On the Energy of a “One-Dimensional” Two-Electron Atom

Abstract

Based on the perturbation theory and variational method long known for a “three-dimensional” atom, the ground and first excited state energies are calculated for a “one-dimensional” two-electron atom in the “one-dimensional ortho-helium” configuration, which can be obtained experimentally in principle, as has been already done for a Na Bose condensate, or produced in a super strong magnetic field B ≫ (2α)²B₀ (B₀ = m²c³/eħ ≈ 4.41 × 10¹³ G). The “screening constant” σ for this atom in the ground and excited states was about 0.20 and 0.17, 0.18, respectively, depending on the relative parity PP' of the electronic states, which is somewhat smaller than in “two-dimensional” and “three-dimensional” variants (in these cases, this constant in the ground state is almost the same and about 0.3). The frequencies of the main spectral lines of a “onedimensional” He atom representing a doublet split over the relative parity PP' are found. The presence of the close lines of this doublet in the emission spectrum of magnetars at frequencies ω_{1, 2} ≈ {1.15; 1.17}α²(c/λC) (α = e²/ħc, λ_C =ħ/mc) corresponding to the “one-dimensional ortho-helium” would suggest the existence of a superstrong magnetic field in such astrophysical objects.