Ground state of the hydrogen molecule in a strong magnetic field

The ground state of a hydrogen molecule in magnetic fields is investigated using a fully numerical Hartree-Fock approach. We found that between $4.2\times {10}^4$ T and $3\times {10}^6$ T the ground state is ${}^3{\Sigma }_u^{+}$ with very weak interaction between atoms. In this field region the hydrogen can form a superfluid phase, predicted earlier [Korolev and Liberman, Phys. Rev. Lett. 72, 270 (1994)]; the state ${}^3{\Pi }_u$ is metastable and may be responsible for the unknown excitonic line observed by Timofeev and Chernenko [JETP Lett. 61, 617 (1995)]. For magnetic fields stronger than $3\times {10}^6$ T the ground state is the tightly bound ${}^3{\Pi }_u.$