Mean lifetime of the bound 2pσ state of ${\mathrm{HeH}}^{2+}$

Recently, experimental evidence for the existence of a bound state of the ${\mathrm{HeH}}^{2+}$ molecular ion was reported by Ben-Itzhak, Gertner, Heber, and Rosner [Phys. Rev. Lett. 71, 1347 (1993)]. This three-body system was predicted by Bates and Carson to have bound vibrational states in the 2pσ electronic state despite the strong repulsion potential between the two nuclei. These 2pσ vibrational states decay via an electronic transition to the 1sσ repulsive ground state with a mean lifetime of about 1 nsec. We have used the ‘‘fragment-fragment’’ coincidence method to measure the mean lifetime of the ${\mathrm{HeH}}^{2+}$ molecular ions which dissociate in flight before reaching the detector. The yield of these molecular ions was measured as a function of the distance between the target cell and the analyzer exit. From this measurement a mean lifetime of 3.9±0.4 nsec was determined. The 2pσ→1sσ transition rates for all vibrational states have been calculated within the Born-Oppenheimer approximation using available oscillator strengths. It is shown that the transition rates decrease with increasing vibrational energy because of the ‘‘stretch’’ of the molecular ion. The distribution of 2pσ vibrational states populated by vertical transitions from stripping the ${\mathrm{HeH}}^{+}$ electronic ground state was evaluated, and the resulting decay curve compares well with the measured one.