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The BETA RAY Experiment

I. Beta Ray Experiment

II. Pre-Labs must be printed separately. BRA Pre Lab Questions and Staff Sign Off Sheets.PRINT, FILL THIS OUT, Get it Signed by 111-Staff, turn in your Signed Pre-Lab Sheet with your report, to the 111-Lab Staff.

III. Beta Ray Procedure

IV. Beta Ray Analysis

Note: To print the sections below click on each link below and print separately

V. Error Analysis Notes

VI. Beta Ray Computer Programs

Reprints and other information can be found on the Physics 111 Library Site

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Contents 1 Before The starting the Lab 2 Introduction 3 Prerequiste Reading Materials 4 What is Hysteresis? 5 Apparatus 5.1 Photomultiplier Tube diagram 6 Procedure 6.1 Set the signal and discriminator levels 6.2 Observe the effects of statistical fluctuations. 6.3 Observe the effect of hysteresis 6.4 Take data using the Beta Ray Scan Program to scan the entire beta ray spectrum 7 A few pointers about the Data Analysis 7.1 What does artifact mean? 8 Data Analysis and Fermi-Kurie Plots

Before The starting the Lab

Read the reprints on beta decays, go over the Fermi theory of weak interactions, and understand the origin as well as the purpose of the Fermi-Kurie plot.

View the 'Radiation Safety Video' From Inside the 111-Lab, Paste into your Browser [ U:\Advanced Lab Share\Safety Manuals and Videos ] and then click on Rad Safety Video located in the My Computer directory on the 111-Lab Network Share Drive, get Radiation Safety form from GSI, then fill it out & sign the Radiation pink form, and get a Radiation Ring.

View the Beta-Ray Video, discuss the pre-lab questions with an instructor, and have the BRA Pre Lab Questions and Staff Sign Off Sheets.....PRINT, FILL THIS OUT, Turn it in

Discuss the Physics about this experiment with the faculty or the GSI's in the 111-Lab before starting.

You should keep a laboratory notebook. The notebook should contain a detailed record of everything that was done and how/why it was done, as well as all of the data and analysis, also with plenty of how/why entries. This will aid you when you write your report.

View the Error Analysis video.

Introduction

Some isotopes of atomic nuclei can decay spontaneously and may emit a combination of electrons, positrons, neutrinos, and gamma rays. Nuclei with atomic numbers greater than 80 and a few light isotopes can also emit alpha particles. In this experiment we study the momentum and energy of electrons, called beta particles or beta rays, emitted when radioactive Cesium-137 decays into Barium-137.

There are two modes of decay because the barium nucleus has two different energy states to which transitions are allowed. The nuclear equations, kinetic energies released, and the branching ratios (relative frequency of occurrence) of these two beta decays are written as follows:

	ΔE=0.514 MeV	BR:93.5%	(1)
	ΔE=1.176 MeV	BR:6.5%	(2)

Additionally, the excited state of Barium *, daughter product in (1), can subsequently decay as follows:

	ΔE=0.662 MeV	BR:90%	(3)
	ΔE=0.662 MeV	BR:10%	(4)

In (4), the excited barium nucleus decays by interacting with a nearby bound electron in a process called internal conversion.

The two beta-decays give a continuous energy spectrum of the emitted electrons, while the internal conversion reaction gives sharp k-, l- and m-peaks in energy (page 125 in the reprints). See Fig. 2a for a representative spectrum. It is a plot of the number of electrons N vs. momentum p. The curve is the sum of the three decays described above that emit electrons. The peak on the low energy side of the k-peak is an apparatus artifact.

Fig 2a:Counts vs. Momentum, Uncompensated

Fig 2b:Counts vs. Momentum, Compensated

Prerequiste Reading Materials

Index to the 111-LAB Reprints: [1]

1. Tables for the Analysis of Beta Spectra; U.S. National Bureau of Standards‡

2. Y. Yoshizawa, "Beta and Gamma Ray Spectroscopy of Cs137",‡ Nuclear Physics 5, (1958), 122-140

3. H. A. Bethe, Elementary Nuclear Theory.

4. E. Segre. "Chapter 9: Beta Decay." Nuclei and Particles: An Introduction to Nuclear and Subnuclear Physics, 2d Ed.

5. M. Siegbahn, Beta and Gamma Spectroscopy, Ch. 3.‡

6. K. S. Krane, Nuclear Physics.

7. Photo-multiplier tube Handbook‡ (Note this is a separate reprint booklet)

8. W. C. Haxton, B. R. Holstein, "State of the science and art of beta decay and neutrinos", Am. Jour. Phys. 68, 15 (2000).

9. I. Feister, "Numerical Evaluation of the Fermi Beta-Distribution Function", Physical Review 78, 4 (1950) ‡\*.

10. L.R.B. Elton, "Chapter 9: Beta Ray Theory", Introductory Nuclear Theory, 2nd ed.; 1966, W.B. Saunders Company,PA;

‡ Contained information on the Fermi-Kurie plots and calculations. The reprints are all available on-line from the [Physics 111-Lab Library Site].

Suggested initial reading: [6, ch 9] [1, §B.2-§B.7] [2, §3]

What is Hysteresis?

In ferromagnetic materials, microscopic regions are separated into into domains. Within each domain, all the atoms have their magnetic moments aligned in one direction. Adjacent domains have their magnetic moments pointing in random directions with respect to their neighboring domains . A large scale sum of their magnetic moments is nearly zero, and the material produces only a small external macroscopic magnetic field.

Domains are separated from each other by "domain walls" which are 100 to 1000 atoms wide. Within the boundary of a domain wall, the individual atomic magnetic moments change directions from that existing within one domain, to the direction existing within the adjacent domain. When an external magnetic field is applied to the ferromagnetic material, the walls move and the domains with magnetization in the direction of the field increase in size and become macroscopic at the expense of adjacent domains that get smaller and disappear. The combined external field and the field of the ferromagnetic material can be orders of magnitude larger than the external field alone, when all the domains are aligned. This external field is generally supplied by a current-carrying coil wound around the ferromagnetic material.

The degree of magnetization as measured by the size of the domains is non-linearly proportional to the applied external magnetic field. Also, for a given external field, the magnetization of the material depends on the past history of the magnetization. For example, start from zero large scale magnetization, and zero external field; increase the external field to any particular value and then reduce it back to zero. The magnetization does NOT return to zero, but remains at some finite value. A reverse external field must be applied to bring the magnetization to zero. The magnetization lags behind the applied field. This effect is known as hysteresis.

The typical but exaggerate hysteresis behavior of a ferromagnetic material is shown in the figure below, where the Magnetic Induction B is plotted vs. the magnetic field intensity H, which is directly proportional to the current in the surrounding coil. The horizontal axis could equally well be labeled ``I" instead of ``H". "0" is the non-magnetized or demagnetized state (B=0, I=0) which can be reached by applying an alternating current and slowly reducing its amplitude to zero. As the current increases from the demagnetized state, the B value lags behind what one might expect and follows the curve to (a') and toward saturation at (a). With large variations in I, the behavior follows a major loop (abcdefa...); while for small variations in I, the behavior follows a minor loop (a'b'c'd'e'f'a'...) or (a'b'a'...) if the current I never becomes negative. Certain points of a hysteresis loop have names: B_r is the remanent value at I = 0 after the material is saturated at (a.) H_c is the coercive field or the coercivity ( i.e. the H or I required to reduce B to zero).

Apparatus

Figure 3a: B-Ray apparatus block diagram

Figure 3b: Detector Detail

The spectrometer is a 'C'-shaped vacuum chamber with magnet coils on top and bottom to produce a uniform magnetic field perpendicular to the radius of the chamber and perpendicular to the plane of the 'C'. A source of ¹³⁷Cs is permanently mounted inside the chamber at one end of the 'C', and a detector is mounted at the other end.

Electrons emitted by the source are subject to the Lorentz force

and travel in a circle to the detector. The relevant equation is:

The radius r is fixed, and the field B is approximately proportional to the current I in the coils (see Appendix on hysteresis). We can therefore write:

We want to measure the momentum spectrum of the electrons, and we can do this by measuring the count N or number of electrons received at the detector in a given time interval, as a function of current I.

However, a correction must be applied to N because of the finite size of the detector aperture: The exit aperture is fixed in width and admits a given range of radii, Δr = constant. These radii cover a range of momenta Δp. The magnitude of Δp is not constant, but instead increases linearly with p, or the current, since p and I are proportional). The plot of N vs. p gives a true representation of the spectrum only if the increasing size of p is compensated or corrected for, by dividing each N by the current I. An illustration of what happens to the data is shown in Figures. 2a and 2b.

The computer controls the current in the spectrometer coils, and hence the field. It starts the current from approximately zero and increases it to maximum in discrete steps called bins or channels. For each bin, the computer counts the number of particles that strike the detector within a period of time and saves these data as a spectrum.

The detector consists of a plastic scintillator that produces a light pulse when an energetic electron strikes it. This light is detected by a photomultiplier tube (PMT) placed near the scintillator, as shown in Figure 3. The PMT produces an electrical pulse whose peak-voltage is proportional to the energy of the incident beta particle. The pulse is sent through a preamplifier, then a linear amplifier, to a single-channel-analyzer (SCA). The SCA generates a pulse for each detector signal that lies between the adjustable lower and upper thresholds. Because the SCA discriminates against noise pulses, it is also called a discriminator. The pulses are sent to the computer to be recorded in the proper channel of the spectrum. The signal can also be displayed on an oscilloscope.

You should know how the photo-multiplier tube works. See Appendix E on the PMT. Include in your write-up an explanation of the PMT and what the pre-amplifier circuit might look like. Also you should view the Photomultiplier Tube Handbook in the Physics Library on reserve, it is a separate booklet.

Photomultiplier Tube diagram

(See Also the RCA Photomultiplier Tube Handbook in the Physics Library)

A Photomultiplier tube is a photon detector that converts single photons into large pulses of electric current by successive multiplying stages.

Procedure

First read VI. Beta Ray Computer Programs describing the operation of the computer data-acquisition program, so you know how to set the current in the magnet to any value you wish.

Set the signal and discriminator levels

1. Familiarize yourself with the relationship between PMT voltage, amplifier gain, and pulse height: Consult the block diagram of the apparatus (media:BRAimage010.gif) and connect the output of the linear amplifier to channel 1 of the oscilloscope. The signal path is PMT to current PREAMP to AMP to a 2 second (-DELAY-LINE BOX to SCOPE (when the scope is triggering internally, the delay-line has no effect, but you will need it later to delay the main pulse). Start with SCOPE parameters of CH 1, 0.2V, 2 (sec/div, CH 1 TRIG, and the Tran-L-Amp Amplifier settings DIFF DL .8, INT 2, GAIN 16. Referring to a sample spectrum, set the coil current (Use the bin setting on the Integrate Single Point program) to a bin corresponding to a high count rate, (the K peak). Observing the signal on the SCOPE, gradually turn up the high voltage (negative polarity) on the photo-multiplier (PMT) until an operating voltage of -800 to -1100 volts maximum is reached. You should see many pulses of various heights. Vary the PMT voltage (always between -800 and -1100V max) and the amplifier gain and observe the effects on the signal gain and noise. Change the coil current to various points on the spectrum and observe how the intensity and height of the pulses change. Note what you see. Remember that you are trying for a maximum signal-to-noise in the pulses. Set the coil current to approximately 0 amps (bin 0) and observe the signal. Theoretically, there should be no signal at zero field. What do you see, and what can you conclude about the nature of the noise in this experiment?
2. Familiarize yourself with the operation of the SCA: The normal operation of a PMT will result in small-amplitude noise pulses. We want to use the discriminator on the SCA to reduce or eliminate the noise, permitting the signal pulses which are larger in amplitude to be passed and recorded. Connect the Tran-L-Amp linear amplifier to the SCA and the rest of the circuit elements as shown in Figure 3, apparatus (media:BRAimage010.gif. Switch the SCOPE to EXT trigger. Now the scope is only displaying pulses that pass the SCA, and the 2 second (-DELAY-LINE compensates for the SCA's transit time.
   

   

   Figure 4a
3. With the Single Point Program, find a bin that corresponds to a high count on the sample spectrum. This program is a one part of two of the Beta Ray Scan Program Utilities, Beta Ray Computer Programs. Refer to that section now. Start with the SCA upper-level threshold (UL) set to 10 and the lower-level (LL) set to 0. There should be no signal displayed on the SCOPE. Increase the LL until a signal appears on the scope, this is the minimum LL setting you may use (approx. 0.36), the SCA will not operate properly at a lower setting. Now increase LL well past this setting and observe the output on the scope
4. You should see something similar to figure 4.a. In this case, most of the low voltage noise signals are passing through the discriminator and registering as counts on the computer. Now, by slowly increasing the LL (Lower Level) setting, you should be able to obtain an output similar to Figure 4.b. In this picture the lower line and a few of the lower voltage pulses beneath the brightest pulse have been eliminated. This effectively eliminates most of the PMT noise as well as some of the lower momentum pulses..
   

   

   Figure 4b
5. The object is to set the LL high enough to eliminate small-amplitude PMT noise while preserving as much of the low-momentum data as you can.
   

   

   Figure 4c
6. The AMP gain should be set around 16, but be careful not to clip the top off your signal. If you set the gain to high on the amplifier it will chip or saturate and look like figure 4C. Now using the Beta Ray Scan program, take a series of quick spectra (Bins 0-2500 by 10; 3 sec/bin; save time by clicking on the Stop Early Button, click only once, after it has completed taking data in the 'up' direction at about channel # 2450 (note that the Stop Button takes about 25 second to really stop the program). This should verify your SCA and amplifier settings. With higher LL settings, you should see the lower momentum portion of the spectrum erode. Compare your spectrum to the sample spectrum. If your spectra look too distorted, you may have to repeat step three. Why don't the near-zero-field data disappear with higher discriminator settings?

Observe the effects of statistical fluctuations.

1. Using the Integrate Single Bin program acquire 50 or 60 observations each, at one second per integration, for two bins with greatly different count-rates. Save the observations in a file, and use them to calculate the means and standard deviations for the two channels. How do they compare to counting statistics?
2. For one bin (one single setting of coil-current), observe the change in fluctuation as you change integration times in a range from 1 to 30 seconds. Based on the lowest count-rate of all channels, for how long should you integrate each channel of your spectrum to achieve a better than 1% error due to statistical factors?

Observe the effect of hysteresis

1. Re-read the [hysterisis section] and the Analyze section of VI. Beta Ray Computer Programs to be sure that you understand how the scan program establishes a hysteresis loop before it begins taking data.
2. Take a quick complete spectrum (Bins 0-2000 by 100; 2000-2500 by 5; 2500-4000 by 100; 2 seconds/bin). Observe the shift in the k-peak between the two directions of current. Using the knowledge that the k-peak always occurs at a given magnetic induction (not at a given current), convince yourself that the observed shift in the spectrum between current up and current down is in the correct direction.

Take data using the Beta Ray Scan Program to scan the entire beta ray spectrum

The current in the magnet is scanned up and down which equals one complete scan. The computer controls the past history of the scans so as to follow the same hysteresis curve every time every time. In adjusting scan parameters, it is more important to integrate for longer times, 60 seconds maximum, than it is to include every point in the spectrum. Print out copies of the scans. We are networked in the 111-LAB so you can choose where to print and what printer to use.

A few pointers about the Data Analysis

What does artifact mean?

If you compare the spectrum taken in this lab to ones taken elsewhere, you will find in your spectrum, an extra peak on the lower momentum side of the k-peak (see figure 2.c "artifact"). Before we automated the scan process with a computer, the current in the magnet was adjusted by hand, and it was impossible to obtain the resolution necessary to see this anomaly. But now, with the advent of the computer, intrinsic errors in the beta ray spectrometer have become apparent.

To understand this, consider a source of finite width s emitting a monochromatic beam of β-rays subject to a uniform transverse magnetic field. Rays (electrons) are emitted in all directions. However, due to the Lorenz force they are confined to travel along arcs of the same radius r. Each electron travels along identical arcs, but not the same distance. Thus a detector of width Δx "sees"

an intensity distribution similar to that of Figure 6b. This implies that in the experiment, when a polychromatic beam is emitted and one "sits" at a bin and counts electrons, the count is smaller than it should be, because some electrons are falling into neighboring bins, due to the width of the intensity distribution. In essence our raw spectrum is the result of what we should see (the true spectrum) with this distribution (the error function) smeared into it. Mathematically this is known as convolution. We would write

G = T * E

So can we mathematically deconvolute our data and find the true spectrum? Yes in some special cases, but not here because the error function is not a constant width as we vary B and take our data. Also, the data are not accurate enough to warrant a detailed mathematical treatment. Instead, we smooth the curve by hand and eye in the region where there is an extra bump on the side of the peak, and proceed with the analysis.

So now we can deconvolute our data and find our true Beta spectrum Figure 6D. Resultant Beta spectrum, see the K-peak at Bin \# 2200 and L-peak to the right of it.

Data Analysis and Fermi-Kurie Plots

The Fermi-Kurie plot is simply an algorithm that transforms your spectrum to another view of the energy spectrum. It uses the formula [B10] in the National Bureau of Standards reference. The expectation of this experiment is to experimentally determine Q₁ and Q₂ , respectively the high and low energy 'Y' intercept points. FK (Fermi-Kurie ) transform makes it easier to determine Q₁ and Q₂ . First you must start with your full data spectrum from channel 0 to 4095 summed up and down data shifted together and then compensated, calibrated, and background-subtracted. Hit "Control+h" to see the key strokes for analyze. Analyze is a DOS program that requires, (8) eight letter names only with no spaces, for names of Files and Folders. Make a Folder in your My Documents folder for your data saving. Use (8) letter name to save your data ending in \*.DAT. The Excel files need to be opened and re-saved as "Text delimited with Tab" files ending in \*.DAT. Then analyze will recognize the files. After you have acquired your data, using the summed up and summed down files save them as the Fileup1.dat and filedn1.dat in excel as "Text delimited with Tab" files. Now close them from excel and open analyze and open the files.

Shift them together by the your calculated number, if they look okay then go on with the analysis.

If they are not perfect with respect to the hysteresis effects, then you will have to adjust the data yourself. You will need to shift each Y value by the different between the Y's at each X. In some instances you will have to average the Y's.

Then take your data and subtract background, No negative numbers allowed. Calibrate your X axis, low and high points for momenta and compensate it "Q" in analyze.

Save this dataset file as a new dataset in analyze(8) letters max. You will want to save the files as you go to each step. Good practice in case of computer cashes, etc. Note that you can save files in ASCII or Binary format.

Now you are ready for the Fermi-Kurie plot;

Crop out unwanted bad data points like negative numbers, etc using the "Alt+C" command in analyze with the use of markers. Fermi-Kurie "Alt+K" you should get something like the below graph.

Fit a line to this curve and get the end-point Y axis, Q2. Pick the area above the noise above the K-peak where it is linear. Now do a inverse Fermi-Kurie plot. You will get something like the following graph.

You should repeat the steps above to get the high energy component and the high energy end-point Q1.

Your result should be the high energy component as seen below.

Your combined graphs should be like the following;

Reduce your data by following the numbered steps listed below, but first read Ref. 1 for detailed explanations of how beta-ray spectra are analyzed. Also read about data analysis.

Use the program "ANALYZE". In your Fermi-Kurie analysis, use units of and for momentum and energy respectively.

As you work on the data, keep in mind what your ultimate goals are: To observe the beta decay spectrum; to model the phenomenon with a Fermi-Kurie plot that incorporates the theory of beta decay; to determine the maximum energy available in the decay process. The above Figure shows four separate phenomena. Your data are the sum of these. We would like to separate this sum into the individual curves shown above, where they are shown overlapping but not added, as they are in the experimental data. See Appendix D about the Fermi-Kurie plot and how the Analyze program functions on making it.

1. From the masses of ¹³⁷Ba and ¹³⁷Cs, calculate the total energy available to the electron mass energy + electron kinetic energy + neutrino energy in the beta decay. What is the maximum kinetic energy with which the ¹³⁷Ba can recoil? Must this kinetic energy be taken into account in your experiment?
2. Use ANALYZE for combining your MYDATUP1.DAT and MYDATDN1.DAT files to reduce the effects of hysteresis and to yield a single data file which you will use in all your analyses. Should you add the two sweeps? Should you displace the two spectra by a constant amount or a variable amount? Should you shift them right or left an amount that depends on channel number? Some thought and justification are needed here. Plot your two raw spectra and your combined spectrum.
3. The momentum resolution Δp is proportional to the momentum p itself (you should derive this), and therefore, Δp is proportional to the current, since I is proportional to p. Divide the number of counts in each channel of your combined spectrum by I (or a number proportional to I). This is your compensated momentum spectrum N_c. Plot N_c vs. η.
   1. Calibrate your momentum scale in units of η by using the accepted value of the k-peak momentum (, or ), the bin in which the k-peak appears, and the bin number that corresponds to zero B-field (and hence zero momentum). Without accounting or correcting for hysteresis effects, how large an error in momentum would you have unwittingly obtained for the k-conversion electron momentum?
   2. Use the region of your spectrum that lies above the highest-momentum beta-particle to estimate the background radiation (you may assume the background is linear) and subtract it from your data. Plot the resultant spectrum.
   3. Make a Fermi-Kurie plot of your compensated spectrum. If the data were perfect, and the theory exact, then the F-K plot would be a straight line. Using a least-square-fit line, determine the end-point of the high-energy beta component. How would the end-point plot change if the neutrino did not have zero rest mass? This need not be a mathematical explanation and Appendix F, for comments about error analysis.
   4. By taking the inverse-Fermi-Kurie plot of the best-fit line obtained above you will have the contribution of the high-energy beta-component to your compensated spectrum (N_c). Subtract the higher energy component from your compensated spectrum to leave only the lower-energy component.
   5. Make a Fermi-Kurie plot of the subtracted spectrum in the vicinity of the end-point of the lower-energy beta spectrum. Determine the end-point of the low-energy component.
   6. Compare the measured line width and the expected spectrometer resolution for the conversion electron peak.
   7. Check out Error Analysis Notes and the video on Error Analysis.

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