HYDROGEN MOLECULE IN A MAGNETIC-FIELD - THE LOWEST STATES OF THE PI-MANIFOLD AND THE GLOBAL GROUND-STATE OF THE PARALLEL CONFIGURATION

The electronic structure of the hydrogen molecule in a magnetic field is investigated for parallel internuclear and magnetic field axes. The lowest states of the Pi manifold are studied for spin singlet and tri plet (M-s = -1) as well as gerade and ungerade parity for a broad rang e of field strengths 0 less than or equal to B less than or equal to 1 00 a.u. For both states with gerade parity we observe a monotonic decr ease in the dissociation energy with increasing field strength up to B = 0.1 a.u. and metastable states with respect to the dissociation int o two H atoms occur for a certain range of field strengths. For both s tates with ungerade parity we observe a strong increase in the dissoci ation energy with increasing field strength above some critical field strength B-c. As a major result we determine the transition field stre ngths for the dressings among the lowest (1) Sigma(g), (3) Sigma(u), a nd (3) Pi(u) states. The global ground state for B less than or simila r to 0.18 a.u. is the strongly bound (1) Sigma(g) state. The crossings of the (1) Sigma(g), (3) Sigma(u), (3) Pi(u) state occur at B approxi mate to 0.18 and B approximate to 0.39 a.u., respectively. The transit ion between the (3) Sigma(u) and the (3) Pi(u) state occurs at B appro ximate to 12.3 a.u. Therefore, the global ground state of the hydrogen molecule for the parallel configuration is the unbound (3) Sigma(u) s tate for 0.18 less than or similar to B less than or similar to 12.3 a .u. The ground state for B greater than or similar to 12.3 a.u. is the strongly bound (3) Pi(u) state. This result is of great relevance to the chemistry in the atmospheres of magnetic white dwarfs and neutron stars.