The Geiger-Muller Tube and Particle Counting

1. 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)

2. 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

3. 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

4. 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

5. 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

6. 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.

7. Equipment and Methods • The interface beefs up G-M tube signal for computer. • Caused problems for us.

8. 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...

9. 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?

10. 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.

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

12. 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.

13. What Went Wrong? • By replacing k with k/2 in the Poisson dist. We were able to make it fit better.

14. 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.

15. 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.

16. 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!!

17. 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.