Download background rate calculation

Muon Lifetime Notes
Be sure you understand the following calculations and repeat them for the
actual conditions in your experiment.
Let’s consider a case in which the singles rate (rate of single pulses from the
counter) is 10 counts/sec and the rate of detected muon stops (which result in
pulse pairs) is 1 stop/100 sec. We look for the muon decay pulse in a 10µs
window after the first pulse from the counter. This is 4.5 lifetimes and includes
most real events.
What singles rate is expected from cosmic rays?
Calculations of accidental rate:
We calculate the accidental background rate, which is due to two unrelated
pulses falling within the 10µs window:
10-5 sec x 10/sec x 10/sec = 10-3/sec=10% of real rate
Study singles rate vs. voltage using the discriminator and scaler (discriminator
set at 30mv, its minimum threshold). DO NOT EXCEED 1300 VOLTS.
Calculate the expected accidental pulse pair rate for each voltage. Make a
rough measurement of the rate of pulse pairs. Use this data to choose an
appropriate voltage setting.
Correcting for accidental background:
The accidental background has an average separation between pulses of 5 µs.
This can be considered as an effective lifetime for the accidental events, which
is averaged in with the real muon events in proportion to their number.
Loss of signal due to background:
If a background count cuts short a real muon decay, or comes prior to real
event by less than 10µs the event time is altered and we lose that real event.
The probability that a real event is lost due to an accidental count occurring in
a
+/-10 µs window for the assumed rates is small and can be ignored:
20µs x 10/sec =2 10-4 = .02%
Delayed time interval:
To study accidental background, record events where the second pulse
comes in a 20-30 µs interval after the first. Only .01% of muons remain at 20
µs, so for the assumed rates, accidental background is 1000x the real rate.
The accidental background in the delayed 10 µs interval should be neatly the
same as in the prompt 10 µs interval.