Cosmic Muons
Positive and negative muons are copiously produced in
the upper atmosphere as the result of hadronic showers
caused by multi-GeV cosmic protons and nuclei. At sea
level, the muon-momentum distribution peaks around
500 MeV/c. Three inch of NaI will cause a minimum
ionizing muon to lose some 36 MeV and even more for a
slower muon due to the rise of ionization density described
by the Bethe-Bloch formula. Hence, a 3-inch NaI crystal
can stop a fraction of the passing muons.
Muon Reactions
When that happens, a positive muon will come to rest
in the crystal, bind with an electron to form “muonium”
and decay with a 2.2 μs life time. In the ensuing
three-body decay, the only charged particle is a positron,
which can carry an energy of up to 53 MeV.
A negative muon will bind with a nucleus, Na or I, and cause
a nuclear reaction. This process happens much faster than
the free-space muon decay, and there is little contribution
to the signature channel we use to recognize a positive muon
decay: Namely the emergence of a very energetic charged particle
more than 2 μs after the muon was stopped. Note that in a
plastic scintillator, the negative muon capture is comparatively
slow, and the effective negative muon life time is similar to
that of the positive muon.
Muon Signature
As the experimental signature for the decay of a stopped
positive muon we look for an initial huge energy deposit
in the NaI crystal (> 6 MeV), which is to be followed by a
secondary energy deposit (> 1.3 MeV) within a time window
of 2 μs to 10 μs after the initial deposit.
We apply the high energy trigger thresholds to suppress any
background from naturally occurring radioactivity.
The good stopping power of NaI ensures that a fair fraction of
the muon-decay positrons will indeed deposit more than 1.3 MeV
in the scintillator.
Device Settings
For this experiment we programmed the eMorpho to use a 1.1 kΩ
transimpedance to convert the PMT anode current signal into a voltage
for the 10-bit ADC with its 1.056 V voltage swing.
We adjusted the PMT high-voltage such that a 662 keV pulse
would produce a pulse height of 55 ADC bins. We then set the trigger
threshold to 500 ADC bins or 6 MeV. Given a typical DC-offset of
120 ADC bins, the dynamic range of the ADC corresponded to about
900 bins or 10.8 MeV.
We programmed the eMorpho to accept waveforms even if the signal
went out of range temporarily, since the stopping muons were
depositing much larger energies.
We set the pretrigger delay to 100 so that the first pulse would
be shifted by 100 samples into the display. This leaves about
900 samples for the post trigger part of the waveform. At a
sampling rate of 80 MHz this corresponds to 11.25 μs,
as shown in the figure below.
A huge stopped-muon pulse (clipping) followed by a 7.2 MeV pulse
from a positron created in the subsequent muon decay.
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