Energy and Screening Constants of a One-Dimensional Helium Atom in Excited States

Abstract

In analogy with earlier calculations by the authors of screening constants and the energy of the ordinary threedimensional helium atom, this same program has now been used for the first time for the one-dimensional atom. For one of the electrons with energy quantum number n′ = 1, found in the ground state, and for the second electron with quantum number n = 2,3,...9 , found in an excited state, we find that in this range the screening constant σn falls monotonically with growth of n, tending to zero in the formal limit n → ∞ , and the absolute value of the energy En in this limit tends to a constant value in complete analogy with the threedimensional atom. Results of numerical calculations of σn and |En| in this range are presented in the form of tables and graphs. The conclusions of this work can in principle be verified since, for example, onedimensional Na atoms in the Bose condensate phase were previously obtained experimentally, and it appears to be entirely possible to also obtain one-dimensional He atoms.