From Physics 111-Lab Wiki

All pages in this lab

I. Theory and Background

II. Staff Sign-off Sheet (BRA) and Pre-Lab Questions

III. Beta Ray Procedure

IV. Beta Ray Analysis

V. Error Analysis Notes

VI. Beta Ray Computer Programs

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Contents 1 Introduction 2 Background Information 3 The Beta Ray Scan Program: 4 The integrate single point program: 4.1 Analysis 4.2 Beta-ray Spectroscopy 4.3 Shift DataSets 4.4 Compensate DataSet 4.5 Fermi-Kurie Transform 4.6 Inverse Fermi-Kurie Transform

Introduction

With the aid of the computer and a LabView program, you can get a rough spectrum in 44 minutes and a full spectrum overnight.

The computer is equipped with an interface DAQ card, PCI-MIO-16E-4, that enables the PC to vary the coil current in either direction from zero to a maximum of approximately 650 mA in 4096 steps. The computer controls the coil current by setting a DAC (digital-to-analog converter) in prescribed steps from 0 to 4095. The DAC outputs its voltage to the power supply that is operating in remote-voltage-controlled current mode. The interface DAQ card also has a edge counter, for counting the beta-particles and background pulses that strike the detector, and digital TTL-output lines, that permit the PC to switch the current direction. Taken together, these pieces form a 4096-channel particle-momentum spectrum analyzer. The program that operates it is a Labview program entitled BetaRay Utils.exe". It will open the two main programs "BetaRay Scan V2.2" and "Single Point Scan V2" but it will NOT start them. They should be run each alone. Wait till one stops before running the other one. If you run both together the LabView will crash. On the Beta Ray computer, this program is accessed by the shortcut on the desktop. If it is not there contact the 111-Staff. Data will be saved in your My Documents folder with a pre-name of "BRA Data" and "Single Point" you should add your run # after this Pre-Name. (ie; BRA Data-1 or Single Point-1)

Background Information

First, it's helpful to define some terms and outline how the system operates. The program can only set the coil-current to fixed values that are determined by the DAC and the power-supply. Each value of current is called a bin or channel. The computer degausses the magnet, sets the current to a bin and then starts counting the number of pulses coming from the detector. This is called integrating a bin. After a period of time, the program stops integrating, takes the number of particles it counted, and moves on to the next bin. After determining the counts for every bin, the program produces a file with entries of Channel Number and counts which constitute a raw spectrum (raw since it is uncompensated for hysteresis effects). The Single Point Program output is Time and Counts. The full Beta Ray Scan program data output file is contains Raw Data or Summed Data with the run number and counts. Single Point Scan Program: when you start the program you need to input the chnanel number 1st thing before clicking the start button on the program. The program will then ask you, if you are saving the data, for a file name ie; Single PointXX , you input the XX variable as a run number. Then input the other parameters needed to run the program.

1. Base File Path: where your file is being saved and what name the computer gave it.
2. Status Ring: information on what the program is doing at the time.
3. Integratiion Time pere Bin # is 60 maximum number.
4. Time/Scan Direction: is the time is will take to complete the up & down scan requested.
5. Estimated Time Remaining: it is up dated at the end of each up/down scan with remaining time.

Note that data is only saved at the completion of each up and down scan. You will see the summed data plot after this time.

This is a good time to point out how your spectra will differ depending on the direction of the changing current. Look at the figure 5B below.

Figure 5b

Figure 5c

The K-peak of the beta spectrum occurs at a specific field strength, marked B_k. If B were directly proportional to coil-current, the K-peak would always be detected at current i_k. Instead, as you take data with the current increasing, the peak occurs at i_ku, and as the current decreases the peak occurs at i_kd. This is true for every point of the spectrum, which means that both spectra you take will be shifted away (in opposite directions of I) from the spectrum you would get if there were no hysteresis. Figure 5C is closer to the real hysteresis curve for the beta spectrometer magnet.

The Beta Ray Scan Program:

Beta Ray Scan is a program that acquires, saves, and plots the number of counts vs. current (bin number), according to the user's input parameters.

Your data will be saved on the 111-Lab server backed up every night by the campus. Data is saved in your own home directory in \\Atlas2\redirect$\your_Directory_name\My Documents\LabVIEW Data\then either "BRA DataXX" or Single PointXX" .

Note you should use Matlab for all your data anlaysis. We have written scripts to help you in you anlaysis. Keep your file names short and desciptive, eg; dataup-1 ending in (.dat), then your data can be read by many other program editors for any changes needed.

The two programs are located on the your desktop. Now at this time please do not run and excute both prgrams at the same time. They will stop working. Do not close them either, just stop them.

After you have started Beta-Ray Scan, you will be asked if you want to save the data that you will be taking. If you choose not to save the data, the data will only be plotted. If you choose to save the data, you will be asked for a file name with the Base File Path as LabVIEW Data\BRA Data or Single Point. The program will save raw data points as they are gathered with the file paths:

[Base File Path] DOWN data (Raw Data Run # [Run #]).xls

[Base File Path] UP data (Raw Data Run # [Run #]).xls

For the Up and Down scan data. The Summed Data will be saved intermittently to the same file with the paths:

[Base File Path] DOWN data (Summed Data).xls

[Base File Path] UP data (Summed Data).xls

For the SUM UP and SUM DOWN data. (Summed data are just that-they are the direct sum of all the previous runs. Think of adding vectors where each component represents a bin number, and the magnitude of that component represents the total number of counts for that bin number).

If you forget where you chose to save the data, don't worry. The Base File Path indicator displays the Base File Path.

Once you have decided whether or not to save the data, you will then have to input the relevant parameters. Here's a list of them and what they do:

• Integration Time per Bin(60s Max): Controls the amount of time (in seconds) the computer will sit on each bin tallying the number of counts; e.g., if you choose 5 seconds, the computer will count at each bin for five seconds. Maximum of 60 second for this variable.
• Delta Bin: The number of bins the computer will skip (won't integrate) between bins that it integrates.
• Number of Up/Down Scans to Make: Each scan consists of data taken as the current increases (UP data) and data taken as the current decreases (DOWN data). And one SUM Total Data file. You should make as many Scans as possible for good data statistics within your time constraints.
• Scan Quality: Determines whether or not the computer will wait for the current to settle as it changes bins (while it's taking data). If you select Scan Quality to be HIGH, the computer will wait 4 seconds for the current to settle before it starts integrating the new bin. If you select Scan Quality to be LOW, it won't wait at all. If you want good data, choose a HIGH scan quality.
• Scan Start Bin #: Controls the bin number which the scan will begin taking data at. (The same hysteresis curve will be swept out regardless of the Scan Start Bin.)
• Scan End Bin #: Controls the bin number which the scan will stop taking data at. The actual end bin number is the closest one to the chosen Scan End Bin # (rounding down) so that the quantity

is an integer. (The same hysteresis curve will be swept out regardless of the Scan End bin #.)

• Time/Scan Direction: Displays the projected time required for each scan (up and down) to be completed (based on the user inputs) in the format hh:mm:ss. For example: 1:23:36 requires one hour, twenty-three minutes, thirty-six seconds to complete a scan.
• Estimated Time Remaining: Displays the projected time required to complete the entire scan sequence (i.e. Time/Scan x # Scans to Make). This indicator updates itself at the end of each scan completed, so it will display the projected time required to finish the total scan sequence (not counting the time required to complete the current scan).

NOTE: Ten scans at 5 sec/bin is better than one scan at 50 sec/bin. (Sample values would are below:

Integration Time per Bin (Max of 60 seconds) = 5

Delta Bin = 5

Scans to Make = 7 (could be 6)

Scan Quality = LOW or HIGH add (1/2 second per bin integrated)

Scan Start Bin = 100

Scan End Bin = 4095

Time/Scan = 01:07:01

Total Time = 15:38:14 this gives you an overnight run.

Once all the desired parameters have been entered, click on the flashing [START TAKING DATA] button. Now everything should go as planned. To know what the computer is doing at any given moment, keep an eye on the Status Ring.

The basic outline for the procedure is as follows:

1. The current is set to 0
2. The current is set to its negative maximum.
3. The current is returned to 0.
4. The current is ramped up to that corresponding to the Scan Start Bin #.
5. The UP data are taken, stopping at the Scan End Bin # or thereabouts.
6. The current is increased to its maximum value.
7. The current is decreased to that corresponding to the Scan End Bin # or thereabouts whatever the last integrated bin was in the UP scan.
8. The DOWN data are taken, stopping at the Scan Start Bin #.
9. The current is returned to zero.
10. The raw UP, DOWN, SUM UP and SUM DOWN data are saved/updated and plotted.
11. The entire procedure is repeated until all the scans have been made.

During the scan process, you may stop the program pre-maturely by clicking on the [STOP EARLY] button (it will appear after the data run(s) begin). Just click it once. If it seems like it's stuck and won't click, that's probably because the computer is busy integrating a bin and hasn't had time to click it. When it's done integrating that bin, the [STOP EARLY] button will latch. The program may integrate one more bin, then it will stop and bring the magnet through the end of the hysteresis loop once or twice (depending on how many runs were left to complete it takes about 25 seconds to stop). Data taken during the interrupted run will be graphed but not be saved or added to the sum data. (the graph of interrupted down data isn't to be trusted, as the bin numbers won't actually correspond to the points integrated).

Note: Since statistical error decreases with larger samples, longer integration times will give you smoother graphs. Below are two examples of the effect of integration-time on the measured spectrum:

You can see from these graphs (even though their small vertical size slightly obscures their resolution) that the longer the integration time, the smoother the graph. On the other hand, it is not always desirable to take too long an integration time. Sometimes instrumental conditions change over time, and if the last point taken is too far removed in time from the first point, then the curve does not truly represent the experiment. Ten scans at 5 sec/bin is better than one scan at 50 sec/bin. Take many scans at a lower integration time.

The integrate single point program:

Beta-Ray Single Point Integration is a program that will sit at a single bin number, magnet current, (determined by the user) and periodically integrate that bin number for a certain amount of time. With this program, one can see how much (if any) instrumental drift there is over long periods of time.

Starting from the computer desktop:

1. Double click on the BetaRay Utils (Both VI programs will open, but NOT start running; Single point Integration V2 and Beta Scan V2.2)
2. Click on the RUN button at the top of the LabView toolbar after you have entered the start bin #.

The following are sample parameters to use:

• Program VI = Beta Ray Single Point Integration

• Integration Time per point = 10 (seconds

• Time Between Points = 1

• Integrate Bin # = 2200 ( the K-peak, enter it before start Run button is clicked)

• Number of Points to Take = 60

Click on enter ( upper left corner) Click on the Run button Question: to SAVE your data or Not to SAVE, your choice.

TOTAL TIME = 00:11:33 (11 minutes and 33 seconds) time enough for you to set the LLD on the discriminator.

To Stop the Program Early, double click on the "Stop Early" Button (Note: Button will change to Stopping, wait about 25 seconds for it to stop) .

After you have successfully started Beta-Ray Single Point Integration, you will be asked if you want to save the data that you will be taking. If you choose not to save the data, the data will only be plotted. If you choose to save the data, you will be asked for a Base File Path Name. The program will save the data after the run with the following path:

[Base File Path] Single Point-# Bin Number 2200.xls

If you forget where you chose to save the data, don't worry. The Base File Path indicator displays the Base File Path. Once you have decided whether or not to save the data (and where), you will then have to enter the scan parameters. Note that all data saving defaults to the your \\~\My Documents\LabVIEW Data\ directory.

• Integration Time per Point: Sets the amount of time the computer integrates for each data point.
• # Points to Take: Sets the total number of points that will be taken.
• Time Between Points: Determines how long the computer will wait after integrating one point before integrating the next point.
• Integrate Bin #: Selects which bin number will be integrated.
• Total Time: Displays the total time the procedure will take in the hh:mm:ss format.

For example: Total Time = 11 minutes and 25 seconds ( 11:25)

• Stop Early: If this button is clicked on, the scan will stop in the middle of the data gathering part (at the end of its integrate/wait sub-cycle), the hysteresis loop will be swept out, and the data will be saved.

The Status Ring will tell you what the computer is currently doing. The hysteresis cycle that the computer sweeps out is identical to that in the Beta-Ray Scan program. Data will be plotted as they are taken.

Analysis

Beta-ray Spectroscopy

Please see the Matlab program for analysis and the Matlab scripts that have been written for this experiment. Below are descriptions of some calculations.

Please see reference  [National Bureau of Standards]about the Fermi-Kurie Transform analysis.

You should read and understand about the Fermi-Kurie-Transform analysis. The reprint National Standards will give you all the needed information to understand this operation. See the fcaulty for more information.

Shift DataSets

This command takes two datasets, assumed to be beta spectra, and shifts them toward each other in order to account for hysteresis effects in the 111-Lab beta-spectrometer. You will be prompted for and 'UP' and 'DOWN' spectrum, at which time you press the alt-key numbers that correspond to the proper DS's. Then you will be asked for the amount to shift. The spectra are then shifted toward each other by means of x-axis rescaling (see that section of this manual for more info). That is, the x-axis is rescaled in the same way as the Calibrate x-axis low and Calibrate x-axis high commands. The shift command is cumulative, if you shift 50 bins and then shift -4 more, you will have a total shift of 46 bins. And the effects of the shift command may be removed with the Reset x-axis scaling command applied to each of the two spectra.

Compensate DataSet

Compensate DataSet creates a new DataSet from the current one by dividing the y-value of each point by its calibrated (scaled) x-value, i.e.

This is useful for processing raw momenta data from semicircular spectrometers, in which the bin-width is proportional to the bin.

Fermi-Kurie Transform

Fermi-Kurie Transform creates a new DataSet that is the Fermi-Kurie plot of the current one [see NBS for complete treatment]. The transform is a theoretical one that changes the DataSet into a straight line. The transformation is:

where is the Quantum-mechanical correction for coulomb effects on the beta-particle as it leaves the parent atom. is calculated using the Bethe-Bacher approximation but the screening effect [ref 3 §12] is neglected (to see why, you should calculate the size of this effect for Cs¹³⁷). This transformation assumes that the x-axis is momentum and has been calibrated in units of m_ec. The resulting x-axis is then kinetic energy in units of m_ec². If the input DataSet begins with negative momenta, Matlab will handle this information and begin processing data.

Inverse Fermi-Kurie Transform

The inverse Fermi-Kurie feature inverts the previous algorithm producing: