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?

Initial Results: Gaussian dist. Obviously something is wrong There are two Gaussian dist. One for even bins one for odd. The even dist. Is larger than the odd.

Initial Results: Poisson Dist. Again the distribution function dose not exactly fit It is to skinny and to tall.

What went wrong? 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 G- M 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.