C. Blondel, W. Chaïbi, C. Delsart and C. Drag

1. y x Jet detector : res. 65 µm FWHM 1 electron each 0.1 ms to 1 ms z a F z0 Détecteur D F S 7 C 3 / 2 e 4 2 m 8 F = U 6  1 : Source and simple lens doublet ("einzellens") 2,5,9,10 : Deflection plates 3,6,8 : Simple lenses 10 0 3 q F h 4 5 12 Detector 2 4 : Wien filter 7 : Deflection 11 : Focalisation quadrupole 12 : Deceleration plates 13 : Interection zone 9 1 11 13 3 Longitudinal and transverse magnetic field coils ion detector détecteur 13 cm B//F solenoid solénoïde z0 2 m negative ion beam jet d’ion négatifs 62 cm laser laser transverse BF coils 23 cm 42 cm B = 1.9 µT B = 27.8 µT B = 56.1 µT B = 82 µT B = 110.4 µT B = 137.5 µT F ~ 291 V/m l = 596.89122 nm The local phase shfit Defining the momentum : One gets a wave-function B-dependent according to Magnetic phase Geometric phase The phase of the interferogram will thus change by Electron affinities Trajectory curvature will make a contribution at a higher order. The expected phase variation, at a fixed position on the detector, will be : Numerically : The shift of the envelope The fringe displacement is such that In the far-field approximation Comparing the gradient and the phase shift One gets: PHOTODETACHMENT MICROSCOPY IN A MAGNETIC FIELD C. Blondel, W. Chaïbi, C. Delsart and C. Drag Laboratoire Aimé Cotton, Univ Paris-sud, Bât. 505, Campus d’Orsay, 91405 Orsay Cedex, France Effect of a magnetic field : longitudinal case The principle of photodetachment microscopy the Green function is known Kramer et al., Europhys. Lett. 56, 471 (2001) Quantum parameters : 2-trajectory interference: same phase as for B=0 (invariance) Mean interfrange Nomber of rings 4-trajectory interference Principle: Y.N. Demkov et al., JETP Lett.34, 403 (1981) Photoionization microscopy: C. Nicole et al., Phys. Rev . Lett.88, 133001 (2002) Molecular photodetachment microscopy : C. Delsart et al., Phys. Rev . Lett.89, 183002 (2002) Geometrical effect on the interference patterns Photodetachment microscopy: C. Blondel et al., Phys. Rev . Lett.77, 3755 (1996) Experimental results Classical trajectories 100mA≡126µT=1.26G The analytic formula American Journal of Physics66, 38 (1998) F = 423 Vm-1 e = 1.2 cm-1 l0 = 0.045 mm a = 0.35 mm Measured pattern diameter D(I) Measured distance R(I) of the pattern centre to the source projection on the detector Calculated fit of the theoretical value of R(I) As expected: Experimental setup Effect of a magnetic field : transverse case Trajectory and fringe shifts ? Experimental results Influence of a magnetic field on the interference phase General problem: in the presence of a Lorentz force, will the trajectory shift be equal to the shift of the interference fringes ? F ~ 195 V/m B = 5.10-8 T Laser interferograms z0 = 0.514 m F between 150 and 450 V/m B0 What does the ring pattern become in the presence of a transverse magnetic field ? Dye laser Negative ion l = 535 @ 710 nm (~ 596 nm) P = 100 to 400 mW stability ~ 10 MHz for 30 min Dl/l (mes.) ~ 2.10-8 waist 20 to 40 µm B0 Beam cinetic energy : 300 to 500 eV  60 to 80 km.s-1 Do electron affinities vary with the magnetic field ? i.e. at 1st order proportionally to the B flux : FluorA(19F) = 27432.451(20) cm-1 OxygeneA(16O) = 11784.676(7) cm-1 SiliciumA(28Si) = 11207.246(8) cm-1 SulfurA(32S) = 16752.9760(42) cm-1 Eur. Phys. J.D33, 335 (2005) e neutral atom ± 8.10-3 cm-1 dispersion due to electric field inhomogeneities hn The interference phase remains invariant ! eA Isotopic shift OxygeneA(17O) = 11784.629(22) cm-1 A(18O) = 11784.606(20) cm-1 Phys. Rev.A64, 052504 (2001) negative ion Fringe shift vs. trajectory shift Fine structure of atoms and ions OxygeneE(2P1/2)E(2P3/2) = 177.084(14) cm-1 Sulfur 32S: E(2P1/2)  E(2P3/2) = 483.5352(34) cm-1 32S: E(3P1)  E(3P2) = 396.0587(32) cm-1 J. Phys.B39, 1409 (2006) j Si- Molecules OHA(16O1H) = 14740.982(7) cm-1 J. Chem. Phys.122, 014308 (2005) SH A(32S1H) = 18669.543(12) cm-1 J. Mol. Spec. 239, 11 (2006) SA0872b R e= 0.926 ± 0.008 cm-1 F = 427 Vm-1 ± 4 Vm-1 The interference pattern moves as a whole ! Accuracy : ± 1 µeV