The Fine Structure Constant

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Malcolm Hunter
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1 3.6, 00 AMO Seinar The Fine Structure Constant Li-Bang Wang Physics Departent, National Tsing-Hua University Origin of fine structure constant Introduced by Soerfeld in 96, as relativistic correction of Bohr odel. non-relativistic relativistic correction En = α 3. 6 c = 4 α c n 4n n ev n 3 ( l + / ) α = e hc 37 Speed of electron / speed of light

2 Fine structure splitting spin-orbit interaction (L S, fine structure) 4 α c 4n n ( j + / ) 3 The sae agnitude as relativistic correction α = e hc 37 The strength of electroagnetic interaction Irrelevant to strong, weak and gravitational forces Standard Model description Usually use coupling constant g to denote the strength of an interaction Electroagneic: g e = (4πα) / Strong: g s Weak: g w and g z Interestingly, g w =g e /sinθ w and g z =g e /sinθ w Cosθ w where θ w =Weinberg Angle Electro-weak unification

3 Unification of all forces Supersyetry vs Standard Model EM force QED the ost well-tested theory Fine structure constant α the ost precisely deterined constant aong four forces α = e hc 37 Need to know e /h α - = (98) Gabrielse, Hanneke, Kinoshita, Nio, and Odo, Phys Rev Lett 97, 3080 (006) 3

4 How to easure α Neutron h/ n easureent h/ A easureent of ato A Magnetic oent of electron Heliu fine structure Muoniu and hydrogen hyperfine structure Quantu Hall effect Ac Josephson effect Neutron h/ n easureent α R = c n e h n R, c, n, e very precisely known. h/ n this is the quantity to easure De Broglie wavelength λ=h/ n v, so easure λ and v will do V: rotating polarization chopper, λ: Bragg diffraction 4

5 Neutron h/ n easureent Krueger E, Nistler W and Weirauch W 995 Metrologia 3 7 h/ A easureent of ato A α R = c A e h A h/ A this is the quantity to easure Concept of photon recoil πpulse πpulse Photon oentu hω Ground state ato excited state ato with p= hω excited state ato with p= hω Photon oentu hω Stiulated eission ground state ato with p= hω Input two photon, output two photon But ato gain kinetic energy p /=h ω / 5

Photon recoil So input photon and output photon have different energy Δω=hk / h/ easured, so is α In real experient, a technique called ato interferoeter is eployed exaple: Weiss D

6 Photon recoil So input photon and output photon have different energy Δω=hk / h/ easured, so is α In real experient, a technique called ato interferoeter is eployed exaple: Weiss D S, Young B C and Chu S 993 Phys. Rev. Lett g factor of electron what is g factor? μ = μb g s h Classical non-relativistic g= QM, Dirac Theory predict g= In reality, g=

7 g factor of electron g can be expanded as a function of fundaental constant α easure g easure αif all the required inforation known g α α = + C + C4 π π + aμτ + a hadronic + a weak + C 6 α π How to easure g Spin precession (Laror) frequency hω = g μ B L s Calibration of the agnetic field by cyclotron frequency: g B hω = q C M ω q ω e M C B L = = ωl ω Measureent on a single electron in a Penning trap α - = (98) C μ B = eh Gabrielse, Hanneke, Kinoshita, Nio, and Odo, Phys Rev Lett 97, 3080 (006) 7

8 Heliu fine structure heliu: siple ato one can calculate Contribution Nonrelativistic energy Relativistic correction Anoalous agnetic oent Mass polarization (SMS) Second-order ass polarization Finite ass correction (NMS) QED correction (Lab shift) Finite Nuclear Size Magnitude Z Z 4 α Z 4 α 3 Z μ/m Z (μ/m) Z 4 α μ/m Z 4 α 3 ln α Z 4 (R N /a o ) electron electron nucleus Heliu spectroscopy Fine structure splitting test theory, deterine α Measure fine structure splitting to khz αto part per 0 8 Soe unsolved probles in theoretical side 3 P 0 3 S 4 He 8

9 Previous attept uncertainty of theory and exp < khz difference = 0kHz and 0kHz 3 P 0-3 P - LENS '04 Harvard '05 York '0 Harvard '05 York '00 N. Texas '00 Theory Pachucki '06 [4] Drake '0 [5] Pachucki '06 [4] Drake '0 [5] Experient Theory Experient Frewquency khz Frequency khz Hydrogen and uoniu Hydrogen, sipler than heliu Theory 00% correct, but Proton is spin ½ particle, (heliu spin 0) Hyper fine structure ore sensitive to probe agnetic oent Muoniu? anti-uon+electron or uon + positron, difficult 9

10 Quantu Hall effect Quantu Hall effect R=h/ne α = e R: resistance, n: an integer hc Can be very precise in principle The difficulty is to calibrate a standard Oh Josephson effect DC Josephson effect: current through an insulating junction due to Tunneling (no E) AC Josephson effect: DC voltage V across the junction ay also give rise to a AC current with frequency ω ω=ev/h, one can easure ω and V very precisely, and deterine e/h to 0-6 Unfortunately αproportional to e /h 0

11 suary The constancy of constant Is the constant really constant?

Stern-Gerlach Experiment

Stern-Gerlach Experiment Stern-Gerlach Experient HOE: The Physics of Bruce Harvey This is the experient that is said to prove that the electron has an intrinsic agnetic oent. Hydrogen like atos are projected in a bea through a