The Ion $H_3^{+}$ in a Strong Magnetic Field

A detailed study of the low-lying electronic states of the $H_3^+$ molecular ion in linear parallel configuration is carried out for $B=0-\mbox {4.414}\times 10^{13}$\,G in the Born-Oppenheimer approximation. It is shown that the ground state depends on the magnetic field strength. It evolves from the spin-singlet $^1 \Sigma_g$ for small magnetic fields $B\leq 5\times 10^{8}$\,G to the weakly-bound spin- triplet $^3\Sigma_u$ for intermediate fields and eventually to the strongly-bound spin-triplet $^3\Pi_u$ state for $5 \times 10^{10}\,$G$\leq B \leq 4.414 \times 10^{13}\,$G. For $B \geq 5 \times 10^{10}\,$G the $H_3^+$ molecular ion is stable towards all possible ionization and dissociation channels.