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Max-Planck-Institut für Plasmaphysik Max-Planck-Institut für Plasmaphysik Fundamental Data of Diatomic Molecules Relevant for Fusion Ursel Fantz and Dirk Wünderlich Molecules in the plasma edge � Recycling Be Beryllium Beryllium H 2 , D 2 , T 2 , HD, HT, DT � Plasma wall interaction: CH, CD, CT, C 2 BeH, BeD, BeT W BH, BD, BT C � Vibrationally resolved data FCF, A ik , σ , X, CR and dissociation model CRP on ‘Atomic and Molecular Data for Plasma Modelling’, IAEA, Vienna 17-19 November 2008

Max-Planck-Institut Max-Planck-Institut Tra nsitions of Di atomic Mo lecules: TraDiMo für Pl für Plasmaphy asmaphysik Based on Schrödinger equation with Born-Oppenheimer approximation Compilation of data Compilation of data Vibrational energies TraDiMo TraDiMo Potential curves Franck-Condon factors bound-bound bound-bound + Dipole transition moment and bound-free Transition probabilities and bound-free transitions transitions Effective mass Isotope relations Basic molecular data Basic molecular data vibrational resolution H 2 , D 2 , T 2 U. Fantz, D. Wünderlich Already available HD, DT INDC(NDS)-457 (2004) HT presented at the 1 st RCM, September 2005 Ursel Fantz, p. 2 CRP Meeting, 17-19 November 2008

Max-Planck-Institut Max-Planck-Institut TraDiMo for molecular hydrogen für Pl für Plasmaphy asmaphysik 20 Energy level diagram and potential curves plotted n=1,2,3, data up to n=4 plotted n=1,2,3, data up to n=4 data compilation data compilation H + 18 2 polynomial fits polynomial fits E [eV] d 3 Π u H(1s)+H(3l) + H 2 D 1 Π u 16 16 g 3 Σ + h 3 Σ + HH 1 Σ g + I 1 Π g i 3 Π g g g J 1 Δ g j 3 Δ g H(1s)+H(2l) 14 14 n=3 e 3 Σ + C 1 Π u u Potential energy [eV] B' 1 Σ + E,F C u EF 1 Σ + g 12 a c 12 GK 1 Σ + B 1 Σ + B g u n=2 double well a 3 Σ + g c 3 Π u 10 10 v=0 metastable 8 8 b repulsive 6 6 b 3 Σ + u v=14 H(1s)+H(1s) 4 4 · · · 2 2 v=3 Singlet v=2 X 1 Σ + v=1 g Triplet 0 0 v=0 0 1 2 3 4 5 H 2 Singlet Triplet system Internuclear distance [Å] Ursel Fantz, p. 3 CRP Meeting, 17-19 November 2008

Max-Planck-Institut Max-Planck-Institut TraDiMo for molecular hydrogen für Pl für Plasmaphy asmaphysik Example: transition probabilities: d 3 Π u → a 3 Σ g + Fulcher band v‘‘ 18.0 q 0 1 2 3 4 v‘ 0 2.41E+07 1.66E+06 9.27E+03 7.75E-02 5.62E-02 1x10 -29 1 1.53E+06 2.07E+07 3.26E+06 2.97E+04 2.82E+00 d 3 Π u 2 1.07E+05 2.84E+06 1.74E+07 4.80E+06 6.23E+04 Potential energy [eV] 3 8.40E+03 3.19E+05 3.89E+06 1.43E+07 6.24E+06 16.0 0 4 5.87E+02 3.64E+04 6.22E+05 4.64E+06 1.15E+07 M el ... M el [Cm] v'=3 -1x10 -29 a 3 Σ + g 14.0 2.5x10 7 -2x10 -29 v''=3 2.0x10 7 -3x10 -29 12.0 1.5x10 7 ] 0 1 2 3 4 1 - [s Internuclear distance [Å] 1.0x10 7 ' ' v ' v 1 A 5.0x10 6 0 8 Ψ *M el Ψ ' -1 6 0.0 0 1 2 3 4 5 6 7 8 9 4 -2 ) 2 3 Π u -3 v'=3 → v''=3 v''(a d 0 3 Σ ( + ' -4 v ) g 0 1 2 Ursel Fantz, p. 4 CRP Meeting, 17-19 November 2008

Max-Planck-Institut Max-Planck-Institut + (v) TraDiMo for molecular hydrogen coupled to H 2 für Pl für Plasmaphy asmaphysik Franck-Condon factors for H 2 *(v) - H 2 + (v) transitions: data up to n=4 v + + + Example: B 1 Σ u → H 2 (X 2 Σ g ) q 0 1 2 3 4 v‘ 0 4.76E-01 3.17E-01 1.36E-01 4.82E-02 1.54E-02 1 3.75E-01 2.73E-02 2.07E-01 1.96E-01 1.12E-01 20.0 2 1.26E-01 3.32E-01 2.93E-02 5.59E-02 1.51E-01 3 2.10E-02 2.53E-01 1.75E-01 1.15E-01 6.82E-04 4 1.56E-03 6.44E-02 3.22E-01 5.91E-02 1.49E-01 ... 18.0 Potential energy [eV] + 2 Σ + H 2 (X g ) 0.6 16.0 0.4 14.0 1 Σ + FCF B u 0.2 12.0 8 0 2 4 6 8 ) 6 0.0 ) 2 Σ + Internuclear distance [Å] 0 1 2 3 4 5 6 7 8 9 4 g X 2 ( + v (B H 2 1 Σ 0 + ( ) ' v u Ursel Fantz, p. 5 CRP Meeting, 17-19 November 2008

Max-Planck-Institut Max-Planck-Institut + (v) TraDiMo for molecular hydrogen coupled to H 2 für Plasmaphy für Pl asmaphysik Franck-Condon factors for H 2 *(v) - H 2 + (v) transitions: H 2 , D 2 , T 2 , HD, DT,HT 0.6 0.6 H 2 H 2 D 2 H 2 D 2 D 2 + + + B 1 Σ u → H 2 (X 2 Σ g ) 0.4 0.4 F FCF Isotope shifts Isotope shifts C F 0.2 0.2 8 8 g )) g )) 6 2 (X 2 Σ + 6 2 (X 2 Σ + 0.0 0.0 0 1 2 3 4 5 6 7 8 9 4 0 1 2 3 4 5 6 7 8 9 4 2 v' (D + 2 v' (H + v v 0 ( B 1 0.6 ( B 1 Σ + 0 Σ + T 2 T 2 ) T 2 ) u u 0.4 FCF 0.2 8 )) 6 + 0.0 Σ g 4 0 1 2 3 4 5 6 7 8 9 2 (X 2 + v' (T 2 v 0 ( B 1 Σ + ) u Ursel Fantz, p. 6 CRP Meeting, 17-19 November 2008

Max-Planck-Institut Max-Planck-Institut TraDiMo for CH für Pl für Plasmaphy asmaphysik Potential curves and transition probabilities 10 8 10 ] -1 s CH 6 CH CH 6 0 1 C 2 Σ + -X 2 Π C 2 Σ + -X 2 Π 4 H Hettema and D R Yarkony, J. Chem. Phys 100, 1994, 8991 [ vv' G C Lie, J Hinze and B Liu, J. Chem. Phys 59, 1973, 1872 8 A 2 8 6 0 4 0 1 2 3 4 5 6 7 8 9 ) + 4 Potential energy [eV] Σ 2 2 C v (X 2 Π ) ( 6 0 ' A vv ’ [10 6 s -1 ] 3 v C 2 Σ + A vv' [10 6 s -1 ] 2 A 2 Δ B 2 Σ - -X 2 Π B 2 Σ - -X 2 Π 4 1 B 2 Σ − 8 6 0 0 1 2 3 4 5 6 7 8 9 ) 2.0 4 2 Σ - CH 2 2 B X 2 Π ( v (X 2 Π ) 0 ' v 1.5 ] -1 s 6 0 1.0 0 1 A 2 Δ -X 2 Π A 2 Δ -X 2 Π [ 0 1 2 3 4 5 vv' 0.5 A Intenuclear distance [Å] Gerö band 8 6 0.0 v' (A 2 Δ ) 0 1 2 3 4 5 6 7 8 9 4 2 v (X 2 Π ) 0 Ursel Fantz, p. 7 CRP Meeting, 17-19 November 2008

Max-Planck-Institut Max-Planck-Institut TraDiMo for C 2 für Pl für Plasmaphy asmaphysik Mulliken D 1 Σ u + - X 1 Σ g D 1 Σ u + - X 1 Σ g + + Potential curves and Einstein coefficients band 70 60 50 C 2 ] 14 s -1 40 0 6 1 30 D 1 Σ + [ 12 A ik u 20 10 6 Potential energy [eV] 10 0 4 u ) Σ + 0 1 2 d 3 Π g v(D 1 2 3 4 v(X 1 Σ + 5 0 6 8 g ) 7 X 1 Σ + g a 3 Π u 7 6 d 3 Π g - a 3 Π u d 3 Π g - a 3 Π u metastable 6 5 Swan band ] 4 ground state s -1 4 Energy gap 0 6 3 1 a 3 Π u - X 1 Σ + 2 [ g A ik 2 0.0887 eV 1 6 0 4 ) 0 1 2 3 4 0 1 2 3 Π g 2 v'(d 3 Internuclear distance [Å] 4 5 0 v ( a 3 6 Π 7 u ) Ursel Fantz, p. 8 CRP Meeting, 17-19 November 2008

Max-Planck-Institut Max-Planck-Institut TraDiMo for BH für Pl für Plasmaphy asmaphysik Potential curves and Franck Condon factors 1.0 B 1 Σ + - X 1 Σ + B 1 Σ + - X 1 Σ + X 1 Σ + → B 1 Σ + 10 BH BH BH W-T Luh and W C Stwalley, J. Molec. Spectr. 102, 1983, 212 FCF 0.5 B 1 Σ + 8 Potential energy [eV] 8 6 6 0.0 0 1 2 4 ) + 1 Σ 3 4 2 B 5 ( v 6 v ( X 1 7 Σ + 0 8 ) A 1 Π 4 1.0 A 1 Π - X 1 Σ + X 1 Σ + → A 1 Π A 1 Π - X 1 Σ + 2 X 1 Σ + FCF 0.5 0 0 1 2 3 4 5 8 6 Intenuclear distance [Å] 0.0 0 1 2 4 ) 1 Π 3 A 4 2 5 ( 6 v (X 1 Σ + ) v 7 0 8 Ursel Fantz, p. 9 CRP Meeting, 17-19 November 2008

Max-Planck-Institut Max-Planck-Institut TraDiMo for BeH für Pl für Plasmaphy asmaphysik 100000 2.0 CH CH J. Pitarch-Ruiz et al, CH BeH BeH J. Chem. Phys. 129, 2008, 054310 90000 A 2 Δ - -X 2 Π A 2 Δ - -X 2 Π 1.5 5 2 Π 4 2 Π 1 2 Δ ] 1 2 Σ - s -1 80000 2 2 Δ 0 6 1.0 1 [ A vv' 70000 5 2 Σ + Potential energy [cm -1 ] 0.5 3 2 Π 6 2 Σ + 4 2 Σ + 8 6 60000 Be( 1 P)+H( 2 S) 0.0 2 2 Π ) Δ 0 1 2 3 4 5 6 7 8 9 A 2 4 3 2 Σ + ( 2 ' v v (X 2 Π ) 50000 0 1 4 Σ + 40000 1 4 Π Be( 3 P)+H( 2 S) 10 BeH BeH 2 2 Σ + BeH 30000 8 A 2 Π - X 2 Σ + A 2 Π - X 2 Σ + A 2 Π A v'v'' [10 6 s -1 ] 6 20000 Be( 1 S)+H( 2 S) 4 10000 X 2 Σ + 2 8 0 6 0 0 1 2 3 4 5 6 7 8 ) 4 Π 2 1 2 3 4 5 A 2 ( v ' ' ' v Internuclear distance [Å] ( X 2 Σ + ) 0 9 Ursel Fantz, p. 10 CRP Meeting, 17-19 November 2008

Max-Planck-Institut Max-Planck-Institut TraDiMo for BeH für Pl für Plasmaphy asmaphysik Einstein coefficients: A 2 Π - X 2 Σ + Isotope shifts Isotope shifts 10 BeD BeD G. Duxbury et al., EFDA–JET–CP(04)03-54 BeD 8 A v'v'' [10 6 s -1 ] 6 4 2 8 6 0 0 1 2 3 4 5 6 7 8 v' (A 2 Π ) 4 2 v'' (X 2 0 + ) Σ 9 10 BeT BeT BeT 8 A v'v'' [10 6 s -1 ] 6 4 2 8 6 0 0 1 2 3 4 5 6 7 8 v' (A 2 Π ) 4 2 v ' ' ( X 2 Σ + 0 ) 9 Ursel Fantz, p. 11 CRP Meeting, 17-19 November 2008

Max-Planck-Institut Max-Planck-Institut Yacora: a flexible code for calculating particle densities für Pl für Plasmaphy asmaphysik Self-consistent solution of coupled systems of linear and non-linear differential equations Collisional radiative modelling Population densities of excited states Collisional radiative modelling + Dissociation modelling Particle densities of radicals Dissociation modelling Example: molecular hydrogen = 10 0 T e =4 eV Coupled system Particle and Coupled system n e =10 17 m -3 v=6 population Relative population n i /n 0 10 -2 v=5 densities v=4 Flexible code 10 -4 v=3 v=8 v=2 � Easy to extend for new processes c 3 Π u v=0 v=1 � Simple change of input data 10 -6 metastable v=14 B 1 Σ + � Based on cross sections (EEDF) u 10 -8 10 -10 10 -8 10 -6 10 -4 10 -2 10 0 Electron collisions Electron collisions Temporal development [s] + heavy particle collisions + radiation + heavy particle collisions + radiation Ursel Fantz, p. 12 CRP Meeting, 17-19 November 2008