}q_{j}}{r_{ij}},$$

where $r_{ij} = |\vec{r}_{i}-\vec{r}_{j}|$. The above equation just considers monopole interaction between charged particles. If I expand $\frac{1}{r_{ij}}$ in terms of spherical harmonics, do you think the spherical harmonics consider multipolar interaction such as dipole and quadrupole between charged particles?

Answer 1

No. Point particles are electric monopoles, so you don’t consider higher order multiples.

A dipole field defines a direction, and a direction cannot be associated with a point scalar particle.

Now you can say the point has a spin 1/2; but still and electric dipole moment (EDM) violates parity, as it flips sign under reflection while a spin does not.

A vector particle defines a direction, but an EDM violates time reversal …EDM is even, angular momentum is odd.

An electric quadrupole moment is OK, as in the deuteron.

Spin ofc demand a magnetic dipole moment.