On the Electric-Dipole Representation in Atomic Physics

The unitary transformation that leads from the minimal-coupling description to the electric-dipole one is analysed in detail. The momentum cut-off function f(k), which is understood in the definition of such a transformation, is obtained explicitly by use of the variational method. We give an expression for f(k) in terms of the electron-density and of the mean-squared value of the electric-dipole moment of the atom in its ground state. A relevant consequence concerns the van der Waals interaction, whose long-distance behaviour turns out to be proportional to R^{-8} .