A detailed study of the ground state of the Coulomb system ( \alpha \alpha ee ) which corresponds to the He _ { 2 } ^ { 2 + } molecular ion in a magnetic field B = 0 - 4.414 \times 10 ^ { 13 } G in parallel configuration ( infinitely massive \alpha - particles are situated along a magnetic field line ) is presented .
The variational method is employed using a trial function which includes electronic correlation in the form \exp { ( \gamma r _ { 12 } ) } where \gamma is a variational parameter .
It is shown that the quantum numbers of the lowest total energy state depend on the magnetic field strength .
It evolves from the spin-singlet ^ { 1 } \Sigma _ { g } metastable state at 0 \leq B \lesssim 0.85 a.u .
to a repulsive spin-triplet ^ { 3 } \Sigma _ { u } state for 0.85 \mbox { a . u . } \lesssim B \lesssim 1100 a.u .
and , finally , to a strongly bound spin-triplet ^ { 3 } \Pi _ { u } state at stronger fields B \gtrsim 1100 a.u .