M. Cizek

Experimental Results for H2 Formation from H- and H and Implications for First Star Formation

Early Rising Hydrogen Formation of molecular hydrogen through electron-expelling collisions of H atoms and H− anions is regarded as a key step in the cooling process that led to assembly of the first stars in the early universe. Kreckel et al. (p. 69; see the Perspective by Bromm) performed highly precise laboratory measurements of the rate of this reaction at a range of different energies. The study required construction of a dedicated apparatus to carefully tune the relative velocity of merged atom and ion beams. The data validated prior theoretically calculated reaction cross sections, which were then extended for use in cosmological models. Precise measurements of molecular hydrogen formation rates help improve models of star assembly in the early universe. During the epoch of first star formation, molecular hydrogen (H2) generated via associative detachment (AD) of H− and H is believed to have been the main coolant of primordial gas for temperatures below 104 kelvin. The uncertainty in the cross section for this reaction has limited our understanding of protogalaxy formation during this epoch and of the characteristic masses and cooling times for the first stars. We report precise energy-resolved measurements of the AD reaction, made with the use of a specially constructed merged-beams apparatus. Our results agreed well with the most recent theoretically calculated cross section, which we then used in cosmological simulations to demonstrate how the reduced AD uncertainty improves constraints of the predicted masses for Population III stars.

Nuclear dynamics of the H collision complex beyond the local approximation: associative detachment and dissociative attachment to rotationally and vibrationally excited molecules

An improved nonlocal resonance model for the description of the nuclear dynamics of the H2 collision complex is developed. The model is based on the ab initio electron-H2 scattering data of Berman et al at short internuclear distances, the ab initio data of Senekowitsch et al for the bound 2 6 C state of H 2 at intermediate distances, and exhibits the correct polarization interaction at large internuclear distances. Cross sections for associative detachment (AD) and dissociative attachment (DA) to rotationally and vibrationally excited molecules were calculated for a wide range of energies and angular momenta with full inclusion of nonlocal effects. The calculated AD rate constant at 300 K is 3:8 10 9 cm 3 s 1 , which is significantly larger than the experimental value reported by Schmeltekopf et al. A series of narrow low-energy orbiting resonances was found in the AD cross section. Our results compare well with previous calculations of DA cross sections within the nonlocal resonance model. The DA cross section for vibrationally and rotationally hot H 2 (T D 1400 K) has been calculated and compared with the experimental data of Allan and Wong. It is demonstrated that the local-complex-potential approximation is an excellent approximation for the associative detachment process, whereas it fails severely for the DA process in H2.

Vibrational excitation of hydrogen fluoride by low-energy electrons: theory and experiment

Vibrational excitation (VE) of HF by low-energ ye lectrons has been investigated experimentally and theoretically. A new nonlocal resonance model has been constructed based on ab initio calculations of the coupling between a discrete state and continuum states. VE and resonant elastic cross sections have been calculated for a set of initial vibrational states of the molecular target. New high-resolution measurements of VE cross sections for the transitions v = 0 → 1, ... , 4h ave b een carried out. The calculated cross sections are in good agreement with the experimental data, indicating that the mechanisms responsible for the rich threshold structures found in the collision cross sections of HF are well understood.

Electron scattering in cooled HCl: boomerang structures and outer-well resonances in elastic and vibrational excitation cross sections

Differential cross sections for elastic scattering and excitation of the v = 1 vibrational level have been measured for rotationally cooled HCl at energies near the threshold for dissociative attachment. The cooling improves the visibility of the oscillatory structure in the v = 0 1 cross section and permits the observation of a similar structure also in the elastic channel. The integral v = 0 1 cross section and the resonant part of the integral elastic cross section have been calculated using a nonlocal resonance model. A high degree of agreement of the details of the measured and calculated structures confirms the correctness of the model and the high accuracy of the ab initio HCl- potential-energy function used as input to the model.

Associative detachment in low-energy collisions between hydrogen atoms and atomic halogen anions

Using an improved nonlocal resonance theory, total cross sections, rovibrational final state distributions and electron spectra for low-energy (<2 eV) associative detachment (AD) collisions between hydrogen atoms and negative halogen ions X- (X = F, Cl, Br) as well as deuterium atoms and F- ions have been calculated. The model involves realistic long-range interactions for the H + X- systems and takes into account the dependence of the dipole-modified threshold exponent on internuclear distance. Good agreement is found between experimental data for the total AD cross sections and the theoretical results. In the calculated electron energy spectra nonlocal effects are manifest through step structure which is (almost) independent of collision energy; this structure should therefore be observable in experiments with rather modest collision energy resolution. For illustration, electron spectra are presented which correspond to realistic experimental conditions with regard to the energy widths of the electron spectrometer and the collision energy distribution. The rovibrational final-state distributions in the HX(v, J) molecules formed are reported for a thermal kinetic energy distribution at T ≈ 300 K; for HF, DF and HCl the rotational-summed vibrational populations pv are compared with previous theoretical and experimental results.

On shooting methods for calculation of potential resonances

Two shooting methods for calculation of potential (shape) resonances are described and their efficiency tested. It is found that although both methods are based on calculation of the Siegert (i.e. exponentially increasing non-normalizable) state, the methods are stable and very accurate values of resonance energies and widths are obtainable. It is hoped that the resonance parameters obtained here can serve as test examples for various approximate methods for calculating resonance energies and widths.

MOLECULAR HYDROGEN FORMATION IN THE EARLY UNIVERSE: NEW IMPLICATIONS FROM LABORATORY MEASUREMENTS

Author Institution: Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027, USA; Charles University Prague, Faculty of Mathematics and; Physics, Institute of Theoretical Physics, 180 00 Praha 8, Czech Republic; Zentrum fur Astronomie der Universitat Heidelberg, Institut fur Theoretische Astrophysik, 69120 Heidelberg, Germany; Department of Physics/PAMO, Universite Catholique; de Louvain, Louvain-la-Neuve B-1348, Belgium

Associative detachment of H{sup -} + H {yields} H{sub 2} + e{sup -}

Using a merged-beams apparatus, we have measured the associative detachment (AD) reaction of H{sup -}+H{yields}H{sub 2}+e{sup -} for relative collision energies up to E{sub r}{ =}0.76 eV on the experimental results due to the formation of long-lived H{sub 2} resonances lying above the H+H separated atoms limit. Merging both experimental data sets, our results are in good agreement with our new theoretical calculations and confirm the prediction that this reaction essentially turns off for E{sub r}(greater-or-similar sign)2 eV. Similar behavior has been predicted for the formation of protonium from collisions of antiprotons and hydrogen atoms.