PHYSICAL REVIEW A 96, 032512 (2017) Spontaneous dissociation and rovibrational structure of the metastable D 2 - anion Ferid Mezdari, 1 , * Nathalie de Ruette, 2 and Xavier Urbain 3 1 Department of Physics, Faculty of Sciences, University of Gabès, 6029 Gabès, Tunisia 2 Department of Physics, Stockholm University, SE-106 91 Stockholm, Sweden 3 Institute of Condensed Matter and Nanosciences, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium (Received 17 August 2017; published 29 September 2017) Long-lived rovibrational states of the metastable D 2 − molecular anion, with lifetimes of the order of microseconds, were studied by recording the time-of-flight difference between D and D − fragments produced by spontaneous dissociation of the D 2 − complex. The simulated time-of-flight spectrum was adjusted to the experimental results, allowing us to extract the resonance energy relative to the dissociation threshold. A single value was found, 22.8 ± 0.3 meV, which is somewhat larger than resonance energies predicted by theory for long-lived D 2 − rovibrational states with (J,v) quantum numbers (37,0), (37,1), and (38,0) [Phys. Rev. A 75, 012507 (2007)]. This discrepancy seems due to the extreme sensitivity of these metastable states to minute features of the potential energy curve. The spectral feature is explained by the competition between autodetachment and spontaneous dissociation decay channels. DOI: 10.1103/PhysRevA.96.032512 I. INTRODUCTION The molecular hydrogen anion is of major theoretical interest as a benchmark to develop models and basis sets for highly correlated, few electron systems. This fundamental negative ion, considered as a collisional system, contributes to the ion chemistry of many astrophysical environments and controlled thermonuclear fusion plasmas. Electron-induced vibrational excitation of H 2 , and dis- sociative electron attachment, i.e., H 2 + e − → H + H − , are mediated by the resonant electron capture to the ground X 2  + u and excited A 2  + g states of H 2 − [1]. The large autodetachment width of those resonances embedded in the electronic continuum, together with the unfavorable Franck- Condon overlap, are responsible for the extreme vibrational and isotopic sensitivity of dissociative attachment [2,3]. The reverse process, associative detachment, i.e., H + H − → H 2 + e − , was recognized as a key formation mecha- nism of ground state molecular hydrogen in the early Universe [4]. The actual shape of the cross section versus collision energy reflects the details of the H 2 − potential energy curve, in particular the presence of a short-range barrier, and the growing influence of the long-range centrifugal barrier with increasing collision energy [2,5]. The existence, structure, and lifetime of the molecular hydrogen anions was, for a long time, a matter of debate, both experimentally and theoretically. Since 1975, mass- spectrometric observations claim the existence of H 2 − ,D 2 − and HD − with lifetimes greater than 10 −5 s[6], although mass-spectrometric detection of H 2 − was already reported in 1958 [7], and again in 1974 [8]. Later on, Bae et al. [9] concluded, after an unsuccessful attempt to produce H 2 − by a two-step electron capture technique, to the nonexistence of the metastable H 2 − complex. After several years of continued experimental effort, the existence of long-lived molecular hydrogen anions was definitely established [10,11] by accelerator mass spectrometry. * feridmez@yahoo.fr These anionic species are produced either by sputtering TiH 2 and TiD 2 with Cs + , or in a discharge ion source. To increase the production yield of H 2 − in a high-voltage corona-discharge source coupled to a supersonic jet, Rudnev et al. [12] used acetylene gas mixed in N 2 and CO 2 instead of pure hydrogen. Whether the mode of production affects the population of the rovibrational levels of H 2 − is still to be investigated. Lifetimes have been measured for all of three isotopologues H 2 − ,D 2 − , and HD − , using an electrostatic ion-beam trap [13]. The measured lifetimes of H 2 − and HD − were 8.2 and 50.7 μs, respectively. For D 2 − , three decay time constants were measured, i.e., 23, 84, and 1890 μs. Rovibrational states of H 2 − and D 2 − were also studied in coincidence photofragmentation experiments [14], as well as in foil- induced Coulomb explosion imaging measurements [15,16]. The photodetachment cross section of the H 2 − anion was measured by beam depletion in a narrow wavelength range [12]. An unexpected oscillatory behavior of the depletion cross section was observed, which was tentatively ascribed to the rotating dipole of the fast-spinning molecule. Theoretical calculations [2,17–19] for the description of the nuclear dynamics of H 2 − collision complex and its isotopic analogues, D 2 − , HD − , and T 2 − were performed within a nonlocal resonance model. The resonances in the X 2  + u electronic state of H 2 − are stabilized against autodetachment by molecular rotation at high angular momenta [19], causing the potential energy minimum of the H 2 − ground state to lie outside of the potential well of H 2 (see Fig. 7). The metastability of these molecular complexes against dissoci- ation is assigned [10] to the existence of a wide centrifugal barrier. Cízek and Horácek [19] computed the lifetimes and resonance energies relative to the dissociation threshold of several rovibrational states of H 2 − ,D 2 − , HD − , and T − 2 molecular complexes. The lifetimes and corresponding energy levels obtained for D 2 − are 61, 16, and 2108 μs and 2, 18, and 19 meV, for (J,v) = (37,0), (37,1), and (38,0) rovibrational states, respectively. These strongly differ from those obtained earlier by R. Golser et al. [10], i.e., 14 and 7.2 μs, for the (37,0) and (38,0) states, respectively. 2469-9926/2017/96(3)/032512(6) 032512-1 ©2017 American Physical Society