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The Stern-Gerlach Effect for Electrons*

The Stern-Gerlach Effect for Electrons*. Herman Batelaan Gordon Gallup Julie Schwendiman TJG Behlen Laboratory of Physics University of Nebraska Lincoln, Nebraska 68588-0111 * Work funded by the NSF – Physics Division. Electron Polarization. example : P = 0.3: 65% spin-up

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The Stern-Gerlach Effect for Electrons*

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  1. The Stern-Gerlach Effect for Electrons* Herman Batelaan Gordon Gallup Julie Schwendiman TJG Behlen Laboratory of Physics University of Nebraska Lincoln, Nebraska 68588-0111 *Work funded by the NSF – Physics Division

  2. Electron Polarization example: P = 0.3: 65% spin-up 35% spin-down

  3. Atomic Collisions (from G.D.Fletcher et alii, PRA 31, 2854 (1985))

  4. Work done at NIST Gaithersburg by M.R.Scheinfein et alii, RSI 61, 2510 (1991)

  5. From The Theory of Atomic Collisions, N.F.Mott and H.S,W. Massey

  6. Anti-Bohr Devices a) N +V S -V (Knauer)

  7. b) (Darwin)

  8. N c) (Brillouin)

  9. 1930 Solvay Conference – “Le Magnetism”

  10. See e.g., • Cohen-Tannoudji, Diu, et Laloë • Merzbacher • Mott & Massey • Baym • Keβler • Ohanian………..

  11. Z I e-

  12. Which ball arrives first ? A) high road B) low road C) simultaneously

  13. x e- Hz vz Hx

  14. CALCULATIONS eigenenergies integrate (spin-flip probability < 10-3)

  15. CHOOSE INITIAL CONDITIONS

  16. require Δzspin~ 1mmuse Bo = 10T, a = 1 cm (¡105A!)→ vz ~ 105 m/s (30 meV)→ t ~ 10μs → Δxi ~ 100μm

  17. H. Batelaan et al., PRL 79, 4518 (1997)

  18. (n, ms) E-(pz2/2m) 1, +1/2 2, -1/2 0 Landau States En = (pz2/2m) + (2n + 1)μBB ± μBB n = (0,1,2,3….) 0, +1/2 1, -1/2 0, -1/2

  19. NB - The net acceleration of the (leading) spin-backward electrons is zero.

  20. Pauli Case Landau Case ΔrΔp ~ ħ/2 ΔrΔp ~ ħ/2 B B

  21. (always || ) MAGNETICBOTTLEFORCES (always || )

  22. Landau Hamiltonian • KE • ~ -μL·B • ~ -μB·B Fully quantum-mechanical calculation (field due to a current loop)

  23. G.A.Gallup et alii, PRL 86. 4508 (2001)

  24. S W F = S/W

  25. 106 Hz TDC φ 1m, 104 turns, 5A 2 cm bore, 10T ~ ~ APERTURES 10μm 1μm Gedanken apparatus

  26. (n, ms) E-(pz2/2m) 1, +1/2 2, -1/2 0 Landau States En = (pz2/2m) + (2n + 1)μBB ± μBB n = (0,1,2,3….) 0, +1/2 1, -1/2 0, -1/2

  27. Δv v Δz; Δt = Δz/v B δ δ δ • Gradient = B/ δ; Gradient force = ±(μBB/ δ); accel/decel = ±(μBB/ meδ) = ± a • If 2aδ << v2,time lag = Δt = 2aδ/v3 • Let B = 1T, δ = 0.1m, Ebeam = 100 keV (β = 0.55) → Δt = 4 x 10-19 s (!) • Since the transit time threough the magnet = 2 ns, R ~ 10-8

  28. Conclusions • The Bohr-Pauli analysis of Brillouin’s proposal is wrong. • More generally, their prohibition against the spatial separation of electron spin based on classical trajectories through macroscopic classical fields fails. • A proper semi-classical analysis of Brillouin’s gedanken experiment yields Rayleigh-resolved spin states. • A rigorous quantum-mechanical analysis (corresponding to reality) yields complete and, in principle, arbitrarily large separation of spin states. • Experiments to observe such spin-spitting are feasible (i.e., not totally insane), but would be very difficult.

  29. x e- Hz vz Hx y z

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