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A detailed study of the ground state of the Coulomb system $(\al \al e e)$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$\al-$particles are situated along a magnetic field line) is presented. Thevariational method is employed using a trial function which includes electroniccorrelation in the form $\exp{(\gamma r_{12})}$ where $\gamma$ is a variationalparameter. It is shown that the quantum numbers of the lowest total energystate depend on the magnetic field strength. It evolves from the spin-singlet${}^1\Si_g$ metastable state at $0 \leq B \lesssim 0.85$ a.u. to a repulsivespin-triplet ${}^3\Si_u$ state for $0.85 {a.u.} \lesssim B \lesssim 1100$ a.u.and, finally, to a strongly bound spin-triplet ${}^3\Pi_u$ state at strongerfields $B \gtrsim 1100$ a.u. The lowest vibrational energy for the latter caseis calculated.Comment: 11 pages, 3 figures, 3 table

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mi>He</mml:mi><mml:mn>2</mml:mn><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math>molecular ion can exist in a magnetic field

He22+molecular ion can exist in a magnetic field