Physics307L:People/Knockel/Notebook/071010: Difference between revisions
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<math>G(x)=\frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{\left(x-a\right)^2}{2\sigma^2}}</math>, | <math>G(x)=\frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{\left(x-a\right)^2}{2\sigma^2}}</math>, | ||
where 1/√(<math>2\pi\sigma^2</math>) is the normalization coefficient. | where <math>a</math> is the mean, <math>\sigma</math> is the standard deviation, and 1/√(<math>2\pi\sigma^2</math>) is the normalization coefficient. | ||
==Equipment== | ==Equipment== | ||
Revision as of 11:36, 12 October 2007
Poisson Statistics
experimentalists: me (princess bradley) and Nikipoo
Goal
By measuring random events that occur very rarely, I hope to analyze how well a Poisson and a Gaussian can fit the data. I believe the random events we are measuring to be cosmic radiation, but I am not sure. We are measuring whatever radiation can make its way through a "house" of lead bricks and then activate a NaI scintillator in the physics building at UNM.
Theory
The Poisson and Gaussian distributions are probability functions. I will assuming you know what probability functions are. Whatever radiation we are measuring is randomly occurring which makes the use of these distributions appropriate.
Poisson Distribution
The Poisson distribution is given by
[math]\displaystyle{ P(x)=e^{-a}\frac{a^x}{x!} }[/math],
where [math]\displaystyle{ a }[/math] is the mean, and [math]\displaystyle{ e^{-a} }[/math] is the normalization coefficient. The standard deviation of the Poisson is
[math]\displaystyle{ \sigma=\sqrt{a} }[/math].
Gaussian Distribution
The Gaussian distribution is given by
[math]\displaystyle{ G(x)=\frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{\left(x-a\right)^2}{2\sigma^2}} }[/math],
where [math]\displaystyle{ a }[/math] is the mean, [math]\displaystyle{ \sigma }[/math] is the standard deviation, and 1/√([math]\displaystyle{ 2\pi\sigma^2 }[/math]) is the normalization coefficient.
Equipment
- photomultiplier tube (PMT) with NaI scintillator
- cables?
- about 40 lead bricks (needed to built a house for the PMT)
- high voltage power supply for the PMT (1000 V should do the trick)
- a means of acquiring data from the PMT so that frequency can be measured accurately (this is the trickiest part!)
I have given the general equipment needed since the specific equipment I am using will not affect the result of counting the signals from the PMT.
As for how a acquired data from the PMT, we used an amplifier to amplify the signal, which we connected to some chip in a computer, which works with really shitty software to, after changing many settings, measure frequency.
Our setup
- We plugged in the high voltage power supply to the power outlet and then to the PMT using ___.
- Without using any radioactive source, we built a lead house around the PMT using the bricks (I think we did this to prevent local radioactive sources from altering the data, but I'm not sure).
- We then used a really weird contraption that connected the power supply to an amplifier to many other stuff to power an amplifier which we connected to the PMT and the computer chip.
- We then changed just about every setting that exists on the software (the shitty graphical interface made this difficult) to allow it to measure frequency (counts during a predetermined unit of time) and put this frequency DATUM into a "bin." The program will fill many of these bins over a long period of time before stopping.
