a p m e q a 6s 6p p t pb - williams college
TRANSCRIPT
A PRECISE MEASUREMENT OF THE ELECTRIC QUADRUPOLE AMPLITUDE IN THE 6s26p2 3P0 → 3P2 TRANSITION IN PBELI HOENIG ’17, DR. MILINDA RUPASINGHE, PROF. TIKU MAJUMDER
Work supported by NSF Grant 1404206
INTRODUCTIONMotivations• Precise measurements and accurate theoretical models of atomic
structure in Cs, Tl and Pb provide atomic-physics based tests ofthe Standard Model.
• Experimental measurement, E related to quantity predicted bySM, QW, according to E = QW C(N,Z), where C(N,Z) is atomicstructure factor.
• The Goldilocks zone: tractable atomic structure and a large nu-clear mass.
Current Precision of Experiment and Theory• Recent advancements [Porsev et al., 2016] in Pb atomic theory re-
vive element’s relevance in atomic physics tests of SM.
Element Theory C(N,Z) Experiment ECs .27% [Porsev et al., 2009] 0.35% [C.S. Wood et al., 1997]Tl 2.5% [Kozlov et al., 2001] 1% [Vetter et al., 1995]Pb 4% [Porsev et al., 2016] 1.2% [Meekhof et al., 1995]
• Currently, few independent experimental measurements of Pbatomic structure to check new wavefunction calculations.
• Our measurements aim to guide the further refinement of thisnewly developed theory.
CURRENT AND RELEVANT WORKPresent Work
• Measure ratio of theElectric Quadrupole (E2)6s26p2 3P0 → 3P2 to Mag-netic Dipole (M1) 3P0 →3P1 transition amplitudesin 208Pb.
Previous Work in the Ma-jumder Lab• In 1999, measurement of
Tl E2/M1 amplitude ra-tio completed [Majumder,Tsai, 1999].
• Measurement of E2/M1 =0.239(4) agrees well withtheory (E2/M1 = .237[Safronova et al., 2005]) andobtained ∼ 1% accuracy.
• Mixed E2/M1 transition,6s26p 2P1/2 → 2P3/2.
• Used a single laser, ana-lyzed a single spectrum toextract ratio; presently wemust alternately record twoseparate spectra.
208Pb Low Lying States
203Tl Low Lying States
EXPERIMENTAL SETUP
SIGNAL DETECTION• The Faraday rotation method detects changes to the overall polar-
ization of the laser light.
I(ν) = IoT (ν)[2φmφpb cos(ωt) +
12φ
2m cos(2ωt) + φ2pb +
12φ
2m
].
• Two oscillating terms whose ratio leads to pure rotation curve:
1f : 2IoT (ν)φmφpb 2f :1
2IoT (ν)φ
2m
Apparatus is sensitive to rotationsdown to 1µrad.
Polarimeter & Glan-Thompsan prism
INDUCING OPTICAL ROTATION
• Longitudinal magneticfield induces Zeeman split-ting amongst magnetic sub-levels.
• Differential phase shift andabsorption for σ+ and σ−polarized light.
• Difference of two disper-sion shapes leads to Fara-day lineshape.
SPECTRA FOR 939 NM AND 1279 NM TRANSITIONS
RESULTS AND INTERPRETATIONPreliminary Result
〈2||E2||0〉〈1||M1||0〉
= .191(03)(10)
Data Interpretation
• Ratio cancels n` leavesf(ν) and 〈T 〉2:φpb ∝ n` 〈T 〉2 f(ν).
• Experimental Faraday peakratio depends on the line-shape parameters.
• Need reliable values forthe Lorentzian and Gaus-sian widths.
Height of convolved shape is scaledup by ten.
〈2|E2|0〉〈1|M1|0〉
=[ F (ω0)expmt,e
F (ω0)expmt,m∗Fpeak,m
Fpeak,e∗ ω0,m
ω0,e∗ gl,mgl,e
]1/2• Ratio depends directly
on: Observed spectral am-plitude, lineshape peak,Landé g-factors, laser fre-quencies.
• Reduced matrix element re-lated to observed ratio ac-cording to Wigner-Eckarttheorem. Propagation of Lorentzian Width
Error.
〈2||E2||0〉〈1||M1||0〉
=
√5
3
〈2|E2|0〉〈1|M1|0〉
FUTURE WORK
Immediate• Explore analysis methods.
Lorentzian width accuracyparticularly elusive.
• More data to be collected• 207Pb measurement (pres-
ence of hyperfine struc-ture).
In Coming Years• Measure atomic polariz-
abilities in nearby electricdipole transitions with theatomic beam unit.
• High vapor pressure of leadand single step transition,but small fractional thermalexcitation.