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

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 $1\sigma_g, 1\pi_u, 1\delta_{g}$areboundstatesofthe$H_3^{2+}$ exotic ion for all magnetic fields studied. We also demonstrate that for magnetic fields $B\gtrsim 2.35\times 10^{12}$Gthepotentialenergysurfacewellcorrespondingtothe$1\sigma_g$ 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.