Muon Decay Muon Decay ExperimentExperimentLevi NeukirchLevi NeukirchUNL CROPUNL CROPSaturday Oct. 14, 2006Saturday Oct. 14, 2006

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MuonsMuons Muons are unstable leptonsMuons are unstable leptons

Average lifetime tAverage lifetime taveave = 2.20 µs = 2.20 µs**

µµ-- e e- - ++ νν ee + + ννµµ¯̄

* * Introduction to Nuclear Physics. Introduction to Nuclear Physics. Kenneth Krane. Wiley & Sons. 1988Kenneth Krane. Wiley & Sons. 1988

ee-- µµ-- ττ--

ννee ννµµ ννττ

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Experimental GoalExperimental Goal Measure muon lifetimeMeasure muon lifetime

– Build a thick detectorBuild a thick detector– Write Labview software to detect muon Write Labview software to detect muon

decay signaturesdecay signatures– Analyze data and calculate average muon Analyze data and calculate average muon

lifetimelifetime

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ApparatusApparatus 4” thick scintillator 4” thick scintillator

plateplate

Trigger detectorTrigger detector Veto detectorVeto detector

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ApparatusApparatus Why this setup?Why this setup?

µ-

e-

Signal on Ch. 1Signal on Ch. 1

11stst Signal on Ch. 2 Signal on Ch. 2

22ndnd Signal on Ch. 2 Signal on Ch. 2

Remember: µRemember: µ-- e e-- + + ννee + + ννµµ __

No Signal on Ch. 3No Signal on Ch. 3

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ApparatusApparatus

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SoftwareSoftware Labview codeLabview code

– Data collectionData collection– Data analysisData analysis

Dedicated to muon decay analysisDedicated to muon decay analysis

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Software: CollectionSoftware: Collection Sets coincidence criteriaSets coincidence criteria Writes data to .txt fileWrites data to .txt file

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Software: AnalysisSoftware: Analysis Reads .txt filesReads .txt files Computes lifetimesComputes lifetimes Writes .xls (MS Excel) histogram fileWrites .xls (MS Excel) histogram file Displays decay time histogramDisplays decay time histogram

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SoftwareSoftware

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Data AnalysisData Analysis

A = AA = A00exp[-λt] exp[-λt] (1)(1)

tt1/21/2 = ln(2)/λ = ln(2)/λ (2)(2)

ttaveave = t = t1/21/2 / ln(2) = ln(2)/λ/ln(2) / ln(2) = ln(2)/λ/ln(2) (3)(3)

ttave ave = 1/λ= 1/λ (4)(4)

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Data AnalysisData Analysis

2000 4000 6000 8000 100000

5

10

15

20

25

30

35

40

45

50

55Run 5 Decay Histogram

# of

Eve

nts

Decay Time (ns)

2857 Events2857 Events

Numerical mean =Numerical mean =

2.125 2.125 µµss

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Data AnalysisData Analysis

A = AA = A00exp[-λt]exp[-λt] (1)(1)

λλ = 0.00046 s = 0.00046 s-1-1

0 2000 4000 6000 8000 100000

500

1000

1500

2000

2500

3000

y=A*exp[R0*t]

Decay Character

Data: Data1_EModel: ExponentialChi^2 = 368.2092y0 0 ±0A 2855.18416 ±4.11335R0 -0.00046 ±9.4533E-7

Par

ticle

s R

emai

ning

Elapsed Time (ns)

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Data AnalysisData Analysis

tt1/21/2 = ln(2)/λ = ln(2)/λ ttaveave = t = t1/21/2 / ln(2) / ln(2)

ttaveave = [ln(2)/0.00046 s = [ln(2)/0.00046 s-1-1]/ln2]/ln2

= 1/0.00046 s= 1/0.00046 s-1-1

ttave ave = 2.174 = 2.174 µµss

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Data AnalysisData Analysis (2.174(2.174µs - µs - 2.202.20µs)/(2.2µs)/(2.200µs) =µs) =

1.2% difference1.2% difference

RunRun # of Events# of Events ttaveave % Error% Error

11 17801780 2.176 2.176 µsµs 1.1 %1.1 %

22 22892289 2.130 2.130 µsµs 3.2 %3.2 %

33 28572857 2.174 2.174 µsµs 1.2 %1.2 %

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AcknowledgementsAcknowledgementsThanks to:Thanks to:

Prof. Dan ClaesProf. Dan Claes Prof. Greg SnowProf. Greg Snow Prof. Herman BatelaanProf. Herman Batelaan Jason KellerJason Keller