Excited states of the hydrogen molecule in magnetic fields: The triplet $\Sigma$ states of the parallel configuration

The hydrogen molecule in the presence of a homogeneous magnetic field is investigated for the parallel configuration in the complete regime of field strengths $B=0\mathrm{}-100$ a.u. Up to seven excitations are studied for gerade as well as ungerade spin triplet states of $\Sigma$ symmetry with a high accuracy. The evolution of the potential-energy curves for the individual states with increasing field strength as well as the overall behavior of the spectrum are discussed in detail. A typical feature of many potential-energy curves is the strong increase of the dissociation energy and decrease of the corresponding equilibrium internuclear distance in the high-field regime. Strong qualitative changes of the potential energies are found particularly within the regime $0.01<~B<~5$ a.u., where we observe among other things the field-dependent evolution of patterns of avoided crossings.