Finite Hydrogenic molecular chain H${}_3$ and ion H${}_2^{-}$ exist in a strong magnetic field

Abstract

The existence and stability of the linear hydrogenic chain H${}_3$ and H${}_2^{-}$ in a strong magnetic field is established. Variational calculations for H${}_3$ and H${}_2^{-}$ are carried out in magnetic fields in the range $10^{11}\le B\le 10^{13}$G with 17-parametric (13-parametric for H${}_2^{-}$), physically adequate trial function. Protons are assumed infinitely massive, fixed along the magnetic line. States with total spin projection $S_z=-3/2$ and magnetic quantum numbers $M=-3,-4,-5$ are studied. It is shown that for both H${}_3$ and H${}_2^{-}$ the lowest energy state corresponds to $M=-3$ in the whole range of magnetic fields studied. As for a magnetic field $B\gtrsim 10^{11}$G both H${}_3$ and H${}_2^{-}$ exist as metastable states, becoming stable for $B\ge 1.9\times 10^{11}$G and for $B\ge 2.7\times 10^{11}$G, respectively. The excited states ${}^4(-4{)}^{+}$, ${}^4(-5{)}^{+}$ of ${\mathrm{H}}_3$ and H${}_2^{-}$ appear at magnetic fields $B>7\times 10^{11}$ and $10^{12}$\,G, respectively.

arXiv comment4 pages, 1 Figure, 4 Tables, the second half of the paper rewritten, Table split into four Tables, results on first two excited states added, estimate on domain of stability H${}_4$ molecule given

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