Abstract
The interaction of an electron with a local static charge distribution (e.g., an atom or molecule) is dominated by the radial 1/r Coulomb potential at large distances. The second-order effect is generated by the non-central electric dipole contribution cosθ/r2. The third-order effect is attributed to the electric quadrupole potential (3cos2θ-1)/2r3. In this study, we used the tridiagonal representation approach to produce a reasonably accurate account for the combined effects of every contribution to the binding energy of the electron with an effective quadrupole interaction. As a result, we obtained the bound states of a valence electron in an atom with both electric dipole and quadrupole moments.
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