Electrostatic multipole contributions to the binding energy of electrons

TL;DR

This paper analyzes how electrostatic multipole moments like dipoles and quadrupoles influence the binding energy of electrons, providing a method to account for these effects in atomic systems.

Contribution

It introduces a tridiagonal representation approach to accurately incorporate multipole contributions to electron binding energies, including an effective quadrupole interaction.

Findings

Effective account of multipole effects on electron binding energy.

Application to bound states with electric dipole and quadrupole moments.

Improved understanding of electron interactions in complex atomic systems.

Abstract

The interaction of an electron with a local static charge distribution (e.g., an atom or molecule) is dominated at large distances by the radial 1/r Coulomb potential. The second order effect comes from the non-central electric dipole contribution cos(theta)/r^2. Moreover, the third order effect is due to the electric quadrupole potential, [3*cos^2(theta)-1]/2*r^3. We use the tridiagonal representation approach to give a reasonably accurate account for the combined effects of all these contributions to the binding energy of the electron but with an effective quadrupole interaction. As an application, we obtain the bound states of a valence electron in an atom with both electric dipole and quadrupole moments.