Using a variational method we study a sequence of the one-electron atomic and molecular-type systems H , H _ { 2 } ^ { + } , H _ { 3 } ^ { ( 2 + ) } and H _ { 4 } ^ { ( 3 + ) } in the presence of a homogeneous magnetic field ranging B = 0 - 4.414 \times 10 ^ { 13 } G .
These systems are taken as a linear configuration aligned with the magnetic lines .
For H _ { 3 } ^ { ( 2 + ) } the potential energy surface has a minimum for B \sim 10 ^ { 11 } G which deepens with growth of the magnetic field strength ( JETP Lett . 69 , 844 ( 1999 ) ) ; for B \gtrsim 10 ^ { 12 } G the minimum of the potential energy surface becomes sufficiently deep to have longitudinal vibrational state .
We demonstrate that for the ( ppppe ) system the potential energy surface at B \gtrsim 4.414 \times 10 ^ { 13 } G develops a minimum , indicating the possible existence of exotic molecular ion H _ { 4 } ^ { ( 3 + ) } .
We find that for almost all accessible magnetic fields H _ { 2 } ^ { + } is the most bound one-electron linear system while for magnetic fields B \gtrsim 10 ^ { 13 } G the molecular ion H _ { 3 } ^ { ( 2 + ) } becomes the most bound .