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All pages in this lab. Note To print Full Lab Write-up click on each link below and print separately

I. Compton Scattering

II. Pre-Labs must be printed separately. COM Pre-Lab .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.Maestro PHA program

IV. Error Analysis Notes

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

Before The Lab

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.

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 Compton Scattering video, discuss the pre-lab questions with an instructor, and get the COM Pre Lab Questions and Staff Sign Off Sheets.....PRINT, FILL THIS OUT, Turn it in signed.

Prerequisite Reading Materials

Index to the Prerequisite Reading Material [1]

1. A. C. Melissinos, Experiments in Modern Physics, (Academic Press, 1966). "Compton Scattering pg. 253-265." #QC33.M4 [pp. 369-384 in second ed.] #QC33.M52

2. R. M. Eisberg, Fundamentals of Modern Physics, (Wiley, 1961), Physics Library Ref. QC173.E38.

3.† Knoll, Radiation Detection and Measurement, (Wiley, 1979). [Ch. 2, 3 (general radiation detection); Ch. 11, 12 (Si(Li) solid state detectors).] #QC787.C6.K56

4.† Gibson, "Semiconductor Particle Spectrometers," from Siegbahn's Alpha-, Beta-, and Gamma-Ray Spectroscopy. #QC173.S536

5.† Goulding, "Semiconductor Detectors for Nuclear Spectrometry." UCRL-16231

6.† LBL-450: "Pulsed Opto Feedback X-ray Spectrometer System Operating Manual and Description."

† These articles are contained in the 111 Lab Reprints (available in the Physics Library and online in the 111-Lab).

Suggested initial reading:

1. Melissinos. pp. 252-265 and pp. 369-384;

2. Knoll (pp. 62-70, 79-96, 306-319 on a different detector but a good description of general detection principles, and 359-385 on semi-conductor detectors); and the "Compton Effect" article attached to this lab manual.

Introduction

The scattering of X-rays by electrons was explored by A. H. Compton in the early part of this century. The reduced frequency of the scattered photons is fundamental evidence for the proportionality of energy to the frequency of light, and for the relativistic kinematics of electrons. In 1929 Klein and Nishina calculated the angular distribution of Compton scattering from free electrons in one of the first applications of quantum electrodynamics (QED). The Klein-Nishina gives the probability that a photon will be scattered into a given solid angle. Today, when applied to electromagnetic processes 50 million times more energetic, QED predictions still appear to be borne out.

Your goals for this lab are to observe and analyze Compton scattering and to learn something about semiconductor detectors. You will use your Compton scattering data to compare your energy shifts with theoretical predictions, to determine the mass of the electron, and to attempt a verification of the Klein-Nishina cross-sectional dependence formula.

Theory

The Compton scattering process consists of a photon scattering off of a (free) electron. The scattering formula is

$\lambda'-\lambda=\left ( \frac{h}{m_ec}\right)\left (1-\cos{\theta}\right )=\lambda_c(1-\cos{\theta})$

where $λ$ ' is the wavelength of the scattered photon, $λ$ is the wavelength of the incident photon, $θ$ is the scattering angle, and $λ c$ is the Compton wavelength of the electron, equal to 2426 fermi (2426 x 10^-15 m). By comparison, the wavelength of a 59.54 keV X-ray is 20824 Fm. You will need to convert the wavelength of the scattered photon into energy, which is measured by the detector. You should do the Compton derivation for yourself, but do not include it in your report. Rather, explain where it comes from, including any conservation laws and assumptions that are used.

The scattered X-ray energy may deviate from this prediction by roughly 1 part in 1000 if the electron from which it scatters is a bound valence electron. Can you explain why this is so?

Apparatus

Source

This experiment uses a ²⁴¹Am (americium) radioactive source to provide the photons for scattering. When working near the source, you must wear your radiation ring, and when handling the source you must wear rubber gloves. Please remember to remove the gloves before touching anything else or you will defeat the purpose of the gloves!

The source is made by placing a small amount of radioactive Am material inside of an aluminum holder as shown. While there is a small amount of lead shielding located behind the Am material, it is not enough to attenuate the radiation. Hence, the sample effectively emits photons in all directions.

There is an energy level diagram for Am posted in the Compton experiment area. (There are more transitions possible than the strongest ones, which are listed below.)

²⁴¹Am Gamma Ray Energy Data

13.5 keV 12.8%

17.3 keV 22.4%

20.9 keV 6.2%

26.3 keV 2.8%

59.54 keV 40%

Detector

The lithium-drifted silicon [Si(Li)] detector detects X-rays primarily by means of the photoelectric effect. In your laboratory report you should briefly explain how X-ray energies are measured by the detector and then converted into the voltage pulses that are accumulated by the pulse height analyzer (PHA). The detector is held in a vacuum and at a temperature of 77 K by liquid nitrogen in an attached dewar. Note that while the detector is protected by a 7 cm diameter polyethylene cap, it is actually only 5 mm in diameter by 3 mm thick, and it is placed 6 mm behind the 10 mm diameter beryllium window.

For information on the spectrometer system, see the LBL-540 manual and Knoll.

The pre-amp is mounted on the LN₂ dewar (pronounced dew - er) connected to the detector. It is then connected to two modules in the Compton electronics rack: the DET. PWR. SUPPLY supplies the reverse bias voltage to the detector, while the 11X 8481-P1 AMPLIFIER SYSTEM amplifies the detected signals and supplies the pre-amp power. The dewar is a double-walled container with a vacuum between the walls, used for storing liquid nitrogen. The Detector Power Supply is bolted to the detector housing. The "Bias volts - 600 BNC connector is not used, nor is one on the side. The connector on the other side goes to the power supply in the rack. The pre-amp is also bolted to the detector housing.

A photon striking the detector generates an output current pulse, which is turned into a voltage pulse and amplified by the pre-amp and amplifier systems. The signal generated by the amplifier is then fed into a "Pulse Height Analyzer" PHA software program called "Maestro" on your Desktop or start menu. The PHA program looks at the voltage pulses, determines its height V (between roughly 0 and 10 volts), and places a count in the channel (bin) corresponding to this voltage. Maestro has 2048 channels in which to place these counts, so each channel is approximately 10/2048 volts wide. After running for some time, then, Maestro yields a histogram of how many times pulses of different voltage heights have arrived at its input. Because the pulse heights are proportional to the detected X-ray energies, we have an energy spectrum-the number of times that photons of different energy arrived at the detector. [See general information on Pulse Height Analyzers or a video, available on 111 Lab web site, for further information on the PHA.]

It takes a finite amount of time for the PHA unit to sense a pulse, determine its height, place it in the proper channel, and then set up for sensing the next pulse. Pulses that arrive too closely together in time cannot be distinguished and yield problems with PHA Dead Time. However, the rates for this experiment are low enough that this should not be a problem.

The Maestro program used in the Compton experiment has 2048 memory channels with a capacity of 1GB pulses each. A computer is needed to acquire and store more data. With the equipment in the rack as descrbed above.

See Error Analysis Notes for further computer information.

The detector electronics are already in place but may need to be connected when you arrive at the Compton experiment, so check the cables. The equipment is easily damaged, and expensive and time-consuming to repair or replace. Ask for help if you do not understand something!

Keep the following in mind:

Do not touch the 0.002" Beryllium detector window. The red polyethylene safety cap should never be removed from the detector face!
Check the logbook to see that the LN2 dewar has been filled within the last 48 hours. If it has not, please tell a staff member.
Do not apply any voltage outside of 0 to -500V to the detector junction-this would burn out the junction. This should not be a problem if you just leave the detector connected.
Do not apply any potential to the detector junction with the pre-amp off: this burns out the pre-amp input FET. To avoid this, turn the DETECTOR HIGH VOLTAGE POWER SUPPLY on last and off first.

Scattering Apparatus

If the detector, ²⁴¹Am source, and aluminum circular arc are all placed on a circle as shown (looking in a horizontal plane), then all of the photons from the source that scatter off of any point on the arc and enter the detector, have the same scattering angle, and are therefore approximately monoenergetic. In your report explain why this is true, and determine the relationship between the angle $φ$ and the scattering angle $θ$ as shown below.

Procedure

Before proceeding, see a staff member to obtain a radiation ring. The ring should be worn on whichever hand will be closer to the source.

The Detector Power Supply powers the rack that the electronic modules are in. Switch it on last.
Remove the 241Am source from the lead box on the floor, leaving it in its plastic case. Wear your radiation ring, and use the rubber gloves when handling the sources! Also remember to remove the gloves before touching anything else or you will defeat the purpose of the gloves. Place the source on a stand at the height of the detector roughly 15 cm away from the detector.
On the 11X 8481-P1 Amplifier System: make sure that the Bias Cut knob is at zero, and that the F. Disc/Off/Norm switch is in the OFF position. (See the procedure in the LBL-540 Manual for detailed information.) Then look at the Bias Amplifier Out output on a scope set up to look at positive pulses 2 microsec wide. Trigger the scope in Normal mode, and use the A Trigger knob to obtain a fairly steady trace. Make sure that you set the trigger knob such that you see the largest pulses. See Figure 3. The pulses that you see represent the charge that is collected in the detector when a photon is detected, and the pulse heights are proportional to the incident photon energy. Set the Amplifier Gain knobs and Stretcher knob so that the largest pulses, corresponding to the 59.54 keV photons, are about 10 volts. (Remember that the PHA requires input pulses to be between 0 and 10 volts.)

Figure 3: Amplified detector signal: Am241 source. Scope: 1 V/div; 2 msec/div.

Figure 4: Fe55 spectrum pulse output
The amplifier "B. A. Out" output is connected to the "V input" of the PHA inside the computer. To start, learn the guidelines for the Maestro PHA program (note that controls are software controls )

Maestro Full Manual:

We are now going to look at the resolution of our system using the "twin peaks" of 55Fe at 5.90 keV and 6.55 keV. Replace the 241Am source with the 55Fe source. Erase any existing data, and begin acquiring data. You should see activity on the scope as the PHA acquires counts. After roughly 30 seconds, stop, and change the vertical scale (Counts Full Scale) on the PHA as necessary to view the spectrum easily on the scope. You should have something that looks like Figure 4. Note that if you have the scale set too small, the taller peaks may "roll-over" from the top of the display to the bottom, yielding a very odd-looking spectrum. If this happens, just increase the maximum scale value and try again. If you have not been able either to obtain the correct signals or to find the spectra of the 55Fe source, or if you have any questions, now would be a good time to talk to a staff member. Can you resolve the peaks here? Being "resolved" is a matter of definition, but for now consider that two peaks of equal intensity are resolved if they cross at the point at which they have fallen to half of their maximum intensity. What is the width of the lines, measured in number of channels? In order to examine your data quantitatively, and to make a plot, download the data to one of the PC's as described in COM Computer Programs or see the instructions posted in the Compton area.
Now we need to calibrate the system and find the radiation flux at the source (to be used in the Klein-Nishina verification). Because the voltage pulse heights coming out of the detector/amplifier system are proportional to the incident photon energy, each channel of the PHA corresponds to a particular energy seen by the detector. We now want to determine the relationship between the channel number and energy.

Figure 5: Am241 Energy Spectrum
Remove the ⁵⁵Fe source and place the ²⁴¹Am source 15 cm away from the detector (directly in front of the detector). Clear the PHA and take a new spectrum. You should see something that looks like the spectrum shown in figure 5. If you are missing the 59.54 keV peak (far right), your amplification/gain is probably too high (such that the voltage corresponding to this energy is greater than 10 volts). Adjust the PHA pulses accordingly. When you see a spectrum where you think you can identify the peaks with the energies listed above, clear the PHA, take data for 5 minutes, and download data to the computer. Determine which channels correspond to which peaks, using a program such as "Analyze", and then run your data through a best-fit line program to determine A and B in the equation relating energy to channel: Energy = A + B*(channel number). Also determine the uncertainties in your fit parameters, and the value for the reduced $χ$ ². To determine the flux, again use a program such as "Analyze" to find the yield (the number of 59.54 keV photons). NOTE: you simply cannot use the number in the bin that corresponds to 59.54 keV, why? Dividing the yield by the amount of time it took to get the spectrum (i.e. 5 minutes) you can find the flux at the detector. You should be able to find the flux at the source using this number and the fact that you know the source target distance (SEE Melissinos, pp. 261-265 under Prerequisite Reading Materials).
We are now ready to observe Compton scattering using the 59.54 keV peak. Chose a scattering angle; set your system up as described in the Scattering Apparatus section above. Shield the detector from direct source radiation using the small sheets of lead, and begin to collect data. Remember that the detector must lie on the circle, and that the detector lies 5-6 mm behind the entrance window. Measure Compton scattering for six different scattering angles. Note: you can see the scattered peaks for the smaller angles (less than 90°) in an afternoon (4 hours), but for the larger scattering angles you will need to do overnight runs, so plan accordingly. In general, longer runs at a given angle yield better data. In your data analysis you will want to compare the number of photons scattered into the different scattering angles, to the numbers predicted by the Klein-Nishina formula (see figure 6), so be sure to keep a record of how long each run is, which scattering target you are using, the distance between source-target and target-detector, and an estimate of how much of the target is illuminated by the source after the lead shielding is in place for every scattering angle. These values will be necessary to calculate quantities such as number of scattering centers and incident flux at the target (see Melissinos 1966, pp. 261-265). You should also consider the effects of background radiation. If you start a run and then leave the area, leave a sign saying "DO NOT DISTURB" along with your names and when you will return. No responsibility is assumed for equipment left running with no indication of when you will return; such equipment may be turned off by the staff. If you are doing an overnight run and do not have the equipment scheduled for the following day, you must come at the start of lab to collect your data unless you make other arrangements.

Figure 6: Klein-Nishina Cross Section using Scattering Angles
For something more complex, you will try to verify the Klein-Nishina formula for scattering within the detector. If we send monoenergetic X-rays directly into the detector without scattering them off of anything first, we should be able to observe Compton scattering off of the electrons within the detector. \[See Knoll, Ref. 6.\] For this effect to occur, the photon must enter the detector, scatter off of an electron, and then exit the detector. Since it is the electron energy that is ultimately processed to become the PHA count that we see, and since this electron energy is dependent upon the scattering angle, we should be able to see the Compton continuum predicted by Klein and Nishina (figure 7). You should complete Questions part 7 before you come to lab to begin taking the following data. Please see a staff member if you do not understand this part of the lab. To obtain only 59.54 keV photons (eliminating the lower energy lines) that are unscattered before entering the detector, use the two 1 mm apertures (lead sheets with small holes on the brass plates) for collimation and the 0.003" Cu and 0.003" Al sheets (mounted on a brass plate) for filtration of the source X-rays. Align holes in the Brass collimator plates to be in line with the detector window. You will need to use three plates and check the alignment of the holes to the detector. Measure the resulting spectrum by doing a long over-the-weekend run-you should see a continuum at lower energies that comes from Compton scattering off of the detector's own electrons as examined in Questions, Part 7. The Klein-Nishina verification portion of this experiment does not work out as the model predicts. You should nevertheless try it, and put some thought into what might be going wrong. Do keep in mind that we are more concerned that you understand what it is that we are testing and what we expect (Questions, Part 7), than that you achieve "the" correct result. After all, in experimental physics it happens that something does not come out as expected at least as often as it does come out as expected. Examining and explaining these situations are often more worthwhile than looking at those in which the answers are already known.

Figure 7: Scattered Electron Energy Distribution using Compton Continuum

Questions

1. What accounts for the unshifted peaks that appear in your spectra taken at the different scattering angles? Can they be due to scattering off of the aluminum nuclei. (See Pre-lab questions.) \[Hint: See Melissinos.\]

2. What is the full-width at half-maximum (FWHM) of your measured 55Fe peaks and of the 59.54 keV 241Am peak, measured in energy? How do these compare with the expected resolution of the detector? (See, for example, Knoll, pp. 89-92.)

3. What is chi-square for the hypothesis that the X-ray energy and scattering angle are described by the Compton relationship?

4. How does the relative number of photons scattered into each scattering angle compare to the Klein-Nishina prediction?

5. Use your results from the scattering runs to determine the electron mass. What is the uncertainty in your value? Accuracy is optimized if the widest possible range of scattering angles is used.

6. In the preceding question, you have assumed that the scattered beam was entirely monoenergetic. Is this actually true? Consider that there are several geometrical effects which cause the scattering angle to deviate from its nominal value-what are they, and how do they affect the results? This is not a trivial question! In particular, do they tend to shift your peaks from where you expect them to be, or do they tend to broaden the peaks about the expected value?

7. In the last part of the lab you attempt to verify the Klein-Nishina prediction for Compton scattering within the detector. The theoretical prediction for this experiment consists of the following:

(a) Prove that the scattered electron energy distribution $\frac{d\sigma}{dq'}$ and the scattered photon angular distribution $\frac{d\sigma}{d\Omega}$ are related by