Deuterium Contamination in Cap

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Deuterium Contamination in µCap

• Brendan Kiburg
• 11/25/03

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Negative muons interacting with hydrogen have
lots of options.
µpd
3Heµ
µ
µd
n
transfer
n?µ
fusion
µp
3Heµ?
d
capture
e ?e?µ
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Deuterium concentration affects the observation
rate.

• Muonic deuterons wander
• Fitting employs event reconstruction technique
• Deuterons wander away from the muon stop in a
  time-dependent manner
• Early to late processes alter the observed rate

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Muonic deuterons wander due to the
Ramsauer-Townsend Effect.

• Consider lowest order partial-wave expansion at
  low E
• ?l0 ? sin2 ?l for ?l 180 then ?0

E must remain low so only l 0 matters ½
wavelength in the box, outside the same
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The µds are hardly influenced by the protium
potential and diffuse quickly at this energy.

• At experimental density, v 10 cm/µs
  .
• µd p ? µd p has RT minimum at 1.6 eV.
• Also see this effect for electrons scattering
  off of argon, krypton and xenon

EEC TRIUMF 94
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Defining an event depends on the TPC and
reconstructed decay electron vector.

• Worry about wandering µd finding walls (high Z ?
  capture).
• Fiducial Volume Cut
• Worry about event reconstruction.
• Will a wandering µd escape this region?
• EPC1, EPC2 will define trajectory.
• An acceptance cone/cylinder can be defined
• This needs to match a muon stop vertex.

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Decay e vectors need to point to muon stops
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Muonic atoms that wander will pull the observed
rate.

• If the muonic hydrogen atom diffuses more than
  the distance between muon stop point and electron
  decay point allowed by the event reconstruction,
  the event is lost in the analysis. As the
  diffusion range increases with time, this
  introduces a time dependent efficiency loss,
  faking a faster decay rate. TP, 10

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Wanderers pull the rate by depleting the pool of
potential decay muons.

• dnp/dt -(?o ?cap)n
• np(t) e - ?t
• but for µd
• dnµd/dt -(?o ?cap ?wander(t))n
• nµd(t) e - ?t

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The number of muons available to decay depends on
the number that havent wandered away.

• n(t)e?t P(no transfer before t)
• P(transfer at t)P(r, t-t)
• ? transfer rate, f t-t
• n(t)e?t e-?t ? ?e-?tp(r, t-t)dt
• n(t)e-(??)t (1 ? ?e?fp(r, f)df)
• If p(r, f) 1 , then just n(t) e?t (you dont
  observe any transfer)
• If p(r, f) 0 , then n(t) e-(??)t (you fully
  observe the transfer)
• We need a good model of p(r, f)

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The correction to the observed lifetime is
largely dependent on the reconstruction radius.
Assumes concentration of 1 ppm. Correction
scales linearly with concentration. Experimental
precision goal of 5 /s
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We must observe something proportional to the
deuterium concentration.

• Simulation
• Me
• Measurements
• Mass spectroscopy
• Data Analysis
• A credible correction cannot only rely on
  simulation, but must come from direct
  observations. TR, 43
• Fusion events monitor this d concentration
  dependent process

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References

• Sakurai, Modern QM
• Mulhauser et. al E742 spokespersons, EEC TRIUMF
  1994
• Kammel/ µCap Internal documents
• Kammel, Clayton, Hertzog, Chitwood discussions