On the Electric-Dipole Representation in Atomic Physics

TL;DR

This paper analyzes the unitary transformation from minimal-coupling to electric-dipole representation in atomic physics, deriving an explicit momentum cut-off function and exploring implications for van der Waals interactions.

Contribution

It provides a detailed analysis of the transformation, explicitly derives the cut-off function using variational methods, and links it to atomic properties and van der Waals forces.

Findings

Explicit expression for the momentum cut-off function f(k)

Long-distance van der Waals interaction proportional to R^{-8}

Connection between atomic properties and interaction behavior

Abstract

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} .