Using a variational method we study a sequence of the one-electron atomic and molecular-type systems H, ${\mathrm{H}}_2^{+},$ ${\mathrm{H}}_3^{2+},$ and ${\mathrm{H}}_4^{3+}$ in the presence of a homogeneous magnetic field in the range $B=0\mathrm{}–4.414\times {10}^{13}\hspace{0.5em}\mathrm{G}.$ These systems are taken as a linear configuration aligned with the magnetic lines. For ${\mathrm{H}}_3^{2+}$ the potential energy surface has a minimum for $B\sim {10}^{11}\hspace{0.5em}\mathrm{G}$ which deepens with growth of the magnetic field strength (A. Turbiner, J. C. López, and U. Solís, Pis’ma Zh. Éksp. Teor. Fiz. 69, 800 (1999) [JETP Lett. 69, 844 (1999)]); for $B\gtrsim {10}^{12}\hspace{0.5em}\mathrm{G}$ the minimum of the potential energy surface becomes sufficiently deep to have longitudinal vibrational state. We demonstrate that for the $\mathrm{}\left(\mathrm{ppppe}\right)\mathrm{}$ system the potential energy surface at $B\gtrsim 4.414\times {10}^{13}\hspace{0.5em}\mathrm{G}$ develops a minimum, indicating the possible existence of exotic molecular ion ${\mathrm{H}}_4^{3+}.$ We find that for almost all accessible magnetic fields ${\mathrm{H}}_2^{+}$ is the most bound one-electron linear system while for magnetic fields $B\gtrsim {10}^{13}\hspace{0.5em}\mathrm{G}$ the molecular ion ${\mathrm{H}}_3^{2+}$ becomes the most bound.

• Received 30 November 1999

DOI:https://doi.org/10.1103/PhysRevA.62.022510