The $H_3^{+}$ molecular ion in a magnetic field in linear parallel configuration

Abstract

A first detailed study of the ground state of the H${}_3^{+}$ molecular ion in linear configuration, parallel to a magnetic field direction, and its low-lying $\Si,Π,\De$ states is carried out for magnetic fields $B=0-4.414\times 10^{13}$G in the Born-Oppenheimer approximation. The variational method is employed with a single trial function which includes electronic correlation in the form $\exp{(\ga r_{12})}$, where $\ga$ is a variational parameter. It is shown that the quantum numbers of the state of the lowest total energy (ground state) depend on the magnetic field strength. The ground state evolves from the spin-singlet ${}^1\Si_g$ state for weak magnetic fields $B\lesssim 5\times 10^8$G to a weakly-bound spin-triplet ${}^3\Si_u$ state for intermediate fields and, eventually, to a spin-triplet ${}^3{\Pi }_u$ state for $5\times 10^{10}\lesssim B\lesssim 4.414\times 10^{13}$G. Local stability of the linear parallel configuration with respect to possible small deviations is checked.

27 pages, 6 figures, 12 tables (the text expanded, several new references added, typos corrected)

References in corpus (9)

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Cited by in corpus (8)

• Charged Hydrogenic, Helium and Helium-Hydrogenic Molecular Chains in a Strong Magnetic Field
• The ground state of the ${\mathrm{H}}_3^{+}$ molecular ion: physics behind
• The $He{H}^{+}$ molecular ion in a magnetic field
• The hydrogen molecule ${\mathrm{H}}_2$ in inclined configuration in a weak magnetic field
• Finite Hydrogenic molecular chain H${}_3$ and ion H${}_2^{-}$ exist in a strong magnetic field
• A note about the ground state of the ${\mathrm{H}}_3^{+}$ hydrogen molecular ion
• The He${}_2^{+}$ molecular ion and the He${}^{-}$ atomic ion in strong magnetic fields
• ${\mathrm{H}}_2^{+}$ in a weak magnetic field