The document summarizes research on two-center interference in ion-molecule collisions during electron capture and ionization processes. It discusses how interference patterns observed in early double-slit experiments can provide insight into these collision processes. Interference is seen in single and double electron capture from diatomic molecules like H2. The interference patterns depend on projectile velocity and orientation of the molecule, and provide a test of quantum mechanical descriptions of the collision dynamics.

1. Two-center interference in ion-molecule collisions: electron capture and ionization Deepankar Misra Stockholm University, Stockholm, Sweden

3. Thomas Young, 1801 Interference in diatomic molecules on electrons: Davisson and Germer, 1927 C. Jönsson, 1961 P.G. Merli et al., 1974 A. Tonomura et al., 1989 Electron capture: Theory Tuan and Gerjuoy, 1960 S. Cheng, C.L. Cocke, et al., 1993 Photo-ionization: Theory Cohen and Fano, 1966 D. Rolls et. al., Nature 2005, K. Kreidi et al., PRL 2008 Ionization: Stolterfoht et al., PRL 2001 Misra et al., PRL 2004 and many others Transfer Excitation: Fast (MeV) H atoms, Schmidt et al., 2008 Double-electron capture: He ++ + H 2 . on neutrons: A. Zeilinger, 1988 on fullerenes: Hackermuller et al., 2004 The double slit experiment Visible light A q+ 

4. e - k i =M p v p i k f = ( M p + m e ) v p f  capture at small distances (  << 1 a.u.)  small projectile scattering angles ( < 1 mrad)  projectile long. momentum change | k f – k i | = n v p /2- Q / v p Fast electron capture from molecules Number of electrons captured

5. e - k i =M p v p i k f = ( M p + m e ) v p f  capture at small distances (  << 1 a.u.)  small projectile scattering angles ( < 1 mrad)  projectile long. momentum change | k f – k i | = n v p /2 Fast electron capture from molecules Number of electrons captured

7. injection from source HF cavity e - cooler CRYRING The Experimental Setup Gas jet  Intense and narrow ion beam  Ideal for low cross section measurements, e.g., ~ 10 -22 cm 2  Beam diameter ~ 1 mm  Gas jet diameter ~ 1 mm  Ultra High Vacuum ~10 -12 Torr (UHV)  Temp T ~ 100 mK target beam neutralized projectiles E -field coincidence

8.  1.3 MeV p + H 2 Interference in electron capture from H 2 a a = 1.4 a.u. = 7.4  10 -11 m k i =M p v p i k f = ( M p + m e ) v p f projectile velocity: v p = 7.2 a.u. projectile momentum: k ~ 13250 a.u.  k = ( k f -k i ) = 3.5 a.u. proj. wavelength:  ~ 2.5  10 -14 m   = 6.6  10 -18 m double slit Tuan and Gerjuoy, Phys. Rev. (1960) Stochkel et al PRA 72 050703 (2005) phase shift  = ( k f -k i ) z z = a cos 

9.  Interference in electron capture from H 2 a a = 1.4 a.u. = 7.4  10 -11 m k i =M p v p i k f = ( M p + m e ) v p f phase shift  = ( k f -k i ) z z = a cos  projectile velocity: v p = 7.2 a.u. projectile momentum: k ~ 13250 a.u.  k = ( k f -k i ) = 3.5 a.u. proj. wavelength:  ~ 2.5  10 -14 m   = 6.6  10 -18 m double slit constructive interference  =    ~ 90° 1.3 MeV p + H 2 Stochkel et al PRA 72 050703 (2005)

10.  Interference in electron capture from H 2 a a = 1.4 a.u. = 7.4  10 -11 m k i =M p v p i k f = ( M p + m e ) v p f projectile velocity: v p = 7.2 a.u. projectile momentum: k ~ 13250 a.u.  k = ( k f -k i ) = 3.5 a.u. proj. wavelength:  ~ 2.5  10 -14 m   = 6.6  10 -18 m destructive interference  =    ~ 51°, 129° 1.3 MeV p + H 2 Stochkel et al PRA 72 050703 (2005) phase shift  = ( k f -k i ) z z = a cos 

11.  a a = 1.4 a.u. = 7.4  10 -11 m k i =M p v p i k f = ( M p + m e ) v p f 1.3 MeV p + H 2 Molecule  LCAO Capture  Brinkmann-Kramers Wang, McGuire, Rivarola (1989 ) Stochkel et al PRA 72 050703 (2005) Interference in electron capture from H 2 phase shift  = ( k f -k i ) z z = a cos 

12.  = 50°  = 90° Schmidt et al Phys. Rev. Lett. 101 083201 (2008) Interference in scat. angle distribution Single hydrogen atom inside the apparatus at a given time  Single hydrogen de Broglie wave interference

13. Double-electron capture from H 2 k i =M p v p i k f = ( M p + 2 m e ) v p f He 2+  DC ~ 10 -22 cm 2  I ~ 10 -17 cm 2 105 0 75 0

14. Double-electron capture from H 2 k i =M p v p i k f = ( M p + 2 m e ) v p f D. Misra, et al., Phys. Rev. Lett 102 153201 (2009 ) Expected destructive interference At first Glance  Simple picture does not seem to work!  A rather strong velocity dependence  Two-center ( LCAO ), two-electron wavefunctions  Does not include two-electron, one center part.  one electron is captured in a direct capture event ( OBK )  The other electron is captured by a “shakeover” projectile velocity: v p = 4.46 a.u. projectile momentum: k ~ 32754 a.u.  k = ( k f -k i ) = 4.46 a.u. proj. wavelength:  ~ 1.0  10 -14 m   = 1.4  10 -18 m

15. Comparison: Single- & Double- Capture d = c a and S p =q/v p c=1.00 c=0.89 c=0.90 c=0.70 c=0.76 c=0.49 Expected position for the minima

16. Comparison: Single- & Double- Capture d = c a S p =q/v p 1.3 MeV H + V p =7.2 a.u. Electron capture takes place when the projectile passes through regions close to either of the target nuclei. d a

17. Comparison: Single- & Double- Capture d = c a S p =q/v p 2 MeV He ++ V p = 4.46 a.u. Electron capture takes place when the projectile passes through regions close to either of the target nuclei. d a

19. Acknowledgement ( Stockholm University and MSL ) H. T. Schmidt M. Gudmundsson N. Haag H. Johansson P. Reinhed A. Källberg A. Simonsson R. Schuch H. Cederquist Max Planck Institute fuer Kernphysik, Heidelberg D. Fischer A. Voitkiv B. Najjari M. Schöffler ( University of Frankfurt and LBNL )

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