Confined quantum systems: dipole polarizability of the two-electron quantum dot,the hydrogen negative ion and the helium atom

Abstract

The dipole polarizabilities of the electronic ground state of three two-electronquantum systems, namely the two-electron quantum dot, the hydrogen negativeion and the helium atom, confined by an anisotropic harmonic oscillatorpotential have been studied for different confinement strengths ωby using the quantum chemical configuration interaction (CI) methodemploying a Cartesian anisotropic Gaussian basis set supplemented by aquantum-chemical standard Cartesian Gaussian basis set, respectively,and a full CI wavefunction. The dipole polarizability of the harmonicoscillator quantum dot may be calculated analytically. It is proportional tothe number of electrons, inversely proportional to the square of ω andhas no electron correlation contribution. This is valid for all states includingthe excited states. The situation is different for quantum systems witha finite nuclear charge, like the hydrogen negative ion and the heliumatom. In general the dipole polarizability of the two-electron quantumdot decreases strongly with increasing confinement strength ω, thepolarizability of the helium atom varying slowly with increasing ω,while the behaviour of the polarizability of the hydrogen negativeion lies between both. Except for the two-electron quantum doteach component of the dipole polarizability tensor, i.e. αxx, αyy andαzz,depends on the confinement along all axes. The electron correlation contributionto the dipole polarizability of the helium atom and of the hydrogen negativeion behaves differently for the different Cartesian components αzz andαxxof the tensor. The different behaviour observed for different Cartesian componentsmay be rationalized by the reduced dimensionality of the systems.