Long-lived anionic states of ${\mathrm{H}}_2$, HD, ${\mathrm{D}}_2$, and ${\mathrm{T}}_2$

A detailed investigation of the long-lived states of the hydrogen molecule anion has been performed within the ab initio–based nonlocal resonance model. The resonances in the $X{}^2\Sigma _u^{+}$ electronic state of $\mathrm{H}_2{}^{-}$ are stabilized against autodetachment by molecular rotation and can be interpreted as orbiting states of $\mathrm{H}+{\mathrm{H}}^{-}$ with high angular momenta $(J=22-27)$. The lifetimes and energies of all long-lived states have been calculated for the hydrogen molecular anion and its isotopic analogs. Recent experimental values of Heber et al. [Phys. Rev. A 73, 060501(R) (2006)] for lifetimes of $\mathrm{H}_2{}^{-}$, $\mathrm{H}{\mathrm{D}}^{-}$, and $\mathrm{D}_2{}^{-}$ can be explained within the model. For $\mathrm{T}_2{}^{-}$, we predict a large number of states with lifetimes up to $\sim 0.1\mathrm{s}$.

Figure 1

(Color online) Potential-energy curves [including the centrifugal term $J(J+1)∕2\mu R^2$] for angular momentum $J=0$ (left) and 20,24,27 (right). The area above $V_0\left(R\right)$ (electron continuum) is shaded. $V_{\mathrm{LCP}}\left(R\right)$ corresponds to the energy of the (electronically) bound state (solid line) or to the pole of $K$ matrix (dotted line).

Figure 2

(Color online) Decomposition of $V_{\mathrm{LCP}}$ into $W_0$ (dashed line with shaded well) and $W_I$ (solid line). The autodetachment region (decay into the electron continuum) is indicated by the dark shaded area.

Figure 3

Summary of the energies and decay widths and lifetimes of narrow resonances in $\mathrm{H}_2{}^{-}$ and $\mathrm{H}{\mathrm{D}}^{-}$. Energies are given relative to the $\mathrm{H}+{\mathrm{H}}^{-}$ threshold. The resonances with high dissociation rates are encircled.

Figure 4

Summary of the energies and decay widths and lifetimes of narrow resonances in $\mathrm{D}_2{}^{-}$ and $\mathrm{T}_2{}^{-}$. The resonances with high dissociation rates are encircled.