A new expansion of the Coulomb interaction

An expansion for the Coulomb 1/r12 interaction is derived which, unlike the classical multipole expansion, converges for all r1 and r2. It allows the long-range component of the total Coulomb energy of a system to be written as an infinite series involving the systemʹs multipole moments. The series is convergent if the system is of finite extent and is asymptotically convergent otherwise.