The Anatomy of a Neutron

Timothy Paul Smith. American Scientist. Volume 98, Issue 6. Nov/Dec 2010.

The atom is made up of three types of particles. There are the negatively charged electrons that zip around the core of the atom at speeds up to 10 percent of the speed of light. Their orbits remind us of planets; their motions are dynamic and exciting. There are also the protons, massive particles that sit at the atom’s core and, by the strength of their attractive positive charges, hold the meteorlike electrons in orbit. These two types of particles determine the atom’s shape, chemistry and dynamics. And then there is the neutron. It is neutral. It is a nonparticipant in the atomic dance where the protons swing their electron partners widely. It appears to be a spectator in the atom, a microscopic pebble. However, the neutron really does have its own life. Its surface is boiling with new particles, and its heart is alive with even tinier particles such as quarks and gluons. In the last dozen years we have developed a clearer view of this active particle. Before, when we have looked at the atom, we were viewing this world at the wrong magnification to see the really vibrant neutron.

To understand the neutron, we need to look at a scale 100,000 times smaller than the atom. To get a feel for that size, consider this: A red-blood cell is about 0.00001 meters across, about 100,000 times smaller than a human being. An atom is 100,000 times smaller than a blood cell, and a neutron or proton is about 100,000 times smaller than an atom. The diameter of these particles is a femtometer (10^sup -15^ meters, or a quadrillionth of a meter), but in the language of particle and nuclear physics, it is usually referred to as a fermi (named for Enrico Fermi, a physicist prominent in the building of the first nuclear reactor). Still, 100,000 is a hard number to visualize. To give a scaled-up example, if an atom were the size of Rhode Island, the nucleus would be the size of a person wandering around inside that state, and except for the electrons orbiting along the border, the rest of the state would be empty.

Within the nucleus itself, the protons and neutrons are tightly packed. Think of a stack of oranges at the market, or better yet a stack of apples and oranges mixed together representing the two types of particles. Collectively the particles are called nucléons because they have many similar physical characteristics, including about the same size and mass. Nucléons have a diameter of 1.7 fermis, so a large nucleus, such as the core of a uranium-238 atom (with 238 nucleons) has a diameter of about 15 fermis.

If we look at the simplest atom, hydrogen, it is made up of a single electron and proton; the neutron is optional. However, if we look at any other element, there will be a neutron present. After hydrogen, the simplest type of atom is helium-3, an isotope of helium; isotopes have the same number of protons but differing numbers of neutrons. Helium-3 is made up of two elections, two protons and one neutron. If you were to remove that neutron, the atom would fall apart: The electrostatic repulsion between the protons is too strong for a stable, long-lived helium-2 atom. But with neutrons present as a buffer between protons, heavier atoms and elements can and do exist.

Although neutrons are necessary parts of all elements beyond hydrogen, they still seem like the dull cousins of protons. Their range of influence is short, and they seem mainly to just sit there. Whereas the two protons in helium are holding onto the electrons while tussling and pushing against each other, the neutron is the peacemaker, the barrier that sits between them. But it is not simply a wallflower in the atomic dance; it is critical in the formation of nearly everything.

Over the past 60 years, physicists have been probing the neutron and the proton to measure their size and to characterize the short-ranged nuclear force, which holds nucleons together. In the past 45 years, researchers have begun to view nucleons as a system made up of smaller particles, namely quarks and gluons. We are now asking, “How do these quarks arrange themselves? Do they form planetary systems with orbits, like electrons within atoms? Or is the inside of a nucleon an amorphous quark-gluon pudding?”

To make the problem of studying nucleons even more difficult—as if working at such miniscule scales was not hard enough—we have never seen a solo-quark, and we don’t expect to. Still, there are ways of teasing information out of a neutron, and today’s experimental and theoretical work is building up an image of its anatomy.

The Early Years

The word neutron was first used in 1899 to describe a hypothetical combination of a positive and negative electron, which might exist in the “ether.” It was an idea that didn’t catch on.

In 1920, legendary British physicist Ernest Rutherford gave the Bakerian Lecture, the premier annual lecture series for the Royal Society of London, and in it he summed up the status of nuclear physics at the time. He knew about the electron; it had been isolated and characterized in 1896. He also knew about the proton: Rutherford had demonstrated that the nucleus of the hydrogen atom—which he named the proton, meaning “first particle”- was found in all atoms. But the nucleus was incomplete. For instance, the nucleus of the carbon atom has the electric charge of six protons, but the mass of 12. To resolve this quandary, Rutherford proposed that the nucleus also had electrons embedded in it, so these electrons would effectively cancel the charge of half of the protons. Rutherford’s nucleus adhered to simplicity. He knew of two particles and so tried to solve the excessmass problem with a combination of these alone, and not with the radical solution of introducing a new particle.

By 1921 a number of experiments were actively looking for this tightly bound proton-electron system, with the word “neutron” repurposed to describe it. In the early 1930s a number of physicists observed a new type of radiation, released when an atom was bombarded with alpha particles (later proven to be helium nuclei), indicating that something had been knocked out of the atom. But it is British physicist James Chadwick who is credited with the discovery of the neutron because he showed that this new radiation was better explained as a particle with mass like a proton’s, rather than to explain it as a photon or an x ray. What he thought he had found in 1932 was Rutherford’s proton-electron bound system, the neutron.

But in Chadwick’s 1935 Nobel prize lecture, he revealed that the protonelectron combination theory was dead and for several major reasons. First, quantum mechanics indicated that a proton-electron system will always look like a hydrogen atom, with a diameter of about 10~10 meters, not the 10”15 meters of a nucleus. Secondly, this new particle does not decay—emit particles when bombarded with energy—like Rutherford’s proton-electron would. Finally its spin, a quantum-mechanical property related to the angular momentum of the subatomic particles, could not be produced from a combination of protons and electrons. Indeed, the neutron is just as much a particle as the proton But that 1935 description of the neutron is where most of us start and stop: The neutron is electrically neutral, it is attracted to other neutrons and protons by a short-ranged nuclear force, and that is all we think we need to know.

The year 1935 was also when the next piece of insight was added. Physicist Hideki Yukawa was working at Osaka University in Japan on the question of what causes nucleons to hang together. The nuclear force is very different from the gravitational force or the electromagnetic force in that it has a very short range of only one or two fermis, whereas the other two forces span galaxies. Yukawa proposed a new class of particles, the mesons, which would travel the very short distance between nucleons and effectively bind them together. The first type of meson, the pion, was not observed for another dozen years, but Yukawa’s reasoning was so compelling that prominent physicists, such as Werner Heisenberg, Enrico Fermi and others, created a full “meson field theory” to explain the nuclear force. By the 1950s it was generally accepted that the nucleons were surrounded by a pion cloud, much like a swarm of insects engulfing your head on a summer evening. The pions are constantly created and absorbed on the surface of neutrons and protons. Because they need borrowed energy in order to be created and are thus quantum-mechanical particles, their lifetime and travel distance is confined by Heisenberg’s uncertainty principle, which governs quantum fluctuations in pairs of certain properties, such as energy and time, or position and momentum.

Rutherford and Chadwick had used radioactive sources to study protons and neutrons, and similarly, the first pions were found in cosmic rays. But after World War II a new tool was developed that allowed the probing of matter in a highly controlled way—the particle accelerator. These devices use electromagnetic fields to propel particles to high speeds, while keeping them confined to a narrow beam, which can then be used to probe the make-up of matter. The energy of the beam is measured in electron volts, the amount of kinetic energy that a free electron gains when it passes through an electric field of one volt. The beam energy of an accelerator is directly related to its resolution. For example, an accelerator with a beam of 1 million electron volts can probe the details of matter about 1,000 times smaller than an atom. An accelerator with a giga-electron-volt beam probes to a length of about 1 fermi. In 1951, a new accelerator at Stanford University produced a beam of 600 million electron volts, so physicists were able to look directly at neutrons and protons for the first time.

An accelerator doesn’t really “see” a neutron; what it does is measure something called a cross-section, which is the probability of the electron probe from an accelerator scattering off the target particle at a certain energy and angle. Theorists independently calculate how the electron should scatter according to their models. By comparing experimental and theoretical cross-sections, we can choose the theory that best fits the data. Cross-section equations can be split into two parts: electric scattering and magnetic scattering. The electrons scatter electrically due to their charge, but they also scatter magnetically because of their spin—they can interact like little bar magnets. We call these two parts the electric form factor and the magnetic form factor. With a clever combination of beam energies and detector angles, experimentalists can measure these events separately and thus disentangle the nucleon’s structure.

In the mid-1950s physicist Robert Hofstadter of Stanford took his university’s accelerator and directed its electron beam at a hydrogen target. At these energies, the beam hardly interacts with the atom’s scarce and quick-moving electrons, so hydrogen is essentially a proton target. Hofstadter measured the proton’s form factors and deduced the proton’s charge and magnetic radius to be about 0.8 fermis. These radii are the distances where the charge or magnetic interaction becomes strong and defines the surface from which scattering can occur.

Measurements of the neutron are more difficult, as we cannot just put a bottle of neutrons in front of the beam. However, we can measure the crosssection of a deuteron, the nucleus of a deuterium atom (an isotope of hydrogen). A deuteron is a proton and a neutron loosely bound together. So if we measure a deuteron’s cross-section and subtract a proton’s cross-section, we are left with a neutron’s crosssection—almost.

When Hofstadter looked at the neutron, he found that the magnetic radius was 0.8 fermis, essentially the same as the proton. But the charge radius of the neutron was zero, as far as the precision of the experiment could tell. This result is not too surprising; the charge radius is related to the charge—and if there is anything we know about a neutron, it is that it has no charge.

Since the Quark Model

Our view of what goes on inside the neutron, proton and pion changed radically in 1964 when Murray Gell-Mann at the California Institute of Technology and George Zweig at the European Organization for Nuclear Research (CERN) in Switzerland independently proposed the quark model. Their theories said that heavy particles (including neutrons, protons and other exotic particles) belong to the group called baryons, which are all made up of three quarks. The mesons—the intermediate particles such as the pion—are made up of a quark-antiquark pair (antiquarks are made of antimatter, and have properties with the same magnitude but opposite charge to quarks). The electionlike light particles are called leptons. They are already fundamental particles, so are not made of quarks.

Quarks come in six types, also called flavors, but most particles (and all the common ones discussed in this article) are made up of the two lightest types of quarks: the up-quarks and down-quarks. One major reason the quark model was attractive to physicists was because, with a few different types of quarks, a plethora of particles could be described. Today the quark model stands at the heart of quantum chromodynamics (alluding to the “colors” of quarks), our best theory for describing particles at the nucleon-and-smaller scale.

A proton is made up of two up-quarks and one down-quark, often written as uud, whereas the neutron is made of two down-quarks and one up-quark (udd). These groups are called the valence quarks; they give the particle its properties that are seen from the outside, such as its particle type and charge. In addition, there are gluons that fly back and forth between quarks and bind them together, much like pions do between nucléons. (The name gluon was selected to signify that they “glue” the quarks together.) Inside the nucleón there is also the quark-sea, an endless supply of quarkantiquark pairs that come into existence for a few fleeting moments and then vanish. The full quantiom-chromodynamics picture of what is happening inside a neutron is complex and notoriously difficult to calculate, so it is common to describe nucleons in terms of the constituent quark model (CQM), which concentrates on just the valence quarks.

Given that protons have an overall charge of +1 and electrons have a charge of -1, the up-quarks have a charge of + 2/3 and the down-quarks have a charge of—1/3 In addition, in the CQM, the three quarks are expected to orbit the group’s center at about the same distance. For the proton, the charges of the uud quarks add up to +1, as they should. Its charge and magnetic radius depend upon where the quarks are orbiting and upon their spins, which agrees with Hofstadter’s results. However, the neutron is a bit different. It still has a magnetic radius, given by the position of the quarks. But what is interesting is that the charges of the up- and down-quarks cancel—and they should do so exactly at all distances from the center. So the neutron has a zero charge and a vanishing charge radius. But this is not the whole story.

We have learned that in addition to electrical charges, quarks have spin This property makes electrons and quarks sound like balls rotating on their axes, which is hard for a pointlike object. However, think of a cue ball bouncing off of the cushion of a pool table: The way it scatters depends on how much “English” or spin is on the ball. The mathematics that describes the interaction of spinning balls also describes particles with spin. In particular, the orientation of the spin is important. Particles interact differently depending on whether they are spinning the same way or in opposite directions.

Quarks also have color charge. Color is the whimsical name given to the strongforce charge that holds quarks together. Color charge is stronger than electrical charge by two orders of magnitude. Because all quarks bind to each other with the same color charge, we at first expect quarks to be symmetrical. But this leads to a curious problem due to the Pauli Exclusion Principle, which governs particle symmetries and states that if more than one particle occupies the same place, the properties of each (such as their spins) must be different. The two down-quarks are symmetric in orbit, and anti-symmetric in color charge, so as a result, their spins must be parallel, and like two magnets, they repel each other. Thus in our simple model, the quark orbits are slightly distorted.

In the proton, this property leads to a very subtle change in the charge distribution. But for the neutron, the effect is more pronounced. Now the downquarks are slightly farther from the center than the up-quark, so the charges will not exactly cancel at each distance from the center. If this model is right, we would expect the neutron to be slightly negative on the outside and slightly positive in the middle. This difference, this deviation from a zero-charge density, is what makes the neutron uniquely interesting. It could tell us something about the balance between spin effects and quantum-chromodynamics effects. If the charge-density distribution of the neutron was measured to be non-zero, it would give us information that would be hard to see in the proton, and this is why the neutron is worthy of independent attention.

Improving the Odds

In the past few years, physicists have developed new techniques to make our equipment more sensitive to the electric charge density and form factor. The first difficulty for an experiment is that there is no simple neutron target. Researchers have made beams of neutrons for use as targets, but the beams don’t contain many neutrons, so the probability of scattering off of them is extremely low. Instead, the usual targets are either deuterium or helium-3. Here I will describe only deuterium, because it is simpler, yet it contains all the interesting physics. When an electron is scattered off of deuterium, it has hit either the neutron or the proton. If you knew which one it was, you would not have to subtract the cross-sections and incur uncertainties as Hofstadter did. The way we accomplish this is to detect not just the electron from the accelerator beam, but also the nucleón ejected from the collision.

Another technique arises from revisiting form-factor separation. Again, this separation is performed by making measurements at different angles and energies, then comparing the crosssections and extracting the form factors. The comparison of different cross-sections is not quite like looking at apples and oranges, but more like comparing a Golden Delicious to a Cortland apple. However, detectors tend to have different sensitivities at different energies and angles, so researchers need to make these measurements and calculations very carefully because’ the difference between the cross-sections is slight.

The new technique makes use of the fact that the spin orientation of the electron and the neutron appear explicitly in their cross-sections. Effectively, if the spins of the electron and neutron are parallel, then the magnetic form factors both add to the cross-section. But if the spins are antiparallel or perpendicular, they don’t. So we still make two measurements, but we are comparing Cortland apples to Cortlands, just with one basket from the sunny side of the tree and one from the shady side. We now measure the cross-section with different spin orientations. If we combine the measurements one way, we can extract the electric form factor, and with a different combination, we are sensitive to the magnetic form factor. The technique sounds simple, but playing with the spin orientation of the beam and target is very difficult.

A Neutron BLAST

With new techniques and technologies in hand, a number of experiments were proposed in the early 1990s to measure the neutron’s electric form factor. These experiments were performed throughout the world, and our truest and best picture of the neutron arises from combining the results from all of them. Each laboratory and experiment brings a unique strength to the effort. Some labs have highly polarized beams, some have dense targets, some have detectors that can see a broad range of energies and angles, some have a narrow range but high precision.

Here I will only describe BLAST, an experiment I have worked on for the last two decades. BLAST stands for the “Bates Large Acceptance Spectrometer Toroid,” located at the Bates Linear Accelerator Center, part of the Massachusetts Institute of Technology and located about 30 kilometers north of Boston. The collaboration that built and operated this detector and experiment included more than 50 scientists, students and engineers from over a dozen institutions.

The Bates Center has two strengths. First, its accelerator produces an electron beam that is 66 percent polarized (meaning that 83 percent of the electrons in the beam have their spins oriented in the same direction), which is quite high for this type of accelerator. Secondly, the accelerator is attached to a storage ring: The beam of electrons is loaded into the ring, a 180-meter loop that they zip around continuously until they collide with a deuteron in the target. The ability to pass a beam through the target many times is particularly important when your target is so thin.

The target used was a beam of polarized deuterium gas. The deuterium was passed through a series of magnets and radio-frequency cavities in order to align the spins of all the atoms. It was a very delicate process that gave us a target of about 70 trillion atoms per cubic centimeter. That density equates to less than a thousandth of normal atmospheric pressure, which by many standards is considered a good vacuum. A single electron can pass through the target 2 million times a second, and continue doing that for up to 20 minutes, before it scatters off of a deuteron. In that time, it will have traveled the equivalent distance of the diameter of the Earth’s orbit, all within the storage ring.

Only a few thousand electrons will scatter from the target every second, and because we want to detect particles that are ejected, as well as a wide range of energies and angles, we wrapped the detector around the target—thus the “Large Acceptance” part of BLAST’S name. “Spectrometer” means that we measure energy or momentum by having the outgoing particles pass through a strong magnetic field. The paths of low-momentum charged particles are curved in the field, whereas high-momentum particles punch straight through.

BLAST, therefore, is a detector wrapped around a complex polarized target, which encases part of a highly polarized beam. The beam has an energy of 850 million electron volts and a current of up to 200 microamperes. For an accelerator, the energy may not be high, but the intensity is impressive: It is greater than that at Fermi National Accelerator Laboratory in Illinois, and similar to the Large Hadron Collider at CERN.

The detector is build like an onion with many layers, with the target at the center. When an electron does hit a deuteron, the electron is scattered, as well as a proton or neutron and sometime a pion. These particles first pass through a chamber filled with hundreds of wires that sense the position of a nearby particle. There are many layers in the wire chamber, which is embedded in a magnetic field, so we can use the multiple sensor responses to figure out the path of the particle and its momentum. Finally the particle passes through several layers of scintillating plastic (which emits light in response to ionizing radiation from the particle) that tell us the time the particle arrived to within 300 picoseconds. About 10 percent of the time the scintillators will also stop the neutrons and tell us how much energy they had.

My contribution to the project was first to simulate the proposed designs for the device, and later to write the computer code that took dozens of measurements of each particle—such as the timing of pulses from the wire chamber or the magnitude of the flashes of light in the scintillators—and converted that information into the particle’s momentum, direction and type. It was a complex puzzle to solve, and it needed to be solved a hundred times a second.

After half a dozen years of design work, the project was funded by the U.S. Department of Energy, and construction started in 1999. From 2003 to 2005 the experiment recorded data almost continuously. The results of the BLAST experiment are some of the best measurements in the world, but only within its limited range of momentum. Therefore, when we look inside the neutron, we will also use data from other laboratories, in particular from the Johannes Gutenberg University in Mainz, Germany, and the Thomas Jefferson National Accelerator Facility in Virginia.

Taking It All In

So what does this new generation of experiments tell us? First and foremost, the neutron’s electric form factor is not zero. It is related to the probability that a neutron can absorb a certain amount of momentum from the impacting electron and remain a simple neutron. When the electric form factor is graphed against electron momentum, it produces a curve with some features that we already knew (see Figure 6). The left-hand end, with low momentum, is related to a scale of large distances. Here the electron sees the neutron with low resolution and interacts with the whole neutron. Because the neutron is neutral, the electric scattering vanishes. At the other end of the scale, the electron is probing with high momentum and so at a very short time scale. If the scale is small enough, the electron can pass through the neutron undisturbed.

It is the shape of the bump in the middle that is of interest. For instance, the slope of the rise of the curve is related to the root mean square (the square root of the mean average of the square of the values, a standard statistical way of measuring the magnitude of a varying quantity) of the charge radius of the neutron, which is -0.11 fermis. A negative number for a radius sounds odd, but what it means is that the outside of the neutron is negative.

The usual physical interpretation of the form factor is that it is the Fourier momentum transformation of the charge distribution. A Fourier transform is a method for converting momentum measurements into position measurements. In this case, we can take that electric form factor curve and transform it to the charge distribution, which tells us that the center of the neutron is positive and the outside is negative (see Figure 6). The bands indicate our present level of uncertainty. Fifteen years ago those bands were much wider, and it was easy to fit a number of models to the data, such as the pion-cloud model or the quark spin-repulsion model. But now the answer seems to be that both are correct. To reconcile this result, we need to go back to our quark picture of the neutron and pion.

The neutron is made up of three valence quarks, along with gluons and quark-anüquark pairs in the quark-sea. So far we have only talked about the valence quarks; now we need to talk about the others. The usual way they are described is with a diagram that shows how the quarks in the nucleon change over time (see Figure 7). The diagram starts at the left with the neutron made up of three quarks (dud). In this example, after some time a gluon is emitted from a d-quark and absorbed by the u-quark. Later a gluon is emitted; it splits into a quark-antiquark pair, which recombine into another gluon that is then absorbed by one of the valence quarks.

The quarks and antiquarks that exist for a fleeting moment are called the seaquarks. But the sea-quarks are as real as the original valence quarks; indeed, the antiquark could have combined with a valence quark, and everything would have balanced. Or the quark-antiquark pair might have formed a new particle, such as a pion, at least for a fleeting moment. The pion would then be either reabsorbed as part of the neutron’s pioncloud, or it could have been exchanged with a neighboring nucleon, then absorbed as part of the nuclear force. So the pion-cloud also can tell us a bit about the activity of gluons and the quark-sea. In the graph of the neutron’s charge distribution in figure 6, the long tail of the graph tells us that there is still a bit of charge outside the classical neutron surface, in a halo or a cloud.

The long tail also tells us something more. The simplest way to put a quark and an antiquark together is in a pion, but it is not the only way. If the quark-antiquark pair have their spins aligned, they form a more massive particle, either a rho-meson or an omegameson, or maybe one of the less common but more exotic mesons such as the phi-meson. In fact, we should be talking about the meson-cloud instead of the pion-cloud.

What about inside the cloud, at less than one fermi, which is normally considered the boundary of a nucleon? Here it looks like the up-quark is near the center, with a radius of about 0.35 fermis and the down-quark is farther out at 0.5 fermis. Some physicists see this description as our best picture of the neutron, containing the meson-cloud, d-quark surface and u-quark core, all derived from the Fourier transform of the electric form factor. But this view, instructive and. appealing as it is, has some problems. What we really wanted to know is what the neutron looks like at rest, but our transformation is halfway between the initial neutron at rest and the final neutron after it has been hit. It is like taking a flash picture and then realizing that the subjects all have unnatural red eyes, or are jumping due to the sudden flash. We like to think our image is of a natural neutron, but it is really a neutron being actively probed.

In the past few years a different procedure has been developed. With it, one transforms the neutron to the Infinite Momentum Frame (IMF), so we are looking at the neutron as if it was traveling at nearly the speed of light. This procedure is relativistically consistent and mathematically correct, but it doesn’t really answer the question of what a neutron looks like at rest. Both the electric form factor and the magnetic form factor are involved in this procedure, because at these velocities the two are mixed. Because the magnetic form factor is negative, the resulting charge distribution looks different. What strikes us immediately, and gives us pause, is the negative core. This result for the neutron’s core is probably why some physicists have been reluctant to accept this procedure.

In the first analysis, the core of the neutron is the center of mass of the three quarks. They all orbit a point someplace in the middle of the three-quark triangle. In the IMF, the neutron is moving relativistically at the speed of light, so it flattens out like a pancake, with the thin dimension in the direction of motion. In this situation, mass is much less important than momentum, so it replaces the role of mass as the center. So what ends up defining the center is that which has the greatest momentum, and that is the down-quarks. Because the down-quark is negative, the center in the IMF is also negative. The IMF is consistent and correct, it is just that it is the answer to a question a bit different than what we thought we were asking. The “center” is not the center of a neutron at rest, which is what we wanted to picture.

A Hazy View

What does a neutron look like? It is not just a tiny, hard rock that sits there. It is not just ballast in the nucleus. It is dynamic. It is constantly ejecting and absorbing mesons of every type. Closer in, the surface is dominated by negative down-quarks. The interior has a region that is home to the positive up-quark. And at the center? This is a region of strong relativistic effects. It looks like it is dominated by the down-quark, but we must be mindful of what we mean by “the center.” As one theorist who works with the IMF told me, “This is not your father’s charge distribution.”

Where do we go from here? We are still learning about how the neutron pulsates and gyrates. With the neutron continuously creating and absorbing mesons, it is a particle that is continuously remaking itself. With new data every year, we will also be revising our vision of these particles until, who knows, we may again adopt the vision of the neutron advocated by Fermi and other particle physicists in the 1940s.