# User:Ginevra Cochran/Notebook/Physics 307L/Poisson distribution

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## Purpose

The purpose of this lab was to explore the Poisson distribution using atmospheric muons and a scintillator-PMT. The Poisson distribution describes a set of events that occur randomly with an average rate.

## Safety

Avoid stripped wires and electrical shock. This lab is not particularly dangerous.

## Equipment

- scintillator/photomultiplier tube
- computer
- Universal Computer Spectrometer power supply
- UCS30 software

## Setup

Turn on the computer, switch on the power supply, and open the UCS30 software, in that order. Set the UCS30 mode to PHA(Amp In), and under Settings, set the High Voltage option to 1200 V. Change Mode to MCS (Internal).

## Procedure

^{SJK 22:50, 21 December 2010 (EST)}Under Settings, we selected successive dwell times from 10ms to 800ms, clicked the Go button, and saved the resulting data into a .csv file, which we then imported into Google Documents.This data was the number of muons impinging on the scintillator in the time selected.

## Data

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## Analysis

For each data set, I used Excel to count the number of channels which had x number of radiation counts, with x ranging from 1 to 35. I saved these sets of points as 2-column vectors and imported them and the original data into MATLAB, where I ran them through the following script:

window = 0.01; maxA = max(A) % maximum counts per window minA = min(A) % mininum counts per window avgA = sum(A)/length(A) % average counts avgsec = avgA/window; % average counts per second stdev = std(A) % standard deviation plot(Avector(:,1),Avector(:,2), '-o')

This generated a maximum and minimum radiation count for each set, as well as an average count, a standard deviation for the data set, and a plot showing the distribution of radiation counts per channel and their frequencies. These results are displayed below.

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This image shows the shift of the peak in the graphs as dwell time is increased. The distribution also becomes wider with increased dwell time.

## Sources

Cristhian Carrillo was my lab partner for this lab. I referenced Professor Gold's manual and the Wikipedia article on Poisson distribution. We received help from Professor Koch and Katie. The photos for this lab are from Brian Josey's and Randy Lafler's lab notebooks.