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Non-Local Nuclear Dynamics

Non-Local Nuclear Dynamics. Martin Čížek Charles University, Prague. 1348. Dedicated to Wolfgang Domcke and J iří Horáček. Studied processes:. A B(v) + e -  AB(v’  v) + e - (VE) AB(v) + e -  A + B - (DA)

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Non-Local Nuclear Dynamics

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  1. Non-Local Nuclear Dynamics Martin Čížek Charles University, Prague 1348 Dedicated to Wolfgang Domcke and Jiří Horáček

  2. Studied processes: AB(v) + e-  AB(v’  v) + e- (VE) AB(v) + e-  A + B- (DA) A + B- AB(v) + e- (AD) AB(v) + e-  (AB)-  A + B-

  3. Outline of Theory • Fixed nuclei calculation as a first step. • Fano-Feshbach projection to get the electronic basis. • Known analytic properties of matrix elements (threshold expansions) used to construct proper model. • Nuclear dynamics solved assuming diabaticity of basis. Review: W. Domcke, Phys. Rep. 208 (1991) 97 http://utf.mff.cuni.cz/~cizek/

  4. HCl + e- Electronic structure for fixed-R Negative ion system (HCl)- Two state Landau-Zener model A+ + B- A + B H + Cl- Main idea behind the theoretical approach (O’Malley 1966): Selection of proper diabatic electronic basis set consisting of anionic discrete state and (modified) electron scattering continuum

  5. Extraction of resonance from the continuum Essence of the method: Selection of a square integrable function (discrete state) describing approximately the resonance and solution of scattering problem with additional constraint (orthogonality to the discrete state) It is show that sharp resonance structures are removed from continuum with sensitive choice of discrete state Example: Scattering of particle from spherical delta-shell. Discrete states – bound states in box with the same size as the shell.

  6. Final diabatic basis set Discrete state … Continuum … Coupling Diabaticity of the basis: Hamiltonian in the basis:

  7. ProjectionSchrödinger equationon basis • Formal solution of second line for (R) into first line • The similar procedure for Lippmann-Schwinger equation yields: Nonlocal vibrational dynamics in (AB)- state • Expansion of wave function

  8. Equation of motion for nuclei where Threshold behavior

  9. It is convenient to define: Then it is Nonlocal resonance model Dynamics is fully determined by knowledge of the functions V0(R), Vd(R), Vd(R)

  10. Summary – our procedure • Model parameters V0(R), Vd(R) and Vdε(R) found from Fano-Feshbach or fit for fixed-nuclei • Analytic fit made for R and e-dependencies in Vdε(R) to be able to perform the transform and efficient potential evaluation • Nuclear dynamics is solved for ψd(R) component • Cross sections or other interesting quantities are evaluated

  11. Results HCl(v) + e-  HCl(v’) + e-(VE)

  12. Results – vibrational excitation in e- + HCl Integral cross section. Theory versus measurement of Rohr, Linder (1975) and Ehrhardt (1989) Differential cross section. Measurement of Schafer and Allan (1991)

  13. Results – vibrational excitation in e- + HCl Elastic cross section. Theory -- resonant contribution (top) versus measurement of Allan 2000 (bottom) Vibrational excitation 0->1. Theory (top) versus measurement of Allan 2000 (bottom)

  14. VE in e-+H2

  15. Interpretation of boomerang oscillations • Dashed line = neutral molecule potential • Solid line = negative ion – discrete state potential • Circles = ab initio data for molecular anion Boomerang oscillations: interference of direct process and reflection from long range part of anion potential

  16. Results HBr(v) + e-  H + Br-(DA)

  17. Results – DA to HBr and DBr Comparison with measurement of Sergenton and Allan 2001

  18. Results H2 + e-↔H2-↔H-+H

  19. M. Čížek, J. Horáček, W. Domcke,J. Phys. B31 (1998) 2571 H+H-→ e- + H2

  20. M. Čížek, J. Horáček, W. Domcke,J. Phys. B31 (1998) 2571

  21. The Origin of theResonances Potentials for J=0 Potential Vad(R) for nonzero J

  22. Resonant tunneling wave function Energy Vad(R) + J(J+1)/2μR2 Cross section AUTODETACHMET

  23. Elastic cross section for e- + H2 (J=21, v=2)

  24. Γ0=2.7×10-4eV

  25. Elastic cross section for e- + H2 (J=25, v=1)

  26. Γ0=2.7×10-9eV Γ1=1.9×10-6eV

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