Electron molecule collision calculations using the R-matrix method Jonathan Tennyson Department of Physics and Astronomy University College London IAEA. Vienna, December 2003

Processes: at low impact energies Elastic scattering AB + e Electronic excitation AB + e AB* + e Dissociative attachment / Dissociative recombination AB + e A + B A + B Vibrational excitation AB(v=0) + e AB(v) + e Rotational excitation AB(N) + e Impact dissociation AB + e A + B + e All go via (AB )**. Can also look for bound states

The R-matrix approach C Outer region e – Inner region C F Inner region: exchange electron-electron correlation multicentre expansion of Outer region: exchange and correlation are negligible long-range multipolar interactions are included single centre expansion of R-matrix boundary r = a: target wavefunction = 0

Scattering Wavefunctions k A i,j a i,j,k i N i,j b j,k j N+1 where i N N-electron wavefunction of i th target state i,j 1-electron continuum wavefunction j N+1 (N+1)-electron short-range functions A Antisymmetrizes the wavefunction a i,j,k and b j,k variationally determined coefficients

UK R-matrix codes L.A. Morgan, J. Tennyson and C.J. Gillan, Computer Phys. Comms., 114, 120 (1999).

Electron collisions with OClO R-matrix: Baluja et al (2001) Experiment: Gulley et al (1998)

Electron - LiH scattering: 2 eigenphase sums B Anthony (to be published)

Electron impact dissociation of H 2 Important for fusion plasma and astrophysics Low energy mechanism: e + H 2 (X 1 g ) e + H 2 (b 3 u ) e + H + H R-matrix calculations based on adiabatic nuclei approximation extended to dissociation

` Including nuclear motion (within adiabatic nuclei approximation) in case of dissociation dE out d (E in ) Excess energy of incoming e over dissociating energy can be split between nuclei and outgoing e in any proportion. Fixed nuclei excitation energy changes rapidly with bondlength Tunnelling effects significant Determine choice of T- matrices to be averaged

D.T. Stibbe and J. Tennyson, New J. Phys., 1, 2.1 (1999). The energy balance method

Explicit adiabatic averaging over T-matrices using continuum functions

Need to Calculate: Total cross sections, (E in ) Energy differential cross sections, d (E in ) dE out Angular differential cross sections, d (E in ) d Double differential cross sections, d 2 (E in ) d dE out Required formulation of the problem C.S. Trevisan and J. Tennyson, J. Phys. B: At. Mol. Opt. Phys., 34, 2935 (2001)

e + H 2 e + H + H Integral cross sections Incoming electron energy (eV) Cross section (a 0 2 )

e + H 2 e + H + H Angular differential cross sections at 12 eV Angle (degrees) Differential Cross section (a 0 2 )

e + H 2 (v=0) e + H + H Energy differential cross sections in a.u. Atom kinetic energy (eV) Incoming electron energy (eV)

e + H 2 (v>0) e + H + H Energy differential cross sections in a.u. Atom kinetic energy (eV) Incoming electron energy (eV) V = 2V = 3

Electron impact dissociation of H 2 Effective threshold about 8 eV for H 2 (v=0) Thermal rates strongly dependent on initial H 2 vibrational state For v=0: Excess energy largely converted to Kinetic Energy of outgoing H atoms For v > 0: Source of cold H atoms ?

Energy (eV) Internuclear separation (a 0 ) DT Stibbe and J Tennyson, J. Phys. B., 31, 815 (1998). Quasibound states of H 2 : g + resonances

Can one calculate resonance positions with a standard quantum chemistry code? R (a 0 ) Energy (eV) R-matrix Resonance position H 2 - potential curves calculated with Gaussian by Mebel et al. D T Stibbe and J Tennyson, Chem. Phys. Lett., 308, 532 (1999) No!

Electron collision with CF x radicals extremely high global warming potential C 2 F 6 and CF 4 practically infinite atmospheric lifetimes CF 3 I low global warming potential C 2 F 4 strong source of CF x radicals new feedstock gases no information on how they interact with low E e – CF x radicals highly reactive, difficult species to work with in labs Theoretical approaches – attractive source of information

Twin-track approach Joint experimental and theoretical project e – interactions with the CF 3 I and C 2 F 4 e – collisions with the CF, CF 2 and CF 3 N.J. Mason, P. Limao-Vieira and S. Eden I. Rozum and J. Tennyson

Electron collisions with the CF Target model X 1, 4 –, 2 +, 2, 2 – and 4 Slater type basis set: (24,14 ) + (, ) valence target states 2 + Rydberg state valence NO Rydberg NO ( ) (24,14 ) (7 …14 3 …6 ) CF (1 2 ) 4 (3 …6 1 2 ) 11 (1 2 ) 4 (3 …6 1 2 ) 10 (7 3 ) 1 final model single excitation single + double excitation

Electron collisions with the CF Resonances 1 E e = 0.91 eV e = 0.75 eV 1 + E e = 2.19 eV e = 1.73 eV 3 – E e ~ 0 eV 2

Electron collisions with the CF Bound states 1 E b (R e ) = 0.23 eV 3 E b (R e ) = 0.26 eV shape resonances E( 1 ) = eV E( 3 ) = eV 3 – at R > 2.5 a 0 1 at R > 3.3 a 0 3 – and 3 C( 3 P) + F – ( 1 S) 1 and 1 C( 1 D) + F – ( 1 S) unbound at R = 2.6 a become bound

Electron collisions with the CF 2 Resonances shape resonances: 2 B 1 ( 2 A) E e = 0.95 eV e = 0.18 eV 2 A 1 ( 2 A) E e = 5.61 eV e = 2.87 eV bound state at R > 3.2 a 0 2 B 1 CF( 2 P) + F – ( 1 S) 3b13b1 7a17a1

Electron collisions with the CF 3 Target representation C s symmetry group X 2 A, 1 2 A, 2 2 A, 2 2 A, 3 2 A, 3 2 A Models 1. (1a2a3a1a) 8 (4a…13a2a…7a) CSF (Ra) 2. (1a…6a1a2a) 16 (7a…13a3a…7a) CSF 3. (1a…5a1a2a) 14 (6a…13a3a…7a) CSF C F o F 1 F 2 a = 10 a o 2.53 a o

Electron collisions with the CF 3 Electron impact excitation cross sections Bound state E( 1 A) ~ 0.6 eV No (low-energy) resonances!

Dissociative recombination of NO + NO + important ion in ionosphere of Earth and thermosphere of Venus Mainly destroyed by NO + + e N + O Recent storage ring experiments show unexplained peak at 5 eV Need T-dependent rates for models Calculations: resonance curves from R-matrix calculation nuclear motion with multichannel quantum defect theory

NO + dissociation recombination: potential energy curves Spectroscopically determined R-matrix ab initio R-matrix calibrated

NO + dissociation recombination: Direct and indirect contributions

NO + dissociation recombination: comparison with storage ring experiments IF Schneider, I Rabadan, L Carata, LH Andersen, A Suzor-Weiner & J Tennyson, J. Phys. B, 33, 4849 (2000)

NO + dissociation recombination: Temperature dependent rates Electron temperature, T e (K) Rate coefficient (cm 3 s 1 ) Experiment Mostefaoui et al (1999)) Calculation

Electon-H 3 + at intermediate energies Jimena Gorfinkiel

Conclusion R-matrix method provides a general method for treating low-energy electron collisions with neutrals, ions and radicals Results should be reliable for the energies above 100 meV (previous studies of Baluja et al 2001 on OClO). Total elastic and electron impact excitation cross sections. Being extended to intermediate energy and ionisation.

Natalia Vinci Iryna Rozum Jimena Gorfinkiel Chiara Piccarreta