Despite of experimental effort over past few decades [1-4] the existence and lifetime of meta-stable negative hydrogen molecular ion remains controversial. We show that long-lived states of molecular hydrogen anion exist within description by nonlocal resonance model proposed in [5] if highly rotating molecule is assumed. The lifetimes are in microsecond region and are thus many orders of magnitude larger than that of resonances noticed previously [5]. Our interpretation of the states also explains the lack of detection of the ions in the experiment of Bae {et al.} [3] which was designed to produce electronically excited quartet states. The nonlocal resonance model is completely described by three functions. The potential energy V_0(R) of the neutral molecule, the potential energy V_d(R) of the diabatic anionic state and the coupling amplitude V_{d\epsilon}(R) between the anionic state and the continuum of electronic states containing one free electron with energy $\epsilon$ and the neutral molecule. The coupling V_{d\epsilon}(R) is large for small internuclear distances R (comparable to equilibrium internuclear distance in neutral H_2). The anion thus decays through an autodetachment of an electron on the time-scales of the order of 10 femtoseconds. For large R the coupling V_{d\epsilon}(R) vanishes and V_d(R) coincides with the energy of the separate atomic anion and the hydrogen atom interacting through the electrostatic polarisation force. Although the anion is stable at these larger R, the nuclei are accelerated towards each other due to attraction in the potential V_{d}(R). The potentials are modified if the molecule rotates. For a moderately large angular momentum J=23-26, the potential well well separated by a barrier from the autodetachment region is formed in V_d(R). The anionic states localised in the well can decay through the tunnelling into the autodetachment region (decay channel H_2+e^-) or the tunnelling through the outer barrier (decay channel H+H$^- --- if this channel is allowed by conservation of energy) but the lifetime is prolonged by many orders of magnitude. It is found that the position of the metastable states is well described by bound statesin outer well in adiabatic potential, but the width (lifetime) of the resonances is controlled by nonlocal dynamics, i.e. adiabatic picture is incorrect. The longest living states have lifetime 0.5 microseconds for H_2 and 14 microseconds for D_2.

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