Max-Planck-Institut für Plasmaphysik CRP on ‘Atomic and Molecular Data for Plasma Modelling’, IAEA, Vienna26-28 September 2005 Compilation and Extension of a Database for Systematic Studies on Diatomic Molecules Ursel Fantz and Dirk Wünderlich  Franck-Condon factors, transition probabilities  Vibrational population  Collisional radiative and dissociation modelling  Rate coefficients TraDiMo Yacora IPProg Examples for molecular hydrogen and hydrocarbons Future applications to CH, BH, BeH and its hydrogen isotopomeres, C 2

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Transitions of Diatomic Molecules: TraDiMo TraDiMo bound-bound and bound-free transitions TraDiMo bound-bound and bound-free transitions Vibrational energies Franck-Condon factors Transition probabilities Isotope relations Potential curves Based on Schrödinger equation with Born-Oppenheimer approximation Dipole moment Effective mass + Compilation of data Basic molecular data vibrational resolution H 2, D 2, T 2 HD, DT HT Already available U. Fantz, D. Wünderlich INDC(NDS)-457 (2004)

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 TraDiMo for molecular hydrogen Energy level diagram and potential curves repulsive double well plotted n=1,2,3, data up to n=4 v=0 metastable data compilation polynomial fits data compilation polynomial fits

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 TraDiMo for molecular hydrogen Vibrational levels in double minima curves: GK 1  g + H 2 : v = 2  GK2 Isotope effect D 2 : v = 2  K1

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 TraDiMo for molecular hydrogen Franck-Condon factors: X 1  g + → d 3  u v v‘

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 TraDiMo for molecular hydrogen Transition probabilities: d 3  u → a 3  g + v‘‘ v‘

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 TraDiMo for molecular hydrogen Transition probabilities for bound to free transitions: a 3  g + → b 3  u + Isotope shifts Continuum radiation

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Vibrational population in excited states of hydrogen Singlet system B 1  u + Triplet system d 3  u but also cascading, predissociation, quenching and … Projection of n 0 v via Franck Condon matrix versus excitation and de-excitation ground state population T vib (X)

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 TraDiMo for C 2, CH, BH, BeH, … Potential curves and Franck-Condon factors: C 2 X 1  g + - D 1  u + a 3  u - d 3  g

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 TraDiMo for C 2, CH, BH, BeH, … Potential curves: CH and BH Polynomial fits CH BH

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 TraDiMo for C 2, CH, BH, BeH, … Franck-Condon factors: X 2  - A 2  Isotope shifts CH CD CT

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 TraDiMo for C 2, CH, BH, BeH, … Transition probabilities: X 2  - A 2  CH CH:  = 540 ns measured value A ik = 1.85  10 6 s -1

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Yacora: a flexible code for calculating particle densities Self-consistent solution of coupled systems of linear and non-linear differential equations Collisional radiative modelling Population densities of excited states Dissociation modelling Particle densities of radicals + Coupled system Particle and population densities = Example: molecular hydrogen Flexible code  Easy to extend for new processes  Simple change of input data  Based on cross sections (EEDF) Electron collisions + heavy particle collisions + radiation Electron collisions + heavy particle collisions + radiation

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Yacora for hydrogen: collisional radiative modelling Vibrational resolution in ground state and electronically excited states Extension of data base  Gryzinski method optically forbidden transitions  Impact parameter method optically allowed transitions  Additional processes predissociation autoionisation, quenching, ….

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Yacora for hydrogen: collisional radiative modelling Electronically excited states: triplet system n=3: electronically resolved Differences in dependence on n e Calculations of individual levels required d 3  u : vibrationally resolved (change in data base)

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Yacora for hydrogen: collisional radiative modelling Projection of n 0 v via q vv’ and A ik versus collisional radiative modelling vib. resolved excitation and de-excitation Triplet system d 3  u Singlet system B 1  u + CR modelling is essential ground state population T vib (X)

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Yacora for C 2, CH, BH, … : collisional radiative modelling Compilation of energy level diagrams and potential curves CH A. Kalemos, A. Mavridis, A. Metropoulos J. Chem. Phys. 111 (1990) 9536 C2C2 C2C2 B.M. Smirnov, A.S. Yatsenko Physics-Uspekhi 39 (1996) 2116 U, 10 4 cm -1 U, eV Electronic states and optically allowed transitions

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Yacora for C 2, CH, BH, … : collisional radiative modelling Compilation of rate coefficients: CH IPProg A Burgess, H P Summers, IPProg code, Mon. Not. R. Astr. Soc. 174 (1976) 345 Validation and isotope investigations and measurements in laboratory plasmas Discrepancies between data sources

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Yacora for C 2, CH, BH, … : collisional radiative modelling IPProg for CH, C 2 IPProg for CH, BH Optically allowed transitions  Excitation energy  Statistical weights  Transition probability

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Yacora for C 2, CH, BH, … : collisional radiative modelling Dissociative excitation for CH, C 2 Direct excitation CH + e  CH* + e C 2 + e  C 2 * + e CH 4 + e  CH* + 3H + e C 2 H y + e  CH* + CH x + e C 2 H y + e  C 2 * + H m + e Particle fluxPhoton flux Example: Photon efficiencies of CH and/or Dissociation modelling

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Yacora for hydrocarbons: dissociation modelling Density ratios C 2 Swan radiation Direct excitation dominates C 2 * ~ C 2 ~ C 2 H 2 Rate coefficients [m 3 /s] CH A-X radiation CH* ~ CH, CH 4 Direct + dissociative excitation … and collisional radiative modelling: effective rate coefficients

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Yacora for hydrocarbons: dissociation modelling Dissociation model for hydrocarbons: model for methane Based on  electron impact processes C x H y + e → C x H y-m + H m + e C x H y + e → C x H y + + 2e; … Erhardt&Langer data completed with Brooks data Janev&Reiter data  heavy particle collisions (optional) CH 3 + CH 3 → C 2 H 6 C 2 H + C 2 H → C 2 +C 2 H 2 Tahara data A.B. Ehrhardt, W.D. Langer, PPPL-2477 (1987)J.N. Brooks et al., ANF/FPP/TM-297 (1999) R. Janev, D. Reiter, Jül3966 (2002) and Jül4005 (2003) Exchange of data base Exchange of data base Importance of heavy particle collisions Importance of heavy particle collisions Formation of higher hydrocarbons (ethane family) Formation of higher hydrocarbons (ethane family) H. Tahara et al., Jpn. J. Appl. Phys. 34 (1995) 1.

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Yacora for hydrocarbons: dissociation modelling Dissociation model for hydrocarbons: model for methane Check data bases (electron impact processes only) CH 4 (t=0) = m -3, T e = 4 eV, n e = m -3 Janev&Reiter dataErhardt&Langer with Brooks data Deviations by a factor of two Formation of higher hydrocarbons is negligible Deviations by a factor of two Formation of higher hydrocarbons is negligible

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Yacora for hydrocarbons: dissociation modelling Dissociation model for hydrocarbons: model for methane Check data bases: electron impact processes and heavy particles CH 4 (t=0) = m -3, T e = 4 eV, n e = m -3 Janev&Reiter dataErhardt&Langer with Brooks data Different pattern for higher hydrocarbons Factor of two difference in C 2 formation Different pattern for higher hydrocarbons Factor of two difference in C 2 formation

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Yacora for hydrocarbons: dissociation modelling Dissociation model for hydrocarbons: model for methane Importance of heavy particle collisions at low T e CH 4 (t=0) = m -3, n e = m -3 Janev&Reiter data T e = 4 eVT e = 2 eV Less electron impact dissociation

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Yacora for hydrogen: dissociation modelling Manifold of hydrogen species Surface recombination H H+H+ H2H2 Ionisation Dissociation Recombination Charge exchange Vibrational excitation ··· Relevance of  vibrational excitation: resonant processes  heavy particle collisions: formation of H 3 +, H -, H 2 (v), H 2 * H, H* H 2 +, H 3 +, H +, Hˉ H 2 (v), H 2 * H, H* H 2 +, H 3 +, H +, Hˉ … T e = 2.5 eV, n e = m -3 T vib = 3000 K, T gas = 450 K, p = 10 Pa Preliminary results

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Yacora for hydrogen: dissociation modelling Consequences on population of atomic hydrogen: coupling to hydrogen species H(n) H H+H+ H2+H2+ H2H2 H-H- recombination dissociative recombination dissociative excitation effective excitation mutual neutralisation H־ + H +  H* + H Collisional radiative and dissociation modelling Input data described in: D. Wünderlich, PhD Thesis University of Augsburg (2004)

Max-Planck-Institut für Plasmaphysik Ursel FantzCRP Meeting, September 2005 Summary Compilation and Extension of a Database for Systematic Studies on Diatomic Molecules Tools available Already done Prospects TraDiMo H 2, D 2, T 2, HD, HT, DT CH, C 2, BH, BeH,… Yacora Collisional radiative model Dissociation model H 2, H CH 4 CH, C 2, BH H 2 IPProg CH, C 2, BHCH, C 2, BH, BeH, … selected statesstates available Compilation Extension Systematic studies ++