Theoretical Study of Charge Transfer in Ion-Molecule Collisions

1. Theoretical Study of Charge Transfer in Ion-Molecule Collisions EmeseRozsályi University of Debrecen2012.09.19. Department of Theoretical Physics

2. C2+ + OH → C+ + OH+ C2+ + HF → C+ + HF+ C2+ + HCl → C+ + HCl+ • By the Wigner and von Neumann non-crossing rule, adiabatic potential energy curves for states of the same symmetry cannot cross. • Potential energy curves for states of the same symmetry can approach each other in a narrow region avoided crossing • The charge-transfer process is driven by means of the nonadiabatic interactions in the vicinity of avoided crossings.

3. Comparison of depth-dose profiles The dose to normal healthy tissue is the least by using carbon-ion therapy. This depth-dose profile is the closest to the desire profile in diagram (a) in terms of tumour coverage, critical organ avoidance and minimised entry channel dosage.

4. Ion-diatomic collisional system B R A ρϴ C

5. Semiclassical treatment The projectile follows straight-line trajectories: X v b R ϑ θ ρZ Y The electronic motion is described by the eikonal equation:

6. Sudden approximation • No appreciable change in the ro-vibrational wavefunction is effected in the time interval in which the electronic transition takes place. • Molecular close-coupling treatment:

7. Semiclassical formalism • For a given nuclear trajectory and fixed : • The coefficients are subject to the initial condition: X Z’ v • Dynamical couplings: R ρ Z X’

8. Cross sections • The probability for transition to the final state is: • The cross section for transition to state , for each value of ρ is: • The total cross section is a sum of the partial cross sections:

9. Franck-Condon approximation • The coefficients are slowly varying functions of ρ it is possible to substitute them with values at the equilibrium distance of the diatomic molecule ρ0 • F0ν is the Franck-Condon factor between the BC and BC+ vibration wave functions at equilibrium geometry for the vibrational level ν=0 and ν, respectively. EIKONXS R.J. Allan, C. Courbin, P. Salas, P. Wahnon, J. Phys. B 23, L461 (1990). LEVEL 7.7 R.J. Le Roy [http://leroy.uwaterloo.ca]

10. States of HF+ MOLPRO H.J. Werner, P. Knowles, MOLPRO (version 2009.1) package of ab initio programs NISTH+F+ ,H++F

11. The quasimolecule CHF2+ Comparison of asymptotic energies (in eV): Three 1+ states and two 1Π states are considered in the process: C2+(1s22s2)1S + HF(1+) 1+ C+(1s22s22p)2P + HF+(2+) 1+, 1Π C+(1s22s22p)2P + HF+(2Π) 1+, 1Π

12. C2++HF 1. 1. C+(1s22s22p)2P + HF+(2Π) 1+, 1Π 2. 2. C+(1s22s22p)2P + HF+(2+) 1+, 1Π 3. 3. C2+(1s22s2)1S + HF(1+) 1+ Potential energy curves, θ=0◦,ρHF=eq., 1Σ+, 1Π. Rotational coupling matrix elements between1+ and 1Π states, θ=0◦,ρHF=eq. Radial coupling matrix elements between 1+ states, θ=0◦,ρHF=eq.

13. C2++HF Total and partial charge transfer cross sections at equilibrium, ϴ=0° ; full line: with translation factors; broken line: without translation factors.

14. Total charge transfer cross-sections, θ=0°, for different values of the vibration coordinate rHF. Total and partial charge transfer cross-sections for the vibration coordinate rHF=1.5 a.u., θ=0°. Total and partial charge transfer cross-sections for the vibration coordinate rHF=2.0 a.u., θ=0°. Radial coupling matrix elements between 1+ states, θ=0°, Dotted line, rHF=2.0 a.u.; full line, rHF=1.73836832 a.u. (equilibrium); dashed line, rHF=1.5 a.u.

15. C2++HF/ C2++OH Total charge transfer cross-sections for the C2+- HF system in the linear approach, θ=0°, for different values of the vibration coordinate rHF. Total charge transfer cross-sections for the C2+- OH system in the linear approach, θ=180°, for different geometries of the OH radical. Total cross sections for the C2+ + HF(=0) →C+ + HF+() charge transfer process (in 10-16 cm2) for different velocities v (in a.u.).

16. Potential energy curves, ρHF=eq., 1Σ+,1Π. θ=90◦ θ=180◦ —ϴ = 0o —ϴ = 20o —ϴ = 45o —ϴ = 90o ·····ϴ = 135o ·····ϴ = 160o ·····ϴ = 180o rad23 rad12 Evolution of the radial couplingsfor different orientations.

17. C2++HF Radial coupling matrix elements between 1+ states for different orientations θ from 0° to 180°. Dotted line, θ=90°; dotted-dashed line, θ=45°; dashed line, θ=135°; thin full line, θ=0°; full line, θ=180°. Total charge transfer cross-sections at equilibrium, for different orientations θ from 0° to 180°.

18. C2++HF Charge transfer cross sections averaged over the different orientations.

19. C2++HCl Four 1+ states and three 1Π states are considered in the process: 1.C+(1s22s22p)2P° + HCl+(2Π) 1+, 1Π 2. C+(1s22s22p)2P° + HCl+(2+)1+, 1Π 3. C+(1s22s22p)2D + HCl+(2Π)1+, 1Π 4.C2+(1s22s2)1S + HCl(1+) 1+ Potential energy curves for the 1+ (full line) and 1Π (broken line) states of the C2+-HCl molecular system at equilibrium, θ=0°.

20. C2++HCl Radial coupling matrix elements between 1+ states, θ=0◦,ρHCl=eq. Rotational coupling matrix elements between1+ and 1Π states, θ=0◦,ρHCl=eq. Total and partial charge transfer cross sections at equilibrium, ϴ=0° ;

21. C2++HCl Charge transfer cross sections forthe C2+ + HCl collision system (in 10-16 cm2). Comparison with the C2+ + HF collision system. The comparative results show that the charge-transfer mechanism is fundamentally dependent of the specific nonadiabatic interactions involved in each system.

22. Publication list • The presentation is based on the following papers: • 1. E. Bene, E. Rozsályi, Á. Vibók, G. J. Halász, M. C. Bacchus-Montabonel: Theoretical treatment of direct and indirect processes in ion-biomolecule collisions, AIP Conf. Proc. 1080, 59-70 (2008). • 2. E. Rozsályi, E. Bene, G. J. Halász, Á. Vibók, M. C. Bacchus-Montabonel: Theoretical treatment of charge transfer in collisions of C2+ ions withHF: Anisotropic and vibrational effect, Phys. Rev. A 81, 062711 (2010). • 3. E. Rozsályi, E. Bene, G. J. Halász, Á. Vibók, M. C. Bacchus-Montabonel: Ab initio molecular treatment of C2++ HF collision system, Acta Physica Debrecina, XLIV, 118 (2010). • 4. E. Rozsályi, E. Bene, G. J. Halász, Á. Vibók, M. C. Bacchus-Montabonel: Ab initio study of charge-transfer dynamics in collisions of C2+ ionswith hydrogen chloride, Phys. Rev. A 83, 052713 (2011). • 5. E. Rozsályi: Charge transfer in collisions of C2+ ions with HCl molecule, Acta Physica Debrecina, XLV, 166 (2011). • 6. E. Rozsályi, E. Bene, G. J. Halász, Á. Vibók, M. C. Bacchus-Montabonel: Analysis of the charge transfer mechanism in ion-molecule collisions.Advances in the Theory of Quantum Systems in Chemistry and Physics;Progress in Theoretical Chemistry and Physics; 22, (355-368), 2012, ISBN 978-94-007-2075-6, Springer. • Further publication: • 7. E. Rozsályi, L. F. Errea, L. Méndez, I. Rabadán: Ab initio calculation of chargetransfer in proton collisions with N2, Phys. Rev. A 85, 042701 (2012).

23. Thanks to... • Dr. Ágnes Vibók, Dr. Marie-Christine Bacchus-Montabonel, Dr. Erika Bene and Dr. Gábor Halász for their support, inspiring comments during the research. • The presentation is supported by the TÁMOP-4.2.2/B-10/1-2010-0024 project.The project is co-financed by the European Union and the European Social Fund.