The mass of charged particles – such as protons and electrons – can be investigated using mass spectrometry whereby a beam of such particles is bent by a magnetic field and the radius of curvature is measured. For chargeless particles – like neutrons – such techniques do not work and we must be more creative. In this experiment, you will use some known facts about neutrons to design and test an experiment with the goal of determining the mass of the neutron. This lab – unlike many others in this course – allows for a significant amount of creativity and will require you to measure, adapt, and iterate in pursuit of improved measurement techniques.

An overhead view of the neutron howitzer and NaI+PMT detector

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 do the following:

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

You will not be provided with a detailed set of instructions on exactly what measurements to take. Instead, you will be given instructions on how to use the detector – a NaI+PMT-type which you should already be familiar with from Introductory Lab: Gamma Cross Sections – and it will be up to you to decide how to address the points listed above. As neither of the above points can be directly achieved by pointing the detector at the source, you will have to instead make measurements of indirect radiation and set up a logic based on different configurations of lead, paraffin, and carbon shielding.

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.

A 30 second exposure of a 5“ diameter NaI crystal adjacent to a 250 $\mu \textrm{Ci}$ Na-22 source. You can see the faint blue light produced by the scintillation process as gammas from the source lose energy to electrons in the crystal. If you were to sit in a completely dark room for 15 to 20 minutes to allow your eyes to dark-adapt, you would be able to see this soft glow from the crystal with your own eyes.

In order to prepare for the lab, you should read over the full theory section below, and – in particular – pay attention to the following questions. Some of these can be answered based on what you find in the theory section, but others may require outside research online. Make sure you can answer the following before you arrive for Day 1:

• The mass of a charged particle can be measured by sending the particle with known velocity through a perpendicular magnetic field and measuring the radius of the circular orbit. (This is called a cyclotron.) Look up the mass of the proton and the mass of the deuteron* and report the value (to as many digits as you can find). Provide a reference for your values.
  • *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 you send a charge-less particle through a magnetic field, it’s trajectory will not bend. We therefore need to think of a different method for determining the mass of the neutron. Perhaps we can infer the mass by observing the formation of a deuteron ($n + p \rightarrow d + \gamma$), where $\gamma$ represents the energy released (as a photon) due to the fact that the bound state of the deuteron has a lower rest mass than the sum of the neutron and proton separately.
  • To make an order of magnitude estimate, approximate the mass of the neutron to be equal to the mass of the proton. Determine the gamma energy as the difference in rest energies between the deuteron and two times the rest energy of the proton. We know from other evidence (e.g. the beta decay of a free neutron into a proton, an electron and an antineutrino) that that the neutron is actually slightly heavier than the proton. Does this mean the expected gamma energy is larger or smaller than your estimate?

Our source of neutrons for this experiment is a “neutron howitzer”. The core of the howitzer consists of 80-grams of ${}^{239}$Pu mixed homogeneously with ${}^{9}$Be. The plutonium decays with the emission of 5.18 MeV alpha particles at a rate of ~$2 \times 10^{11}$ decays/sec (or, about 5 Curies). Some of these alphas in turn interact with the beryllium to produce neutrons by the process

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 $10^5$ produce a neutron by the above reaction, giving a flux of ~$8 \times 10^6$ neutrons/sec.

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.

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

Table 2: Maximum permissible doses above background (where background rate is about 360 mrem/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, $\textrm{CH}_2$. 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 $E_{avg} = k_BT = 0.025 ~\mathrm{eV}$ ) 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.

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: $\sigma_{thermal} \le 10^{-16}\textrm{cm}^2$. 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 ($1~\textrm{b} = 10^{-24}~\textrm{cm}^2$) and can penetrate to greater depths. 

The fact that the neutron has no electrical charge makes it difficult 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 photon (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.

If our neutron howitzer is indeed producing energetic neutrons, some of them should be producing deuterons and capture gammas by the process given in Eq. (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 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.

Before you begin to collect the bulk of the data, you will complete a number of specific tasks, each of which is focused on a skill or technique which you need to understand in order to complete the experiment. Successfully completing these tasks, as determined by the instructors during the lab, will count for a total of 25% of the grade of this lab.

The detector is a NaI scintillator coupled to a PMT. You are already familiar with this type of detector from Introductory Lab: Gamma Cross Sections. If you need to review how this detector works, see the NaI Detector Physics and Pulse Height Spectra page.

For this experiment, you will make use of the fact that the size of the pulses from the PMT is proportional to the energy of the gamma which struck the NaI crystal. Pulses from the PMT are sent to a SpecTech UCS spectrometer which measures their total integrated charge and displays a histogram of pulse height sizes on the computer. You can use radioactive sources which produce gammas of known energy to calibrate the pulse height axis.

1. In-software calibration (5 points)

We will start by using the known energies emitted by ${}^{60}$Co as calibration references.

Do the following:

• 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 NaI detector and photomultiplier tube (PMT). 
• Verify that the high voltage and anode output cables are appropriately connected to the NaI 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 -1000 V.

• 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 ~15%, 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. In such a case, you will need to know exactly what you did and how you set things up. (Remember, for example, to record the distance between the howitzer and your detector cart in case either object is moved between sessions.)

Figure 2: Neutron howitzer and the detector inside the lead “chamber”.

Continuing, do the following:

• Collect a spectrum.

  • From the Nuclear Decay Schemes, identify the energies corresponding to the two emitted gammas and identify the corresponding features on the spectrum.

• Remember that you ultimately will want to measure the centroid of a peak corresponding to a gamma of greater than 1 MeV (as determined in the Preparation Question). In order to make sure that such a peak will appear be on screen, adjust the gain so that energies of at least 3 MeV will be on screen. (You can assume that the relationship between channel and energy is linear.) Note the gain settings in your 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.
• 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.

In order to measure the mass of the neutron we are making the following assumptions:

1. That energetic neutrons from the source are interacting with protons in the paraffin shielding material, producing capture gammas as described in the theory section above.
2. That the rest masses of the proton and deuteron are already known from mass spectrometry. (You can look these values up in the literature.)

The experiment then boils down to identifying the capture gamma and measuring its energy. 

The detector can be used to measure the spectrum of the radiation coming from the howitzer with various shielding configurations. Once the full energy peak of the capture gamma has been identified, measuring its energy is straight-forward, assuming the detector has been calibrated as described in Sec. 3. The tricky part is demonstrating that the full energy peak is from the capture gamma which requires a bit of detective work. This task can be accomplished using the following:

• Given assumption #1 above, the howitzer should be a source of capture gammas, regardless of whether or not the ports are open or closed. So, with the ports closed, the howitzer should be a strong gamma source with very little neutron radiation escaping.
• When a port is open, it will emit a collimated beam of energetic neutrons in addition to the capture gammas.
• We use three different materials that interact with particles and gammas in this experiment:
  • Lead bricks are provided for use in shielding the detector. Lead is more effective at attenuating gammas than neutrons. (Measure the ratio of gamma attenuation to neutron attenuation for the thickness of lead shielding that you choose to use.)
  • Paraffin (a material containing both protons in the form of hydrogen atoms, and carbon nuclei) blocks are provided.
  • Blocks of graphite (a form of pure carbon) are provided.

You will be expected to make measurements which not only demonstrate that capture gammas are being produced in the howitzer, but to quantify the result in terms of a statistical significance as well. As you work through this experiment do not forget to consult with the lab instructors who will challenge your results. Keep in mind that this is intended to be an iterative process where your analysis of initial measurements leads to new ideas and a better measurement. This experiment is more about learning the process of thinking through how to approach and improve a measurement than it is about obtaining the mass of the neutron.

Armed with a plan, you are now ready to build up your evidence and to make the most precise measurement of the capture gamma energy that you can.

It is expected in this experiment that you will take data, analyze it, revise technique and repeat – possibly multiple times – until you achieve statistically significant results.

As you progress, do not forget to continue recording relevant information in your lab notebook as you did for the exercises.

You have one week to perform a full and complete analysis of the data you collect in lab and submit the following assignments. You can score up to a maximum of 75 points total on these assignments.

As a first step, establish the origin of the peak which you plan to claim as the capture gamma peak. Be quantitative and precise!

Do the following:

With the origin of the peak established, show how you use this peak (along with your calibration) to determine the mass of the neutron.

Do the following:

You will need to write a complete and persuasive conclusion that includes a comparison of your results to expectations/literature and puts the results in proper context.

Do the following:

[1] M. E. Anderson and R. A. Neff, "Neutron energy spectra of different size 239Pu-Be(α, n) sources", Nucl. Instr. and Meth. 99, 231 (1972). This work measures the neutron energy spectra of Pu-Be sources of various sizes.