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 AB + e AB + e Electronic excitation AB + e AB* + e Vibrational excitation AB(v”=0) + e AB(v’) + e Rotational excitation AB(N”) + e AB(N’) + e Dissociative attachment / Dissociative recombination AB + e A + B A + B Impact dissociation AB + e A + B + e All go via (AB-)** . Can also look for bound states

The R-matrix approach Inner region: Outer 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  Outer region e– Inner region C F C R-matrix boundary r = a: target wavefunction = 0

R-matrix method for electrons: inner region wavefunction (within the Fixed-Nuclei approximation) Yk = A Si,j ai,j,k fiN hi,j + Si bj,k fjN+1 fiN= target states = CI target built from nuclear centred GTOs fjN+1= L2 functions e- inner region hi,j = continuum orbitals = GTOs centred on centre of mass H H a A = Anti-symmetriser ai,j,k and bj,k variationally determined coefficients

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

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

Determine choice of T-matrices to be averaged ` Including nuclear motion (within adiabatic nuclei approximation) in case of dissociation 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 Determine choice of T-matrices to be averaged

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

Explicit adiabatic averaging over T-matrices using continuum functions

Need to Calculate: 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 C.S. Trevisan and J. Tennyson, J. Phys. B: At. Mol. Opt. Phys., 34, 2935 (2001)

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

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

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

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)

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

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

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

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

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)

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 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)

Total elastic cross section

Elastic DCS (differential cross section) at 90º

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

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).

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