The muon lifetime experiment
PART V: Four different versions of the experiment

THIRD EXPERIMENT - Runs 10 to 11
TAC to MCA (i.e. full NIM)

Idem previous version, this time with TAC output to multi-channel analyzer(MCA) direct input. This is the best quality instrumentation available in the neighbourhood. One question still remains: is a constant-fraction discriminator (CFD) necessary? The question is: do we have different risetimes for muons and electrons?.

Common to all experiments: BIG scintilator, HV=2000V, Ortect 436 discriminator, Canberra 2143 time analyzer and TN-7200 MCA.

Variables: TAC range and discriminator level.

Experimental layout

Run 10

TAC range 10 μs. Discriminator level = 4.5, output rate (START) ~10 Hz. Reduced probability of eventual stops (see calculations).

4000 stoped and detected muons y ~4 days (416082 seconds). Muon stop rate ~1 every 100 seconds. Measured τμ = 2.37 μs

Full histogram (4096 channels)

Reduced histogram (128 channels)

Mean value approximates lifetime very well because there is a very small probability of eventual STOP (almost no background). But it is not exact because the tail of the exponential was not recorded.

In order to record at least 5 &tau and fit better, the TAC range should be 20 μs. Repeat experiment.

Run 11

TAC range 20 μs.
Discriminator level = 2.8 -> output rate (START) fluctuating between 25 and 10 Hz along the days (depends on light, climate, preassure?).

Tue Jul 14sunny25 Hz
Wed Jul 15sunny25 Hz
Thu Jul 16clouded12 Hz
Fri Jul 17....
Mon Jul 20partially clouded18 Hz
Tue Jul 21rainy10 Hz9 C
Wed Jul 22rainy, very cold0 C
Thu Jul 23sunny, very cold13 Hz2 C
Fri Jul 24sunny, cold14 Hz7 C

Probability of eventual STOP approximately equal to probability of valid STOP when 25 Hz (see calculations). This means that there should be more background in the histogram, but I can't tell how much as rate fluctuates. Rising a bit the probability of eventual STOPs provides a better background reference and allows recording with lower discriminator level, reducing the true event rejecting. Decay rate should improve.

Run 11 Full histogram

Run 11 Reduced histogram

Fit result:

τμ = 2.065 μs

Nice result: this time τμ < 2.2 μs (see muon capture).

Mean value does not reflect lifetime because there is a significant background. While muons have a mean life of 2.2 μs, background in the 16 μs range has an 8 μs mean. After fitting, background rate can be calculated with this data.

OCTAVE FIT (see scripts)
octave:1> mu11
eventos:9541 fit:2.03 media:3.40
octave:2> NN=128;N1=4;N2=128;mu11_fix
fit = 2.0655
fondo = 16.205
residuos = 0.97600
media_calc = 3.1307
media = 3.3978
octave:3> media_calc=((fondo*NN)*8.0+(8502-(fondo*NN))*fit)/eventos
media_calc = 3.1307
octave:4> NN*fondo
ans = 2074.2
octave:5> eventos-NN*fondo
ans = 7466.8

From 9541 events, NN*fondo = 2074.2 are eventuals -> 7466.8 muon decays.
Real time RT=866000 s.
Decay rate = 1 muon / 116 s
Eventuals = 1 / 417 s


Like in the previous experiment, a disadvantage of this method is that absolute time information of the events is not recorded, so rate vs. time calculations are not available.