The exotic $H_3^{2+}$ ion in a strong magnetic field. Linear configuration

Abstract

An accurate study of the lowest $1{\sigma }_g$ and the low-lying excited $1{\sigma }_u$, $1{\pi }_{u,g}$, $1{\delta }_{g,u}$ electronic states of the exotic molecular ion $H_3^{2+}$ in linear configuration parallel to a magnetic field is carried out. The magnetic field ranges from $10^{10}$ G up to $4.414\times 10^{13}$ G where non-relativistic considerations are justified. The variational method is exploited and the {\it same} trial function is used for different magnetic fields. It is shown that the states of positive $z$-parity $1{\sigma }_g,1{\pi }_u,1{\delta }_g$ are bound states of the $H_3^{2+}$ exotic ion for all magnetic fields studied. We also demonstrate that for magnetic fields $B\gtrsim 2.35\times 10^{12}$ G the potential energy surface well corresponding to the $1{\sigma }_g$ state contains at least one longitudinal vibrational state. It is also shown that the negative $z$-parity states $1{\sigma }_u,1{\pi }_g,1{\delta }_u$, are purely repulsive in the whole range of magnetic fields studied, $B=10^{10}-4.414\times 10^{13}$ G.

26 pages, 6 figures, 4 tables