The hydrogen molecule ${\mathrm{H}}_2$ in inclined configuration in a weak magnetic field

Abstract

Highly accurate variational calculations, based on a few-parameter, physically adequate trial function, are carried out for the hydrogen molecule \hh in inclined configuration, where the molecular axis forms an angle $\theta$ with respect to the direction of a uniform constant magnetic field $\mathbf{B}$, for $B=0,0.1,0.175$ and $0.2$a.u. Three inclinations $\theta =0^{\circ },45^{\circ },90^{\circ }$ are studied in detail with emphasis to the ground state $1_g$. Diamagnetic and paramagnetic susceptibilities are calculated (for $\theta =45^{\circ }$ for the first time), they are in agreement with the experimental data and with other calculations. For $B=0,0.1$ and $0.2$a.u. potential energy curves $E$ vs $R$ are built for each inclination, they are interpolated by simple, two-point Padé approximant $Pade[2/6](R)$ with accuracy of not less than 4 significant digits. Spectra of rovibrational states are calculated for the first time. It was found that the optimal configuration of the ground state for $B\le B_{cr}=0.178$a.u. corresponds always to the parallel configuration, $\theta =0$, thus, it is a ${}^1{\Sigma }_g$ state. The state $1_g$ remains bound for any magnetic field, becoming metastable for $B>B_{cr}$, while for $B_{cr}<B<12$\,a.u. the ground state corresponds to two isolated hydrogen atoms with parallel spins.

arXiv comment31 pages, 11 Tables, 7 Figures (2 new), following referee's suggestions parts 4,5,6 essentially rewritten, to be published at Journal of Quantitative Spectroscopy and Radiative Transfer

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Cited by in corpus (1)

• The molecule ${\mathrm{H}}_2$ in a strong magnetic field revisited