Hydrogen molecule in a magnetic field: The lowest states of the Pi manifold and the global ground state of the parallel configuration

Abstract

The electronic structure of the hydrogen molecule in a magnetic field is investigated for parallel internuclear and magnetic field axes. The lowest states of the $\Pi$ manifold are studied for spin singlet and triplet$(M_s=-1)$ as well as gerade and ungerade parity for a broad range of field strengths $0\le B\le 100a.u.$ For both states with gerade parity we observe a monotonous decrease in the dissociation energy with increasing field strength up to $B=0.1a.u.$ and metastable states with respect to the dissociation into two H atoms occur for a certain range of field strengths. For both states with ungerade parity we observe a strong increase in the dissociation energy with increasing field strength above some critical field strength $B_c$. As a major result we determine the transition field strengths for the crossings among the lowest ${}^1{\Sigma }_g$, ${}^3{\Sigma }_u$ and ${}^3{\Pi }_u$ states. The global ground state for $B\lesssim 0.18a.u.$ is the strongly bound ${}^1{\Sigma }_g$ state. The crossings of the ${}^1{\Sigma }_g$ with the ${}^3{\Sigma }_u$ and ${}^3{\Pi }_u$ state occur at $B\approx 0.18$ and $B\approx 0.39a.u.$, respectively. The transition between the ${}^3{\Sigma }_u$ and ${}^3{\Pi }_u$ state occurs at $B\approx 12.3a.u.$ Therefore, the global ground state of the hydrogen molecule for the parallel configuration is the unbound ${}^3{\Sigma }_u$ state for $0.18\lesssim B\lesssim 12.3a.u.$ The ground state for $B\gtrsim 12.3a.u.$ is the strongly bound ${}^3{\Pi }_u$ state. This result is of great relevance to the chemistry in the atmospheres of magnetic white dwarfs and neutron stars.

submitted to Physical Review A

References in corpus (2)

• The hydrogen molecule in magnetic fields: The ground states of the Sigma manifold of the parallel configuration
• Hydrogen Molecules In Superstrong Magnetic Field: II. Excitation Levels

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