Transcript The Geiger-Muller Tube and Particle Counting

The Geiger-Muller Tube and
Particle Counting
• Abstract:
– Emissions from a
radioactive source were
used, via a Geiger-Muller
tube, to investigate the
statistics of random events.
Unexpected difficulties
were encountered and
overcome.
• Collaborators
– Michael J. Sheldon (sfsu)
– Justin Brent Runyan (sfsu)
Overview
• Background
– Statistics
• Poisson / Gaussian distribution functions
– equipment and methods
• Initial Results
• What went wrong?
– Speculation
– A workable hypothesis
• The search for a solution
• Conclusion
Poisson Distribution Function
• Conditions for Use
– You Have n independent trials.
– The probability (p) of any particular outcome is
the same for all trials.
– n is large and p is small
• The Poisson function says:
– f(x, ) = ^x* e^- / x!
– Where  = np
Gaussian Distribution Function
• The Gaussian says
– g(k;x,) = 1/ (2)^1/2 * exp -((k-x)^2/ 2^2)
– where k is the specific event, x is the mean and
 is the standard deviation.
– For our experiment an estimate of the error is
 = x^1/2
Equipment and Methods
• Source of random
events: Gamma
Radiation from Co-60
• Co-60 has long half
life compared to the
length of the
experiment
• # of emissions/t is
random
Equipment and Methods
• G-M tube allows
observation of -ray
emissions
• Tube is filled with low
pressure gas which is
ionized when hit with
radiation.
• G-M tube sends week
pulse to interface.
Equipment and Methods
• The interface beefs up
G-M tube signal for
computer.
• Caused problems for
us.
Equipment and Methods
• Signal from interface fed into computer.
• We counted number of emissions in given
time intervals.
• Data was analyzed with scientist, graphs
created with excel and MINSQ.
• We tested statistical theories:  = x^1/2 , fit
of Gaussian/ Poisson dist. Functions etc...
Initial Results
• To see if  = x^1/2 we did several runs with
t = 10 sec
• Our results were not so hot.
• However multiplying by 2^1/2 helped?
Run
# of sources # of intervals
1
2
3
4
2
4
2
2
X (mean)
19
57
21
35
341
385
285
275
X^1/2
18
20
16
17
Initial Results: Gaussian dist.
Histogram
• Obviously something
is wrong
• There are two
Gaussian dist. One for
even bins one for odd.
• The even dist. Is larger
than the odd.
80
70
60
40
30
20
10
Bin
63
69
51
57
39
45
27
33
0
15
21
Frequency
50
Initial Results: Poisson Dist.
• Again the distribution
function dose not
exactly fit
• It is to skinny and to
tall.
What went wrong?
Histogram
100
90
80
60
50
40
30
20
Bin
68
62
56
50
44
38
32
26
20
0
More
10
14
Frequency
70
• How do we solve this
problem.
• By expanding the
width of the bins we
included odd and even
counts in a single bin
and got a nice
Gaussian.
What Went Wrong?
• By replacing k with
k/2 in the Poisson dist.
We were able to make
it fit better.
Speculation: What’s really going
on?
• Brent speculated that the radiation from the
source was coming out in pairs so that
usually both particles made it into the
detector and we got even numbers of
counts.
• Pfr. Bland knocked this down.
• The real problem was that the computer was
double counting the signal from the
interface.
A Workable Hypothesis
• The pulse from the GM tube was short and
weak.
• The signal out of the
interface was long and
of constant voltage
and duration.
• The computer was
consistently double
counting this signal.
The search for a solution.
• We knew that a capacitor was needed to
round out the pulses from the interface.
• First we could not reproduce the problem.
• We could not get at the problem.
• The multitude of signal wires was
confusing.
• We were desperate!!
Conclusion
• We had all given up when….
• The Magic combination was Blue to Yellow
Green and Black.
• We were not able to run any simulations.
• Questions still remain about what line the
signal ran on and why this combination
worked.