We will use a source of high energy neutrons in the lab to perform studies on the interaction of neutrons with nuclei.  You will devise a series of measurements which you will use to:

• Confirm that deuterons are produced by the interaction of neutrons with protons.
• Measure the mass of the neutron.

It is not expected that you will figure out an optimal series of measurements on your first attempt. Progressing through the experiment will be an iterative process where you try out some ideas for collecting data, do some preliminary analysis, evaluate your results with the assistance of the instructors, refine your methods, and repeat. This iterative process is similar to how research experiments in a professional lab are performed and is the real point of this instructional experiment.

Our source of neutrons for this experiment is a “neutron howitzer”. The core of the howitzer consists of 80-grams of 239Pu mixed homogeneously with 9Be. The Pu decays with the emission of 5.18 MeV alpha particles at a rate of ~2 x 1011 decays/sec (or, about 5 Curies). Some of these alphas in turn interact with the beryllium to produce neutrons by the process

This reaction is exothermic with a Q-value of 5.7 MeV, so neutrons with energy up to almost 11 MeV are emitted from the source. Most of the alpha particles lose energy by ionization in the source before interacting, but approximately 4 out of every 105 produce a neutron by the above reaction, giving ~107 neutrons/sec.

{ ${/download/attachments/201099056/DSC08825.jpg?version=1&modificationDate=1546987047000&api=v2}$ The four ports of the howitzer should be plugged and locked when not in use and one should never look into a port or unnecessarily spend time in front of it.

CAUTION: One must avoid being exposed to the direct beam of the neutron howitzer. (There is no danger in handling the small 1-10 μCi button and rod gamma sources used for calibration.) The radiation dose rates for the neutron howitzer, and maximum permissible doses are given in the Tables 1 and 2 below.

Table 1: Measured neutron howitzer radiation dose rates (in mR/hour) due to neutrons and gammas, separately

Table 2: Maximum permissible doses above background (where background rate is about 360 mR/year)

To shield against these energetic neutrons, the source is surrounded by a thick layer (~30 cm in thickness) of paraffin, a molecular chain of hydrogen and carbon, CH2. Recall that neutrons do not interact electromagnetically (they have zero charge), so the main method for energy loss is through collisions. Since neutrons and protons (i.e. hydrogen nuclei) have nearly the same mass, the neutron loses half its energy, on the average, for each collision with a proton. The mean free path of the neutrons in paraffin (i.e. the distance between collisions) is a few centimeters, so most neutrons which escape the paraffin volume have undergone enough collisions to lose most of their energy. When these neutrons do escape, they will have been thermalized (that is, reduced in energy to _E_avg = k_B_T = 0.025 eV) and are no longer dangerous.

We do, however, want some safe access to the high energy neutrons, and this is achieved though the four side ports where the shielding can be removed. Each port has a plug made of lucite (another hydrocarbon material) which will thermalize or block neutrons when inserted, or allow a direct beam to escape when removed. The energy spectrum of the neutrons emerging from an open port of the source is shown in Fig. 1.

{ ${/download/attachments/201099056/Neutron_Energy.png?version=1&modificationDate=1546987048000&api=v2}$ Figure 1: Experimentally-measured neutron energy spectra for two Pu-Be sources comparable in size to the one used in this experiment. (source: [1])

The cross sections for thermal neutrons can be enormous: _σ_thermal ≤ 10-16 cm2. Such values mean that thermal neutrons travel very short distances before being scattered. At higher energies, cross-sections are smaller and typically measured in barns (1 b = 10-24 cm2) and can penetrate to greater depths. 

The fact that the neutron has no electrical charge makes it a bit tricky to measure its mass.  The mass of charged particles and nuclei can be measured through the technique of mass spectrometry. So, if we assume that the masses of the proton and the deuteron (a deuteron is a bound state of a proton and a neutron) are known from mass spectrometry, we can find the mass of the neutron from the following interaction by which deuterons are produced,

A gamma-ray (called the capture gamma) is produced because the bound deuteron has a lower total energy than the separate neutron and proton. Using conservation of energy, if the masses of the proton and deuteron are known and the energy of the capture gamma can be measured, then the mass of the neutron can then be calculated.

NOTEBOOK: Look up the masses of the neutron, proton and deuteron and calculate the energy of the expected gamma. It is on the order of 2 MeV. (Note that the deuteron is a bound nucleus with one proton and one neutron, while deuterium is the bound state of a deuteron nucleus with an electron. The two have slightly different energies since there is some binding energy associated with the electron.)

If our neutron howitzer is indeed producing energetic neutrons, some of them should be producing deuterons and capture gammas by the process given in (2). A NaI+PMT detector can be used to detect and measure the energy of gamma-rays coming from the howitzer.  

Measuring the energy of a gamma-ray is easy. The experimental challenge lies in demonstrating that the detected gammas were produced by the formation of deuterons, as opposed to being from some other unrelated source of radiation. This is the part of the experiment which we are challenging you to figure out.

{ ${/download/attachments/201099056/fig_2.png?version=1&modificationDate=1546987048000&api=v2}$Figure 2: Neutron howitzer and the detector inside the lead “chamber”. We will use the known energies emitted by cobalt-60 as calibration references.

• Make sure that the port from the neutron howitzer is closed.
• Use lead to shield the detector from radiation produced by the howitzer.
• Place the Co-60 rod source in the chamber in front of the 5“ NaI detector and photomultiplier tube (PMT). 
• Verify that the high voltage and anode output cables are appropriately connected to the NaI detector (labeled “Detector B” or “Detector II”). 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.
• 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 by double-clicking on USX on the desktop.
• Collect a spectrum. It may be necessary to adjust the coarse and/or fine gain to move all features on-screen. If the “Dead Time” meter reads more than ~20%, move the source further away from the detector face to lower the count rate.

It is important that you make detailed notes of how you perform this calibration in your lab notebook. It is likely that you may need to refine your calibration procedure after preliminary analysis of the data. So you will need to know exactly what you did and how you set things up.

<blockquote> NOTEBOOK: Make sketches indicating the locations of the detector, howitzer and any shielding you make use of. Include distances and dimensions of important elements of your setup. </HTML>

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). | 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? HINT: Consider both the typical time scale of a sodium iodide crystal pulse (look back to the notes from your first lab or plug the detector output into a scope) and the lifetime of the intermediate state in the relaxation of Ni-60 to the ground state as shown on the decay scheme. Once you determine the origin of this peak and know its energy, this point can be used as a third calibration point. </blockquote></HTML> In the drop-down menus, select “Three-Point Calibration” and use the values of the energy and channel to calibrate the x-axis. Verify that the peaks now appear with the correct energies. 3.2 Calibration fit with additional sources (winter only) The in-software calibration method described above has several limitations. It does not incorporate the uncertainties on the measured peak channel positions. It does not explicitly provide the fit function and cannot produce uncertainties on the fit parameters determined. 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. Remove the Co-60 rod source and replace with one button of Cs-137. Collect a spectrum. Do not adjust the gain! > 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. Remove the Cs-137 source and replace with one button of Na-22. Collect a spectrum. Do not adjust the gain!