Reactive Collisions of Electrons with H 2. cations and isotopologues : Computations and comparison with measurements

Transcription

1 Vienna Reactive Collisions of Electrons with H 2 + cations and isotopologues : Computations and comparison with measurements Ousmanou MOTAPON University of Douala, Cameroon

2 OUTLINE 1 Introduction 2 The processes 3 Theory: MQDT 4 Above threshold DR and DE of HD + and isotopologues 5 RVE/SEC of HD + and isotopologues 6 Summary

3 OUTLINE 1 Introduction 2 The processes 3 Theory: MQDT 4 Above threshold DR and DE of HD + and isotopologues 5 RVE/SEC of HD + and isotopologues 6 Summary

4 INTRODUCTION (1/3) DR and related processes are important in a variety of contexts: interstellar medium, planetary atmospheres, fusion plasma devices, plasmas of technological interest ( displays, combustion ), plasma assisted depollution, plasma of aeronautical interest (re-entry of spacecrafts), etc. Experiments have gained significantly accuracy during the recent years in

5 INTRODUCTION (2/3) Methodological developments in theory (Wave Packet Methods and MQDT) have been necessary to account for the new features observed. As well, a sustained effort has been made to get acquainted with the states, interactions and mechanisms in systems subjected to investigations.

6 INTRODUCTION (3/3) As far as the stepwise MQDT is concerned Important improvements have been brought through the description of the role of rotational couplings at low collision energy, and the consideration of two ionic thresholds in DE computations. A satisfactory agreement has been obtained between theory and experiments in the applications to benchmark H 2 + and HD + systems.

7 OUTLINE 1 Introduction 2 The processes 3 Theory: MQDT 4 Above threshold DR and DE of HD + and isotopologues 5 RVE/SEC of HD + and isotopologues 6 Summary

8 THE PROCESSES IN COMPETITION!!!

9 OUTLINE 1 Introduction 2 The processes 3 Theory: MQDT 4 Above threshold DR and DE of HD + and isotopologues 5 RVE/SEC of HD + and isotopologues 6 Summary

10 MQDT APPROACH Time independent method; Inspired from Seaton (1966), applied to molecules by Fano, Jungen, Greene. Reaction zone and different channels Applied to DR by A. Giusti-Suzor (1980); Based on the concept of channel and distinction between short and long range interaction; Unified treatment of direct and indirect mechanisms; ionization Reaction zone AB** a dissociation Dissociative excitation Simultaneous treatment of DR and competing processes.

11 Vienna MQDT STEPS :1/3

12 Vienna MQDT STEPS :2/2 :2/3 g. Cross sections evaluation

13 MQDT APPROACH Account for the Rydberg-valence interactions within all the relevant molecular symmetries In the case of rotational calculations: Simultaneous treatment of compatible symmetries => mutual assistance (Rotational couplings!!!)

14 Vienna Recent developments on Dissociative Excitation MQDT STEPS :2/2 :3/3 Extension of the theory to include ion excited state => Two ionic vibrational continua

15 Vienna Recent developments on Dissociative Excitation MQDT STEPS :2/2 :3/3 The 2 nd order K matrix associated to the new description is: The contributions to DE cross sections are: HD + Chakrabarti et al PRA 87, (2013)

16 Vienna Mechanisms: Open vs closed channels CLOSED channels Total Energy OPEN channels DR: Dissociative Recombination DE: Dissociative Excitation IC: Inelastic Collisions = ro-vibrational EXCITATION SEC: SuperElastic Collisions = ro-vibrational DE-EXCITATION

17 OUTLINE 1 Introduction 2 The processes 3 Theory: MQDT 4 Above threshold DR and DE of HD + and isotopologues 5 RVE/SEC of HD + and isotopologues 6 Summary

18 ABOVE THRESHOLD DR AND DE OF HD + : MOLECULAR DATA All S and P, gerade and ungerade, singlet and triplet, except 3 S g +, that has an unfavourable Rydberg valence interaction We consider the first five dissociative states in each symmetry. They correlate to H/D(n=1)+H/D*(m), 2 m 7 *Where H/D stand for any H isotope Chakrabarti et al PRA 87, (2013)

19 ABOVE THRESHOLD DR AND DE OF HD + : MOLECULAR DATA (MOLECULAR STATES FOR 1 S g+ ) Chakrabarti et al PRA 87, (2013)

20 ABOVE THRESHOLD DR AND DE OF HD + : MOLECULAR DATA (MOLECULAR STATES FOR 1 P g )

21 ABOVE THRESHOLD DR OF HD + : CROSS SECTIONS (THEORY VS EXPERIMENT) Chakrabarti et al PRA 87, (2013) DR cross sections from the ground state of HD + : Dashed blue (solid red) curves: second-order calculations with dissociative excitation neglected (accounted). Black dot-dashed curve: computation of Takagi. Circles: measurements of Tanabe et al. Triangles: measurements representing the Heidelberg data in Al-Khalili et al.

22 ABOVE THRESHOLD DR OF HD + : CROSS SECTIONS (COMPARISON WITH OTHER COMPUTATIONS)

23 ABOVE THRESHOLD DR OF HD + : CROSS SECTIONS (THEORY) Contribution of each pair of atomic states resulting from dissociation HD + : Relative atomic H(n) or D(n) final states yields

24 ABOVE THRESHOLD DR OF HT + : CROSS SECTIONS (THEORY) Partial contributions to the DR cross sections of HT +. Similar data are available for H 2+, HD 2+, D 2 + and DT +.

25 ABOVE THRESHOLD DR OF HD + & ISOTOPOLOGUES: CROSS SECTIONS (THEORY) DR cross sections of HD +, HT +, D 2 + and DT +, above the dissociation threshold:illustration the effect of isotopic substitution

26 DE/DR OF H 2+ : CROSS SECTIONS Chakrabarti et al 2013, Motapon et al, J.Phys. Conf.Ser. 300,

27 DE OF HD + AND D 2+ : CROSS SECTIONS (THIS WORK VS PREVIOUS COMPUTATIONS) HD + D 2 +

28 DR AND RVE/RVD OF H 2 + AND ISOTOPOMERS: WHAT CAN BE DONE NEXT? Including higher dissociative states Higher resonant states and their autoionization widths are accessible ) Computations for v i + > 0

29 OUTLINE 1 Introduction 2 The processes 3 Theory: MQDT 4 Above threshold DR and DE of HD + and isotopologues 5 RVE/SEC of HD + and isotopologues 6 Summary

30 Vienna HD + & Isotopologues Very low energy reactive collisions: STATE TO STATE ROTATIONAL TRANSITIONS AND DISSOCIATIVE RECOMBINATION

31 MOTIVATIONS Provide updated DR rate coefficients for the benchmark H 2 + ion, and isotopologues Account for the rapid rotational cooling of HD + ions and isotopologues

32 WHAT RELEVANT QUANTITIES COMPARABLE WITH EXPERIMENTS? Anisotropic rate coefficients Anisotropically convoluted cross sections Isotropic rate coefficients (for Astrophysical purpose)

33 HD + Monitoring of the time evolution of the rotational levels -> SEC rate coefficients (Shafir et al.2009)

34 NEW COMPUTATIONS VS PREVIOUS WORK Motapon, Pop, Argoubi et al.

35 NEW COMPUTATIONS VS PREVIOUS WORK Motapon, Pop, Argoubi et al.

36 NEW COMPUTATIONS VS PREVIOUS WORK Motapon, Argoubi, Pop et al.

37 NEW COMPUTATIONS VS PREVIOUS WORK Motapon, Argoubi, Pop et al.

38 NEW COMPUTATIONS VS EXPERIMENT Comparison between MQDT computations (2011), Shafir et al (2009) and Schwalm et al (2011) : Anistropic rate coefficient at near zero energy of the incident electron (in units of 10-6 cm 3 /s) computed with kt t =2.8 mev and kt l =45 mev *300 K Boltzmann average over the 11 lower rotational levels (N i+ =0 to 10) Process MQDT (2011) A. Faure (in good agreement with Shafir et al (2009) and Schwalm et al (2011)) DR* > > > > > > > > > Motapon, Argoubi, Pop et al.

39 NEW COMPUTATIONS Cross sections for the rotational transitions of H 2+, HD +, and D 2 + molecular ions by collisions with very low energy electrons, exhibiting eventual isotopic effects.

40 NEW COMPUTATIONS: VERY LOW ENERGY DR New DR cross sections of HD +, at very low electronic energy, with full consideration of rotational effects.

41 NEW COMPUTATIONS: VERY LOW ENERGY DR New DR scaled rate coefficients of HD +, at very low electronic energy, with full consideration of rotational effects.

42 OUTLINE 1 Introduction 2 The processes 3 Theory: MQDT 4 Above threshold DR and DE of HD + and isotopologues 5 RVE/SEC of HD + and isotopologues 6 Summary

43 SUMMARY Refinements in our MQDT approach code enable: Description of DE with 2 ionic cores Full rotational description (involving new processes at very low energy) Detailed analysis of the resonances Computations performed for H 2 + and HD + for DR, and RVE/RVD (IC, SEC) are in good agreement with experiments and former computations Computations performed for the DE of HD + leads to a good agreement with other theoretical approches as well as experiments Plan to extend to higher electron energies and to perform computations for all v Plan to investigate the above threshold DR and DE of of He 2 + with the 2 ionic core approach

44 THE TEAM/COLLABORATORS I. F. Schneider, K. Chakrabarti, N. Pop, F. Argoubi, M. D. Epee Epee, T. Tchakoua, D. Backodissa, J.Zs. Mezei, F. O. Waffeu Tamo, F. Lique, X. Urbain, M. Telmini, D. Schwalm, A. Wolf University of Douala, Cameroon University of Tunis, Tunisia University of Timisoara, Romania University of Le Havre, France, University of Kolkata, India UCL, Louvain la Neuve, Belgium TSR/MPIK Heidelberg, Germany

45 Vienna THANKS FOR YOUR ATTENTION