Negative molecular ion in a strong DC field

We study the simplest model of a negative molecular ion, i.e., two attractive 3D zero-range potentials (ZRP) separated by a distance $R$, in a static electric (DC) field ${\bf F}$. For this model, both the Green function and the equation for its poles (resonances) are expressed in terms of Airy functions. For a weak field $F$, we obtain simple analytical expressions for the decay rate and polarizability for an arbitrary orientation of ${\bf F}$ with respect to the molecular axis. We also present large scale calculations of the Stark-shift and decay rate as functions of $R$ and $F$. Our analyses show that decay rates are largest if the molecular axis is orthogonal to ${\bf F}$. The poles of the Green function as functions of $F$ are found numerically to include not only those for the quasistationary states but also an infinite number of broad resonances which merge to a continuum when $F$ tends to zero (as found previously for 1D [1] and 2D [2] two ZRP models). We also analyze the complex quasienergies of molecular ions in a low-frequency AC field using an adiabatic approximation [3]. [1] H.J. Korsch and S. Mossmann, J. Phys. A {\bf 36}, 2139 (2003); [2] G. Alvarez and B. Sundaram, Phys. Rev A 68, 013407 (2003); [3] B.Borca et al., J. Phys. B {\bf 34}, L579 (2001).