NOTEBOOK: Sketch the gamma spectrum produced by Co-60 in your notebook and save the spectrum to file. From the Nuclear Decay Schemes, identify the energies corresponding to the two emitted gammas and identify the corresponding features on the spectrum. Record the channel corresponding to the centroid for each (with uncertainty).</HTML> |
NOTEBOOK: Remember that you ultimately will want to measure the centroid of a peak corresponding to a gamma of about 2 MeV; make sure that such a peak will appear be on screen (give yourself plenty of extra space) and adjust the gain if necessary to make room before recording final values. Note the gain settings in your notebook.
NOTEBOOK: In addition to the two peaks, you should find a third peak at higher energy (> 2 MeV). Can you explain the origin of this peak?
Once you determine the origin of this peak and know its energy, this point can be used as a third calibration point.
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3.2.2 Calibration fit with additional sources (winter only)
The in-software calibration method described above has several limitations.
Therefore, it is preferable to collect data in raw channel number and then, at home, do a more complete calibration to convert from channel to energy.
NOTE: It does not hurt to do the in-software calibration described above even if you plan to do a better calibration later. When exporting the data in the *.tsv format, both the channel number and calibrated energy values are saved. In this way, you may use the rough calibration values from the software as a guide while in lab, but do the proper calibration when producing final plots and analysis.
In winter quarter, we will use the Co-60 energy points above, as well as_ additional calibration points_ from Na-22 (two gammas) and Cs-137 (one gamma). With these additional points, we can fit the data to a linear function and properly incorporate all of our uncertainties. More details on how to perform this post-experiment calibration will be given below under Analysis. For now, simply collect the additional Na-22 and Cs-137 spectra and record the centroid values.
| > NOTEBOOK (winter quarter only): Sketch the gamma spectrum produced by Cs-137 in your notebook and save the spectrum to file. From the Nuclear Decay Schemes, identify the energy corresponding to the single peak and record the channel corresponding to the centroid. |
| > NOTEBOOK (winter quarter only): Sketch the gamma spectrum produced by Na-22 in your notebook and save the spectrum to file. From the Nuclear Decay Schemes, identify the energies corresponding to the two peaks and record the channel corresponding to the centroids. |
3.3 Measuring the gamma energy
Most of the neutrons passing through the paraffin shielding of the howitzer are slowed and ultimately captured by the reaction of Eq. (2). Therefore, the shielding itself is a strong emitter of capture gammas. They are readily observed by placing the NaI crystal within a few feet of the howitzer.
To obtain a spectrum of the capture gammas, we will do the following:
Leave the port on the neutron howitzer closed.
Remove any remaining calibration sources and place them behind the shielding near the door.
Remove the lead bricks from between the howitzer and the detector.
Collect a spectrum using the PHA software.
NOTE: You are observing both the direct gamma spectrum as well as a weak background due to the neutrons. The neutrons do not interact strongly with the detector (which is a high-Z material – good for gamma detection, but poor for neutron detection), but they will deposit some energy. We will make no measurement of this, but only note that it contributes to the background.
Do the best job possible to measure the energy of this gamma. In so doing you will indirectly determine the mass of the neutron, since the mass of the proton and deuteron can be directly measured by mass spectrometry.
NOTEBOOK: Sketch the direct howitzer spectrum (to scale) in your notebook and save to file. Identify the capture gamma peak and record the peak centroid (in channel and energy) with uncertainties.
NOTEBOOK: In addition to the capture gamma peak, you should see another peak at lower energy (< 1 MeV) which is not part of the neutron background. Based on its centroid, can you determine the origin of this peak?
3.4 Establishing evidence for the deuteron reaction
We have observed a gamma peak, but we have not yet verified that this peak is due to the formation of deuterons. Let us now collect evidence to support this hypothesis.
3.4.1 Shielding
Lead is a high-Z material and therefore attenuates 2 MeV γ-rays more heavily than fast neutrons. Let us make a series of measurements which show that placing 4” of lead between the howitzer and the detector attenuates the gammas more heavily than the fast neutrons from an open port. To make this measurement, consider the following:
When the port is closed, neutrons are shielded so that only capture gammas produced in the paraffin are emitted from the howitzer.
When the port is open, fast neutrons and capture gammas are emitted from the howitzer.
Attenuation is given by the ratio of the rate with lead to the rate without lead.
NOTEBOOK: Measure and record the count rates in all four combinations of port open, port closed, with lead shielding, and without lead shielding. Determine how to combine these measurements to get the rate of just gammas and the rate of just neutrons. Compute the ratio of each rate with shielding to that without shielding and show that the lead will eliminate most of the gammas while allowing most of the neutrons of interest to pass.)
3.4.2 Evidence for deuteron production
We have to this point assumed that the photons we detect are due to the reaction of Eq. (2), but let us perform a test to build evidence to support this hypothesis.
Use the arrangement shown in Fig. 2 and consider the following logic:
The gamma peak appears when there is no lead shielding (regardless of whether the port is open or closed) and disappears when the lead shielding is added.
When the port is closed, no fast neutrons make it to the detector, but when the port is opened, some fast neutrons will pass through the lead.
If we place paraffin inside the chamber (that is, between the lead shielding and the detector), the neutrons passing through the lead may interact with the paraffin to produce deuterons. Because of the lead shielding, we know that any photons detected must have been produced inside… verifying that the photons we initially observed are due to some “neutron plus paraffin” reaction.
However, paraffin is made of both carbon and hydrogen. In order to exclude a reaction between neutrons and carbon, we can replace the paraffin with solid carbon (graphite) and expect the photon peak to disappear again.
The idea is to place the NaI detector in a lead chamber to shield it from the capture gammas coming from the source. In the lead chamber one can place ~6“ of paraffin or 6” of carbon in front of the NaI. One measures the differences in the number of capture gammas with the chamber empty, filled with paraffin and filled with carbon. If the γ-rays are due to the deuteron reaction, then one expects a higher rate of capture gammas when the paraffin is in place as compared to when the chamber is empty or full of carbon. Use the PHA software to measure the rate of events in the full energy peak associated with the ~2 MeV capture gammas for each of the three different absorber materials in the chamber.
4 Experimental procedure: Neutron cross section and measurement of the size of the nucleus (Day 2)
WARNING: Do not switch the high voltage cable on the power supply from one detector to the other while the high voltage is turned on. Instead, make sure that both toggle switches are off before removing one power cables and make sure that it remains off when reattaching the new cable.
4.1 Fast Neutron Detection
4.1.1 Detector types
| Different materials interact with particles in different ways. This is why there is not one type of particle detector, but many. Gammas interact mainly with electrons, so for the first experiment we a crystal of sodium iodide (an electron-rich, high-Z material) as our detector. Neutrons interact through direct collisions, so for the second experiment, we actually want a low-Z material where the nuclei are comparable in size to the neutrons themselves. Therefore, we will use a plastic scintillator (rich in hydrogen and carbon atoms). |
4.1.2 Plastic scintillator detection
| In the first PHYS 211 experiment, we studied the many interactions of photons with matter and the features of NaI pulse height spectra. There, it was possible for a gamma to deposit all of its energy in the detector leading to a full energy peak. With neutrons in plastic, however, no such feature will appear. Instead, we observe continuous spectra. Consider the following sequence of events: |
A neutron enters the plastic and scatters from a proton (hydrogen nucleus) initially at rest.
The proton carries away some kinetic energy (any value from zero up to the full energy of the incident neutron), while the neutron continues with the remaining energy – either to collide again or to escape the detector.
The protons quickly lose their kinetic energy through Coulomb interactions with other particles in the scintillator resulting in light pulses.
These light pulses are coupled to a photomultiplier tube (PMT) which in turn produce a pulse whose total charge is proportional to the kinetic energy of the proton.
Therefore, the pulse height spectrum we obtain represents the energy deposited in the scintillator by the scattered protons and not necessarily the energy of the incident neutrons.
4.1.3 Detector response
While the plastic detector is better suited for detecting neutrons than photons, there is still some response to incident gammas. However, because the interaction mechanism is different for these two processes, the amount of light output (and therefore the size of the PMT output) will be different. Fig. 3 shows this response. Note that the response to protons is much less than of electrons of the same energy.
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Figure 3: Relative light output for electrons (resulting from incident gammas) and protons (resulting from incident neutrons) losing energy in the plastic scintillator.
4.2 Energy calibration
4.2.1 Region of interest
For this experiment we want to measure the cross section only of the highest energy neutrons, those in the range of about 7 to 10 MeV. We choose this range because at lower energies, the neutron cross section becomes dominated by the neutron's de Broglie wavelength rather than the size of the scattering nucleus. To be sure that we're detecting only neutrons in this range, we must count proton interaction over the same range. To set this region of interest, we must first perform an unusual 1-point calibration.
Normally, to calibrate a detector, we subject the detector to particles of known energy and look at the resulting spectrum. We do not, however, have access to a neutron source of known energy, so we cannot perform a neutron calibration with other neutrons as desired. Instead, we can use gammas of known energy and the relative light output plot of Fig. 3 to get a rough idea where neutrons of our desired energies will appear.
Let us again use the Na-22 button sources. Recall that these sources emit 511 keV and 1.27 MeV gammas. When the full energy of the gamma is deposited in the scintillator, that event contributes to a full-energy peak in the gamma spectrum. However, since the plastic has low-Z, (and therefore low electron density), the probability for Compton scattering followed by photoelectric effect is also low. Thus, we generally see a Compton edge in the gamma spectrum, but do not see a full-energy peak.
Recall the Compton scattering formula:
| { ${/download/attachments/132350246/eqn_3.png?version=2&modificationDate=1442414710000&api=v2}$ | (3) |
where E is the energy of the incident gamma, E' is the energy of the scattered gamma, θ is the scattering angle (measured relative to the incident gamma direction), and _mc_2 = 511 keV is the electron rest energy.
NOTEBOOK: Rearrange Eq. (3) to express the energy of the Compton edge for an incident gamma of energy E.
NOTEBOOK: Calculate the energy of the Compton edge for the two peaks of Na-22. From Fig. 3, estimate the relative light output for a electron produced in the scintillator with energy 1 MeV. Estimate the relative light output for a proton of 7 MeV. What is the ratio of these two relative light outputs?
Your calculations should show that a 7 MeV proton yields about 3 times the light intensity (pulse height) of the Compton edge of the 1.27 MeV Na-22 gamma. We will set our region of interest to collect only counts at this energy and above.
4.2.2 Calibrating the PHA
Let us now “calibrate” the channel axis.
Place a layer of 4“ of lead in front of the plastic scintillator detector (labeled “Detector I”), but leaving a small gap between the shielding and the face of the detector. (See Fig. 4.) The purpose of this shielding it to block gammas from the paraffin from entering the detector, so make sure to layer the bricks high enough to block all paths.
Place a few Na-22 button sources in front of the detector and photomultiplier tube (PMT), but inside the shielding.
Verify that the high voltage and anode output cables are appropriately connected to the detector. These cables should be routed through the wall into the next room. With the high voltage cable plugged into the power supply, turn on the voltage and set it to -1250 V. (Remember that these are different cables and a different power supply than the NaI detector used on Day 1.)
Attach the anode output BNC cable to the pre-amp input of the pulse-height analyzer (PHA).
Turn on the PHA and start the PHA software (USX on the desktop).
Collect a spectrum. Adjust the coarse and/or fine gain to move all features on-screen. If the “Dead Time” meter reads more than ~10%, remove some sources or place them further away from the detector face.
NOTEBOOK: Sketch the gamma spectrum produced by Na-22 in your notebook and save the spectrum to file. You will not see two peaks, but you should find two broad Compton edges. Record the channel corresponding to each; note that you will have to estimate the location of the “edge” due to the width of the features. Based on the factor of 3 determined above, make sure that the neutrons we are interested in (E > 7 MeV) will be on screen; adjust the gain again if necessary. Note the final gain settings in your notebook.
NOTE: We will only use the Compton edge due to the 1.27 MeV gamma as a calibration point. The lower-energy Compton edge due to the 511 keV gamma sits on a steep background and is quite distorted. A single point is sufficient for the rough determination of region of interest we use here.
As this is a 1-point calibration, we will leave the x-axis in channel units. It is sufficient to have only the rough estimate for the E > 7 MeV region.
Clear any existing regions of interest and set a new one from three times the 1.27 MeV Compton edge to the last channel.
4.3 Cross section data collection
Set up the target stand and detector as in Fig. 4. It should be noted that the “neutron beam” is also rich in gamma-rays from the paraffin shielding which are detected in the plastic scintillator by Compton scattering. Leave the 4“ of lead shielding used for the calibration in place to continue to attenuate these gammas.
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Figure 4: Apparatus for cross section measurement
You now will collect count rate as a function of absorber thickness in order to determine the cross section of ~8.5 MeV neutrons through several absorbers – copper, aluminum, carbon and lead.
NOTEBOOK: For each absorber and for each thickness (including zero thickness), collect a spectrum and record the gross counts within your region of interest and live time in a table. Compute the rate (with uncertainties). It will be useful to plot the data as you go to make sure the results are as expected. This can be done on the computer and pasted in your notebook later.
You may also want to measure the residual (background) rate in the detector when the direct beam is totally blocked. When fitting your data, you will of course want to include a constant background, but this independent measurement can be used as a consistency check.
NOTEBOOK: Measure the background rate by inserting the maximum amount of lead absorber that will fit on the stand along the beam path. This rate is easily 10% of the full rate with no absorber.
5 Analysis
5.1 Day 1 Calibration (winter quarter only)
| During the day 1 calibration, you collected spectra for Co-60, Na-22 and Cs-137. From these, you can identify a total of six energy peaks – 511.0 keV, 661.6 keV, 1.173 MeV, 1.275 MeV, 1.332 MeV, and 2.506 MeV. |
REPORT: Plot the calibration spectra and identify the three peaks. Determine the peak centroids (with uncertainties). You may fit the peaks to Gaussians, or you may identify the peaks “by-eye”; either is OK so long as you properly estimate uncertainties.
From the peak centers, you can perform a calibration to extract a function converting channel to energy, E(ch). However, your dominant uncertainties are in the channel (peak centroid), so we must first fit ch(E) and then invert the function (and the associated uncertainties).
REPORT: Plot your calibration points (with uncertainties) and fit to the form ch = AE + B. Invert this equation (and the uncertainties) to find the function E = A' ch + B'.
5.2 Quantitative evidence for the deuteron reaction and calculation of the mass of the neutron
One of the goals of the Day 1 experiment is to determine the mass of the neutron by using the energy of the gamma produced in the deuteron reaction (assuming that the mass (rest energy) of the proton and deuteron have been measured elsewhere using, for example, mass spectrometry.)
However, before we can rely on the measured gamma energy, we must first establish that the observed peak is indeed due to the production of deuteron.
REPORT: Using your measured count rates for the different day 1 trials, present a quantitive case that the observed peak is due to deuteron production. It is not sufficient to qualitatively state the peak “appears” or “disappears” under different circumstances; you should be able to establish rigorous, statistically significant quantitative evidence.
Once you have given evidence for the origin of the peak, measure the peak centroid and determine the gamma energy. As our PHA spectra give count rate as a function of channel, we must use the calibration function (determined above), to convert to energy. You may do one of the following:
convert the x-axis for all plots to energy and determine the gamma peak centroid in energy units, or
determine the gamma peak centroid in channel and convert only that value to energy.
Regardless of your method, incorporate the calibration uncertainties into your peak energy uncertainty if significant. (If not significant, justify why it can be neglected.)
REPORT: Using Eq. (2) and literature values for the mass (rest energies) of the proton and deuteron, determine the mass (rest energy) of the neutron (with uncertainties).
5.3 Neutron cross sections
| Just as in the Gamma Cross Sections lab, we expect the count rate of the neutrons which pass through the absorber material to be an exponential function which decays as the absorber thickness increases: |
| R(x) = R(0)e-λx = R(0)e-ρNA_σx/m_a_,_ | (4) |
where R is the rate, λ is the linear attenuation coefficient (typically with units of cm-1), σ is the cross section (typically with units of cm2), ρ is the mass density (mass per unit volume, typically with units of g/cm3), _N_A is Avogadro's number, and _m_a is the atomic molar mass (average mass per mole, typically with units of g/mol).
REPORT: Plot your gross count rate as a function of absorber thickness for each material. Fit this data to an exponential (like that of Eq. (4)) plus a constant background and extract a value for the cross section with uncertainties.
5.4 Cross section as a function of nuclear radius
The Ramsauer model of neutron cross sections (see, e.g. Refs. [2-4]) suggests that nuclei present a cross section that is equal to twice their “effective area”,
where R is the radius of the nucleus and λ is the de Broglie wavelength of the neutron,
| { ${/download/attachments/132350246/eqn_5.png?version=2&modificationDate=1442419367000&api=v2}$ |
