2. C. Blondel, W. Chaïbi, C. Delsart and C. Drag Laboratoire Aimé Cotton, Univ Paris-sud, Bât. 505, Campus d’Orsay, 91405 Orsay Cedex, France PHOTODETACHMENT MICROSCOPY IN A MAGNETIC FIELD The principle of photodetachment microscopy Effect of a magnetic field : longitudinal case Experimental setup Quantum parameters : Nomber of rings Mean interfrange Detector ion z0z0 The analytic formula 7 6 5 4 3 2 1 8 9 10 11 12 13 1 : Source and simple lens doublet ("einzellens") 2,5,9,10 : Deflection plates 3,6,8 : Simple lenses 4 : Wien filter 7 : Deflection 11 : Focalisation quadrupole 12 : Deceleration plates 13 : Interection zone Beam cinetic energy : 300 to 500 eV  60 to 80 km.s -1 x y detector : res. 65 µm FWHM 1 electron each 0.1 ms to 1 ms z 0 = 0.514 m F between 150 and 450 V/m Dye laser = 535 @ 710 nm (~ 596 nm) P = 100 to 400 mW stability ~ 10 MHz for 30 min  (mes.) ~ 2.10 -8 waist 20 to 40 µm Photodetachment microscopy: C. Blondel et al., Phys. Rev. Lett. 77, 3755 (1996) C D F U negative ion neutral atom h  eAeA Si - SA0872b R j F = 427 Vm -1 ± 4 Vm -1  = 0.926 ± 0.008 cm -1 Accuracy : ± 1 µeV Electron affinities Fluor A( 19 F) = 27 432.451(20) cm -1 Oxygene A( 16 O) = 11 784.676(7) cm -1 Silicium A( 28 Si) = 11 207.246(8) cm -1 Sulfur A( 32 S) = 16 752.9760(42) cm -1 Eur. Phys. J. D33, 335 (2005) Oxygene A( 17 O) = 11 784.629(22) cm -1 A( 18 O) = 11 784.606(20) cm -1 Phys. Rev. A64, 052504 (2001) Oxygene E( 2 P 1/2 )  E( 2 P 3/2 ) = 177.084(14) cm -1 Sulfur 32 S  : E( 2 P 1/2 )  E( 2 P 3/2 ) = 483.5352(34) cm -1 32 S: E( 3 P 1 )  E( 3 P 2 ) = 396.0587(32) cm -1 J. Phys. B39, 1409 (2006) OH A( 16 O 1 H) = 14 740.982(7) cm -1 J. Chem. Phys. 122, 014308 (2005) SH A( 32 S 1 H) = 18 669.543(12) cm -1 J. Mol. Spec. 239, 11 (2006) the Green function is known Kramer et al., Europhys. Lett. 56, 471 (2001) 2-trajectory interference: same phase as for B = 0 (invariance) 4-trajectory interference jet d’ion négatifs détecteur solénoïde 2 m 23 cm 42 cm 62 cm 13 cm laser Longitudinal and transverse magnetic field coils detector B//F solenoid negative ion beam laser transverse B  F coils Jet S Classical trajectories 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) 100 mA ≡ 126 µT = 1.26 G Effect of a magnetic field : transverse case Trajectory and fringe shifts ? Negative ion General problem: in the presence of a Lorentz force, will the trajectory shift be equal to the shift of the interference fringes ? What does the ring pattern become in the presence of a transverse magnetic field ? Experimental results Laser The interference phase remains invariant ! B  0B  0 B  0B  0 ± 8.10 -3 cm -1 dispersion due to electric field inhomogeneities 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) American Journal of Physics 66, 38 (1998) F = 423 Vm -1  = 1.2 cm -1 0 = 0.045  m a = 0.35  m Fq m 2/3 0 3 24    Isotopic shift Fine structure of atoms and ions Molecules Geometrical effect on the interference patterns As expected: Experimental results Influence of a magnetic field on the interference phase i.e. at 1 st order proportionally to the B flux : Defining the momentum : The local phase shfit The interference pattern moves as a whole ! In the far-field approximation The shift of the envelope Fringe shift vs. trajectory shift Do electron affinities vary with the magnetic field ? Geometric phase Magnetic phase Trajectory curvature will make a contribution at a higher order. The expected phase variation, at a fixed position on the detector, will be : One gets a wave-function The phase of the interferogram will thus change by Numerically : z a Fz 0 Détecteur B-dependent according to and the phase shift The fringe displacement is such that Comparing the gradient One gets: Principle: Y.N. Demkov et al., JETP Lett. 34, 403 (1981) F ~ 291 V/m = 596.89122 nm B = 1.9 µTB = 27.8 µTB = 56.1 µT B = 82 µT B = 110.4 µTB = 137.5 µT F ~ 195 V/mB = 5.10 -8 T