Analyzing Decay Time Data



Analyzing Decay Time Data

Pedro Flores

As one of the Quarknet interns this year, I have been placed responsible for taking data from our muon decay detector, and analyzing it so that we can decipher what the lifetime is. I was able to complete what I could with our data using Excel, but unfortunately, our experiment had technical problems. The method I used to analyze our data, though, is correct, and can be repeated easily with our configuration.

Our configuration was made up of a very unique design. We used four scintillator panels, arranged in a box formation (Fig. 1). These panels sent information to a data acquisition (DAQ) board, the Quarknet in our case, which could read the four pulses. From there we sent the pulses to an amplification system where it was then sent to a second DAQ board, the Field Programmable Gate Array (FPGA) from Xilinx that could decipher the pulses and only give us the lifetime of a muon (Fig. 2).

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The data received from the FPGA is sent to a notebook file (Fig. 2), where it is copied and pasted into Excel. First, we arrange the data in descending order to sort the data into a much more readable format. Then, since the data is in counter tics and not time, it is essential to convert each tic to time. To do this, we multiplied each term by 20 since each tic represents 20 nanoseconds. Following this, we multiply those terms by 10-9 to change them into seconds. Lastly, we divide each term by 10-6 to convert the counts into microseconds. This process can be quickly done be multiplying all of the values by 2x10-2.

Now that the values are in microseconds, we can now use excel to arrange the values into a histogram and then plot the data. Before you begin, you must determine whether or not you wish to set you histogram bins, which is the number of categories that your data will fall into (i.e. you want 20 bins for 4000 data points, so you divide the amount of points you have by 20 and find out how big each increment should be. In this case, you should make a new column that would go up by 200 until 4000.) In order to plot the data in a histogram, excel must have the “Analysis ToolPak” installed, so that you can then use the “Data Analysis” feature. Once the add-in is installed, go up to tools and choose “Data Analysis”(Fig.3). This will bring up another window where you will choose the Histogram option (Fig. 4).

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After choosing this option, a new screen will be brought up, where we set the parameters of the histogram. (Fig. 5) The “Input Range” is where we put our data from the FPGA, and the “Bin Range” was determined in another row using the method I had mentioned earlier. The “Bin Range” is optional, but may cause some ambiguity in your data. For our purposes, the “Output Options” is not used and the only setting needed is to ensure that the data does not overwrite your initial data by checking that the choice is set to send the data to a “New Worksheet Ply”.

After the data has been processed, you should see two new columns labeled “Bin” and “Frequency”. (Fig. 6) Now the data can be put onto a graph by simply using the “Bin” for the “X Range” and “Frequency” for the “Y Range” on an “XY (Scatter) graph. [pic]

Lastly, in order to fit a line to the graph, you must first remove any values of zero in your data. Then select the graph and bring down the chart menu at the top, where you will see a choice, “Add Trendline”. (Fig. 7) Choosing this will bring up a new menu that will allow you to choose the type of graph that you wish to fit. (Fig. 8) choose the appropriate graph, and go to options and make sure to select the option to show the function.

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The form of the exponential equation is y=a*b^(x/t) where t is your lifetime. So, lastly, in order to find your lifetime you will take the number that is multiplied to “x” and invert it to get your lifetime.

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Numbers represent lifetime in 20 ns tics

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