Tvorba molekul H 2 sr áž kou H + H - a jejich v ý znam pro vznik prvn í ch hv ě zd

1. Tvorba molekul H2 srážkou H + H- a jejich význam pro vznik prvních hvězd Martin Čížek, Jiří Horáček, Přemysl Kolorenč, Karel Houfek Jiří Eliášek, Martin Formánek, Martin Váňa, … • úvod do problematiky • přehled jevů e+H2 • přehled jevů H+H- • nesouhlas s experimentem a nové měření pro AD • význam pro fyziku raného vesmíru • více o teorii

2. 1meV 10meV 0.1eV 1eV 10eV 100eV rotational excitation J=1,2,… E=15meV,… - H2 vibrational excitation v=1,2,… E=0.5eV,… ion-atom channel H-+ HE=3.7eV dissociated H + H + e-E=4.5eV+e vertical The most fundamental system of electron-molecule collision physics: e- + H2 ground state ( , J=0,v=0) E=0+e electronic excitation e- + H2E=… ionization, …

3. Born-Oppenheimer approximation picture The same states once more in different view H+ H + e- State energy [eV] H-+ H Proton-proton distance [Bohr]

4. DA - AD H2 e- + H2 * Processes at low energy e- + H2 H- + H CT VE etc D CD H+ H- e- + H + H Dissociative attachment (DA) Dissociation by electron impact (D) Associative detachment (AD) Charge transfer (CT) Vibrational, rotational and electronic excitation (VE, etc)

5. Electron molecule collisions H2+e- Čížek, Horáček, Domcke:J.Phys.B 1998

6. Wigner casps Examples: complete cross sections for e+HBr e- + HBr (v=0) Boomerang oscillations Threshold peak → e- + HBr Cross section [Å2] → e- + HBr (v’=1) v’=2 v’=3 v’=4 v’=5 → H+ Br- v’=6 Electron energy [eV]

7. Associative detachment in H+H- H- + H → e- + H2 Čížek, Horáček, Domcke:J.Phys.B 1998

8. 10% 0.3meV D + D-→ D2 + e- H2-

9. The Origin of theResonances Potentials for J=0 Potential Vad(R) for nonzero J

10. H2-

11. Elastic cross section for e- + H2 (J=21, v=2)

12. Elastická srážka e- + H2 (J=25, v=1) H2-

13. Γ0=2.7×10-9eV Γ1=1.9×10-6eV

14. Záporný ion molekuly vodíku - shrnutí • 1965-1975 pozorování H2- vyletujících z plazmatu (Demkov, Hurley, Aberth, a další) • 1984 Bae, existence H2- a D2- zpochybněna (možná záměna s D-, typické doby života 10-15-10-13s) • 2005-2006, Golser a kol. pozorování H2- a D2- v hmotnostních spektrech (jasné rozlišení D- a H2-). R. Golser, H. Gnaser, W. Kutschera, A. Priller, P. Steier, A. Wallner, M. Čížek, J. Horáček and W. Domcke. Phys. Rev. Lett.94 (2005) 223003 10-6 H2-

15. Záporný ion molekuly vodíku - shrnutí • 2006-7 naměřené doby života (Heber a kol. – „storage ring“) souhlasí s našimy výpočty M. Čížek, J. Horáček and W. Domcke, Phys. Rev. A, 75 (2007) 012507, 1-7. • 2009 „Coulomb explosion imaging“ potvrzuje přímo velká J H2-

16. Associative detachment in H+H- H- + H → e- + H2 Čížek, Horáček, Domcke:J.Phys.B 1998

17. Examples: complete cross sections for H+Cl- H + Cl-→HCl(J,v) + e-

18. Examples: cross sections for H+H- at J=23

19. AD: H- + H → e- + H2, review of data before 2010reaction rates collected by D.W.Savin 2006 1967 1967-9 1979 1989 1991 1998

20. Asymptotic behavior of H+H- interaction Quantum chemistry (Senekowitsch et al. 1984) much more attractive then the asymptotic formula (which is OK for R>15)

21. AD: H- + H → e- + H2, review of data before 2006

22. First stars

23. Significance for early Universe chemistry Simplified model for gas chemistry and hydrodynamics: γ, e-, H+, H, H-, H2+, H2 first molecules in the universe ! cooling medium in formation of first stars

24. Hlavní reakce pro rovnovážné hustoty molekulárního vodíku: H + e-→ H- + γ H + H-→ H2 + e- H + H+→ H2+ + γ H + H2+→ H2 + H+ H2+ + e-→ H + H H+ + H2→ H2+ + H H + e-← H- + γ H+ + H-→ H + H First stars

25. Úloha molekulárního vodíku při chladnutí kolabujícího vodíkového plynu: ¨ nH2/nH=2.10-6 nH2/nH=2.10-4 First stars

26. Vliv neurčitosti reakční rychlosti na kolaps plynového oblaku First stars

27. Vliv neurčitosti reakční rychlosti na kolaps plynového oblaku First stars

28. Asociative detachment experiment H. Kreckel, H. Bruhns, A. Miller, D. W. Savin Columbia Astrophysical Laboratory, Columbia University, New York 456 LASER-diodes AD experiment

29. H. Kreckel, H. Bruhns, M. Čížek, S. C. O. Glover, K. A. Miller, X. Urbain, D.W.Savin Science, vol.328 iss.5987 (2010) 69-71+ online suplement AD experiment

30. Důsledky pro simulace tvorby hvězd Např: Neurčitost v charakteristické hmotnosti vznikajících hvězd se zmenšila z faktoru 20 na faktor 2

31. Důsledky nového měření pro znalost rychclostní konstanty Kreckel, Bruhns, Čížek, Glover, Miller, Urbain, Savin: Science 2010 Martinez, Yang, Betts, Snow, Bierbaum 2009 Astrophys. J.705,L172 University of Colorado, Boulder AD experiment

32. Possible source of error in normalization of flowing afterglow results ? Densities of H in the flowing afterglow are determined from measured rate [J. Chem. Phys. 60, 5086 (1974)] of the reaction Cl- + H → HCl + e- which is in disagreement with theory by factor of 1.6 [K. Houfek et al. Phys. Rev. A 66, 062702 (2002)] Call for new absolute measurement!

33. Nontrivial quantum effects? Opening of H+H+e- channel

34. Impact of the second discrete state Eliášek, Čížek, preliminary results

35. Impact of metastable states (orbiting resonances) H- + H → e- + H2(v,J) State energy [eV] ← H-+ H Proton-proton distance [Bohr]

36. Final cross section K. A. Miller, H. Bruhns, M. Čížek, J. Eliášek, H. Kreckel, X. Urbain, and D. W. Savin: Phys. Rev. A in press

37. Final cross section – logarithmic scale K. A. Miller, H. Bruhns, M. Čížek, J. Eliášek, H. Kreckel, X. Urbain, and D. W. Savin: submitted to Phys. Rev. A

38. Few details on theory

39. Historical development • Idea of discrete state in continuum old – substantiated by Feshbach (1958, 1962) and Fano (1961). • Application to molecular processes by Chen (1966), O’Malley (1966), Bardsley (1968), Nakamura (1971). • Role of diabaticity of the basis discussed in particular by O’Malley (1971); key role of the nonlocal term for threshold effects – Bardsley (1968) • Treatment of the nonlocal dynamics substantiated by Domcke and Cederbaum in 80’s, analysis of the fixed-R analytic structure of the model by Domcke. • Domcke (1991) Phys.Rep. – review • 90’s Horáček, Domcke: numerical methods for realistic models • Other similar approaches: single-pole approximation of R-matrix (Fabrikant), effective range expansion (Gauyacq)

40. Main idea: crossing of diabatic states Vd(R) V0(R) +  Vad(R)

41. Diabaticity of the basis Houfek et al. 2008, Phys. Rev. A 77, 012710

42. Illustration using simple two-dimensional model • Motivation for such a model • it is not easy to obtain exact results for real systems(even for e + H2, actually quite difficult system) • validity of approximate methods is usually testified if calculated cross sections agree (more or less) with experimental ones, but experiments are not always available – like for radicals, or high vibrational levels Model Hamiltonian – one nuclear (R) and one electronic (r) degree of freedom incoming electron vibrational motion - potential energy of the neutral molecule- Morse potential - angular momentum of the electron- p-wave (l = 1) or d-wave (l = 2) - interaction potential- bound state of the electron for large R- resonance for small R Barrier for incoming electron → shape resonance for small R Houfek, Rescigno, McCurdy, Phys. Rev. A 73 (2006) 032721Houfek, Rescigno, McCurdy, Phys. Rev. A 77 (2008) 012710

43. Diabaticity of the basis Houfek et al. 2008, Phys. Rev. A 77, 012710: Nonlocal resonance calculation essentially exact (with proper choice of discrete state)

44. Theory: expansion of Hamiltonian

45. Theory: alternative formulations • (Integro-)Differential equation ( + boundary conditions) • Integral equation • Time-dependent formulation

46. Theory: integral equation formulation A+B-: e+AB:

47. Theory: integral equation formulation Effective potential: Nonlocal, energy-dependent, nonhermitian

48. Theory: integral equation formulation Vibrational excitation: e+AB(vi) → e+AB(vf) + background scattering (adiabatic nuclei approximation) Dissociative electron attachment: e+AB(vi) → A + B- Associative detachment: A + B-→ e + AB(vi)

49. Theory: differential equation formulation

50. Theory: time-dependent formulation Memory kernel: Source term: