title: Convergence of the multipole expansions of the polarization and dispersion interactions for atoms under confinement.
abstract: The multipole expansion of the polarization interaction between a charged particle and an electrically neutral object has long been known to be asymptotic in nature, i.e., the multiple expansion diverges at any finite distance from the atom. However, the multipole expansion of the polarization potential of a confined hydrogen atom is shown to be absolutely convergent at a distance outside the confinement radius, R(0), of the atom. The multipole expansion of the dispersion potential between two confined hydrogen atoms is also shown to be absolutely convergent provided the two atoms satisfy R > 2R(0), where R is the inter-nuclear separation. These results were established analytically using oscillator strength sum rules and verified numerically using a B-spline description of the hydrogen ground state and its excitation spectrum.
authors.affiliation: Department of Physics, Henan Normal University, XinXiang 453007, People's Republic of China.
authors.forename: Yong-Hui
authors.initials: YH
authors.lastname: Zhang
authors.forename: Li-Yan
authors.initials: LY
authors.lastname: Tang
authors.forename: Xian-Zhou
authors.initials: XZ
authors.lastname: Zhang
authors.forename: Jun
authors.initials: J
authors.lastname: Jiang
authors.forename: J
authors.initials: J
authors.lastname: Mitroy