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R-matrix calculations of electron molecule collisions

e -. R-matrix calculations of electron molecule collisions. Jonathan Tennyson University College London. Outer region. Inner region. ADAS Workshop Armagh, Oct 2010. Processes: at low impact energies. Elastic scattering A B + e A B + e. Electronic excitation

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R-matrix calculations of electron molecule collisions

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  1. e- R-matrix calculations of electron molecule collisions Jonathan Tennyson University College London Outer region Inner region ADAS Workshop Armagh, Oct 2010

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

  3. 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  The R-matrix approach C R-matrix boundary r = a: target wavefunction = 0

  4. H H R-matrix method for electrons: inner region wavefunction (within the Fixed-Nuclei approximation) Yk=ASi,j ai,j,k fiN hi,j+ Si bj,k fjN+1 fiN= target states = CItarget built from nuclear centred GTOs fjN+1= L2functions e- inner region hi,j = continuum orbitals= GTOscentred on centre of mass a A= Anti-symmetriser ai,j,k and bj,k variationally determined coefficients

  5. Molecules of interest for fusion Electron collisions with: H2+ H2, D2, T2, HD, HT, DT C2 H2O HCN/HNC HCCH In progress CH4 CH+

  6. Electron impact dissociation of H2 Important for fusion plasma and astrophysics Low energy mechanism: e- + H2(X 1Sg) e- + H2(b 3Su) e- + H + H R-matrix calculations based on adiabatic nuclei approximation extended to dissociation

  7. ` • 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 ds(Ein) dEout Including nuclear motion (within adiabatic nuclei approximation) in case of dissociation Determine choice of T-matrices to be averaged

  8. The energy balance method D.T. Stibbe and J. Tennyson, New J. Phys.,1, 2 (1999).

  9. Explicit adiabatic averaging over T-matrices using continuum functions

  10. Total cross sections, s(Ein) • Energy differential cross sections, ds(Ein) • dEout • Angular differential cross sections, ds(Ein) • dq • Double differential cross sections, d2s(Ein) • dqdEout • Required formulation of the problem Need to Calculate: C.S. Trevisan and J. Tennyson, J. Phys. B: At. Mol. Opt. Phys., 34, 2935 (2001)

  11. e- + H2 e- + H + H Integral cross sections Cross section (a02) Incoming electron energy (eV)

  12. e- + H2(v=0)e-+ H + H Energy differential cross sections in a.u. Atom kinetic energy (eV) Incoming electron energy (eV)

  13. e- + H2(v>0)e-+ H + H Energy differential cross sections in a.u. V = 2 V = 3 Atom kinetic energy (eV) Incoming electron energy (eV)

  14. e- + H2 e-+ H + H Energy differential cross sections as a function of incoming electron energy Atom kinetic energy (eV) Extended to D2, T2, mixed isotopologues, C.S. Trevisan & J. Tennyson, Plasma Phys. Controlled Fusion, 44, 1263 (2002)

  15. Electron – water rotationally resolved cross sections: Differential cross sections (DCS) at 6 eV Cho et al (2004) * Jung et al (1982) DJ=1 DJ=all DJ=0

  16. Electron – water (rotationally averaged) elastic cross sections Integral cross section A Faure, JD Gorfinkel & J Tennyson J Phys B, 37, 801 (2004)

  17. C2 states Electron – C2: G. Halmova, JD Gorfinkel & J Tennyson J Phys B, 39, 2849 (2006).

  18. Uracil • Electron capture mainly due to DNA and RNA bases, because these have extended aromatic system • Scattering electron can temporary be attached to an unocuppied π* orbital, giving rise to a shape resonance

  19. Shape resonances in e--uracil Positions (and widths) in eV of 2A” resonances cc-pVDZ, a=13 a0, 15 virtuals, CAS(14,10) Method Res 1 Res 2 Res 3 SEP SE 2.25 (0.26) 4.43 (0.41) 8.62 (2.69) 0.31 (0.015) 2.21 (0.16) 5.21 (0.72) CC 0.134 (0.0034) 1.94 (0.168) 4.94 (0.38) Obs 0.22 1.58 3.83 A Dora, J Tennyson, L Bryjko and T van Mourik J Chem Phys, 130, 164307 (2009)

  20. 2A’ 6.17 (0.15) 7.62 (0.11) 8.12 (0.14) 2A” 0.134 (0.0034) 1.94 (0.168) 4.94 (0.38) Resonances in electron -uracil: Shape and Feshbach Positions (and widths) in eV of 2A’ and 2A” resonances CC, cc-pVDZ, a=13 a0, 15 virtuals, CAS(14,10) Symmetry Res 1 Res 2 Res 3

  21. Total elastic cross section

  22. Elastic DCS (differential cross section) at 90º

  23. X 1A’ 3 1A’ with Born correction X 1A’ 3 1A’ without Born correction X 1A’ 2 3A’ Electron impact electronic excitation cross section

  24. UK molecular R-matrix codes: • General and flexible for electron-molecule collisions • Treat a variety (all) low-energy processes • Particularly good for ions • New R-matrix with pseudo-state (RMPS) leads to greater accuracy and extended energy range J. Tennyson, Electron - molecule collision calculations using the R-matrix method, Phys. Rep., 491, 26 (2010).

  25. www.worldscibooks.com/physics/p371.html “The best book for anyone who is embarking on research in astronomical spectroscopy” Contemporary Physics (2006)

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