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H2+ ion in a strong magnetic field: Lowest gerade and ungerade electronic states

A. V. Turbiner·J. C. Lopez V.·A. Flores-Riveros
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Abstract

In the framework of a variational method with a single trial function an accurate study of the lowest gerade 1g and ungerade 1u electronic states of the molecular ion $H_2^+$ in a magnetic field is performed. Magnetic field ranges from 0 to 4.414x10^13 G and orientations of the molecular axis with respect to the magnetic line 0 \leq theta \leq 90 are considered. A one-parameter gauge dependent vector potential is used in the Hamiltonian, which is finally variationally optimized. A well pronounced minimum on the total energy surface of the (ppe) system in both 1g and 1u states is found for all magnetic fields and orientations studied. It is shown that for both states the parallel configuration (theta=0) at equilibrium always corresponds to the minimal total energy. It is found that for a given theta for both states the magnetic field growth is always accompanied by an increase in the total and binding energies as well as a shrinking of the equilibrium distance. We demonstrate that for B\gtrsim 1.8x10^11 G the molecular ion can dissociate, H2+ -> H + p, over a certain range of orientations (theta_cr \le theta \le 90), where the minimal thetaa_cr \simeq 25 occurs for the strongest magnetic field studied, B=4.414x10^13 G. For B<10^12 G the ion H2+ in 1g, 1u states is the most compact, being in the perpendicular configuration (theta=90), whereas for B\gtrsim 10^12 this occurs for an angle < 90. For the 1g state in any orientation, with the magnetic field growth at B \sim 10^11 G, a two-peak electronic distribution changes to single-peak one.

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A. V. Turbiner, J. C. Lopez V., A. Flores-Riveros. 2002-01-11. H2+ ion in a strong magnetic field: Lowest gerade and ungerade electronic states. https://arxiv.org/abs/astro-ph/0107596

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