Muon Lifetime Experiment: A Model

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Muon Lifetime ExperimentA Model
presented by Steve Kliewer
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Overview

• Experimental design
• Parameters affecting expected count rate
• Source of muons
• Detection of muons and electrons (detector
  efficiency)
• Capture of low energy muons
• Decay of muons into electron
• Loss of electrons in cavity
• Expected frequency of timed muon decay.

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Purpose
To better understand the processes involved in
muon capture, decay, and detection so that we can
better predict the effects of changes in geometry
and cavity medium.
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The Muon Lifetime Experiment Design
A muon enters thru A and is trapped in the
cavity. After a time it decays and an electron
exits thru A, B, C or D. A frequency graph of
counts vs decay time is analyzed
80 cm
A
C
D
20 cm
B
Muons, no matter how old they may already be,
decay exponentially. N N0 e-t/? dN/dt -N /
? ? -N / dN/dt This is the Muon Lifetime
20 cm
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The Muon Lifetime Experiment Continued
Timing starts when count A and not( B or C or
D) Timing stops when count A xor B xor C xor D
or timeout
80 cm
A
C
D
20 cm
B
The cavity is filled with phone books ?
Density 0.64 g/ cm3 V Volume 32000 cm3 A
Top Surface area 1600 cm2
20 cm
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Expected Count Rate
ND N? f1 f2 f3 ND frequency of timed
muon decay (counts/s) N? Frequency of
incoming, trappable muons f1 Fraction of
incoming muons that are detected (detector
efficiency) f2 Probability that a decay
electron will escape f3 Fraction of escaping
electrons that are detected
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Cosmic Rays in Space

• Primary Cosmic Rays are particles accelerated
  by astrophysical sources e.g. AGN,
  supernovae, solar flares
• Mostly made up of protons (some electrons and
  helium, C, O, Fe nuclei)
• Energies from a few GeV to more than 100 TeV
• They are charged particles and therefore are
  affected by magnetic fields both interstellar as
  well as Earths.

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Cosmic Ray interactions
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Cosmic Rays Particles

• Particle Mass ? mean life Primary
  decaySym MeV/c2 s
• p Proton 938 gt 1025 n/a
• ? Pion, charged 140 2.6 x 10-8 ? ??
• ?0 Pion, neutral 135 8 x 10-17 2 ?
• K Kaon, charged 494 1.2 x 10-8 ? ?? K0 Kaon,
  neutral 498 10-10 ? ?-, 2 ?0
• E Electron 0.51 gt1024 n/a
• ? Muon 105.7 2.2 x 10-6 e ??e ??
• ?e Neutrino, Elec lt3eV gt1025 n/a
• ?? Neutrino, muon lt0.2 gt106 s ?

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Cosmic Rays in Our Atmosphere

• Primary Cosmic particles interact with our
  atmosphere via strong force, bremstrahlung,
  Cerenkov radiation, as well as ionization
• Strong Interactions produce kaons pions
• These particles decay almost immediately into
  ?, ?, e, ?, ?
• ? rays interact by electron-positron pair
  production
• ? particles decay very quickly to ? e.
• electrons are quickly stopped by the dense
  atmosphere
• Most ? are produced at 15km altitude, They
  lose about 2 GeV to ionization and arrive at the
  surface with a mean energy of about 4 GeV.

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Cosmic Rays at Sea-Level

• From the Review of Particle Physics
• Mean energy is 4 GeV
• Energy spectrum (dN/dE) is flat below 1 GeV
• Low energy muons (E lt 1 GeV) are mostly
  vertical. (Solid angle 1 sr)

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Muon Energy Spectrum
Derived from Fig. 20.4 of Particle Data Review
dN/dE 0.004 µ/(GeV cm2 s sr) For energies up to
1 GeV
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Muon Trapping
Muons will be trapped in the paper-filled, 30 cm
deep cavity if they have energies 0 lt Eµ lt 50
MeV ?Eµ 50 MeV ?E 1.21 R 11 dE/dx 1.2
MeV/cm
Based on pdg.lbl.gov ? 0.64 g/cm3
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Incoming Muon Rate

• The expected rate of trapped muons is
• N? dN/dE ?E A S dN/dE count rate
  per GeV per cm2 per steradian ?E Range of
  muon energies trapped A Area of top of
  detector S Solid angle of incoming muon
  directions that are included
• N? 0.004 (1/GeV cm2 s sr) 0.05 GeV 1600 cm2
  1 sr
• N? 0.32 muons/s 19 muons / min

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Detection scintillator PM

• The passage of muons is detected using a
  plastic scintillator (polyvinyl toluene)
• dE/dx 2 MeV/cm
• Refractive index 1.58
• Max emission 425 nm
• Pulse width 2.5 ns
• The PM tube and electronics detect the pulse with
  an efficiency, f1, which is determined
  experimentally
• f1 0.9 f3

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Decay
µ? e ??e ?? Rest masses mµ 106 MeV/c2
Me 0.5 MeV/c2 M?e 3 eV/c2 M?? 0.19
MeV/c2 105 MeV of kinetic energy will be randomly
partitioned between the resultant three
particles.
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Electron energies
E2 m2 p2 (c 1) As long
as m ltlt E then E p Momentum and energy must be
conserved. The momentum (energy) of the electron
can be, at most, ½ (i.e. 52 MeV) of the available
momentum.
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Electron Range
?E 1.9 R - 5.9 dE/dx 1.9 Mev/cm
The average distance to escape the cavity is 12
cm. Therefore, We will assume that Electrons
will be trapped in the paper filled cavity if
they have energies 0 lt Ee lt 14 MeV ?Ee 14 MeV
Based on pdg.lbl.gov ? 0.64 g/cm3
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Electron Energy Spectrum
Electrons with energies up to 14 out of 52 MeV (
.26) will be lost. The fraction of electrons
that will escape the cavity, f2 .8
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Expected Count Rate
ND N? f1 f2 f3 ND frequency of timed
muon decay (counts/s) N? Frequency of
incoming, trappable muons dN/dE ?E? A
S A W L ?E? 1.21
H 11 f1 Fraction of incoming muons that are
detected (detector efficiency) f2 Probability
that a decay electron will escape ?Ee / 52
MeV 1 - (1.9 R - 5.9) / 52 f3 Fraction
of escaping electrons that are detected ND 0.32
muons/s 0.9 0.8 0.9 ND 0.2 decays/s 12
decays/min
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Conclusion

• We should expect a count rate of decay
  electrons from trapped muons of about 10 per
  minute