Grad Research

My dissertation research focused on the study of the internal charge structure of neutrons. The world of modern nuclear physics focuses more on the structure of neutrons and protons (collectively called nucleons) and the details of the force that binds them together. In order to understand this binding force between nucleons we need to have a good understanding of the internal structure of the nucleons. Over the last 30-40 years there are have been many experiments focusing on the improvement in these measurements so that models of the nucleons can be tested and improved. Recent experiments at the NEKHEFF (Neitherlands), Stanford Linear Accelerator (SLAC), Jefferson National Laboratory (Jlab), and others have focused on using the polarization transfer technique to better understand the internal charge and magnetic distribution within the nucleons. My dissertation work was one of these experiments.

Nucleons are made of smaller particles we call quarks. These quarks are considered to be point-like particles meaning they have no structure themselves. They do, although, have intrinsic (internal) properties. It’s these properties that we are constantly using to help further our understanding of nucleons in general since they are built of quarks. One of the most interesting properties of quarks is that fact we can’t find them in nature alone. They always come in pairs (mesons) or triples (baryons).

The exact reason why they only come in two’s and three’s is not really known but what is known is that attempting to separate a quark from its partner(s) results in the creation of 2 or more quarks if the energy is large enough. This stems from the nature of the color force which is the force that binds the quarks together. This is call Quantum Chromo Dynamics. As the quarks move away from each other the force increases in strength much like the force a spring exerts increases as you attempt to stretch it more and more. This differs from the electric and gravitational forces which decrease with distance. Once enough energy has been stored in the bonds of this force then the bonds will spontaneously break and form a quark/anti-quark pair. The quark/anti-quark pair is a meson (at low energies it’s a pion) and the nucleon is often left in an excited state.

What about the charge in the neutron? Well, there are six quark flavors: Up, Down, Strange, Charm (or Beauty), Top, and Bottom quarks. The two most common and lowest massed quarks are the Up and Down quarks. Why that is so is another discussion in itself. These quarks have fractional electronic charge which means they carry a fraction of the charge of the electron which for simplicity I will call -1e. The Up quark carries +2/3e charge and the Down quark carries -1/3e charge. The proton has two Up quarks and one Down quark yielding a net charge of +1e and the neutron has two Down quarks and one Up quark yielding a net charge of 0.

The electric form factor, for the proton or neutron, is a physicist’s way of measuring the spatial charge distribution within the volume of the nucleon. We call it a form factor since it turns out that it is easier to control how much momentum is transferred from a projectile/probe particle (an electron) to the nucleon than it is to control the distance of closest approach. This leads to a quantity that is dependent on the momentum transfer rather than xyz. This is fine since the theorists like it this way. It is possible translate between the two systems via a boosted Fourier Transform, which to be honest I have never done the math.

The big thing to get out of this is that if we measure the distribution of the electric charge inside neutrons and protons to high precision then we will have a better understanding on how they interact with each other and in groups. This is necessary for understanding the nuclear force and nuclear matter. They also play a key role in the extraction of strange quark contribution to the nuclear force which is a whole discussion in itself.

If you wish to read the technical details of the experiment you can read my dissertation (click here) or one or more of the papers published papers. Unfortunately, I’m not allowed to publish the papers here but I can put the links and references on this page. For everyone else, just continue reading.

The JLab experiment E93-038 (‘E’ for experiment, ‘93’ for 1993, ‘38’ for the 38 th proposal submitted that year. Yes this was an accepted experiment before I graduated from HIGH SCHOOL. Some things in nuclear physics don’t move very fast and at the time the laboratory wasn’t even ready to deliver its first beam. Anyway, the original proposal had the collaboration measuring 5 different data points from about

. After years of work, simulations, and increase in beam time requests the proposal was paired down to three data points over the same range.

Data was collected between late September 2000 and April 2001 with an extension due to catastrophic target failure (okay … it blew up). We ran 80-100 microamp polarized electron beam on a 15-cm long liquid deuterium target. The electron scattered off protons and neutrons in the target giving some of its polarization to the neutron and we detected coincident electron hits in the High Momentum Spectrometer (HMS) and our neutron polarimeter (NPOL). The coincident detection eliminates a larger portion of the background which stems from the fact that a lot of particles are sprayed around the experimental area.

A dedicated dipole magnet in front of NPOL was used to both sweep protons out of the path to NPOL and precess the spin of the neutron in the scattering plane. The spin precession of the neutron polarization was key to measuring the electric form factor. By measuring the amount of polarization transferred to the neutron from the electron, we can determine the electric form factor of the neutron assuming we know the analyzing power of NPOL which we do not. To get around this, the polarization transfer is measured at two precession angles using the dipole magnet to precess the neutron spin and then a cross ratio is formed to extract the electric form factor. This results in a cancellation of most of the systematic uncertainties and we can then use the data to estimate the contribution to the asymmetry from the systematic sources. This contribution, which is small, is then folded into the final uncertainties in the measurement.

The result of the experiment is displayed in the following plot. The three E93-038 measurements are displayed as solid black squares. At the time of the data’s publication it was the only high precision electric form factor data that went past . The dashed line is an empirical fit to all the data prior to our work using a dipole model for the electric charge distribution. It has little basis in theoretical physics but is a guide for future experiments. After our work, Jim Kelly (J.J. Kelly, PRC 70, 068202 (2004)) performed a new fit to the data using the same concept of a dipole empirical model and obtained the solid black line.

What is not shown in this plot is the number of theoretical calculations which attempt to predict or fit the neutron form factor and proton form factor data. All of these models have some make some assumptions that affect their accuracy in predicting what is really going on inside the neutron. The reasons for the model assumption are usually the fact it is not possible to work out the math in complete detail due to the complexity and nature of the nuclear force. Assumptions have to be made in order to make the calculations workable in a reasonable amount of time. Either way a good set of high precision data is needed in order to discriminate between good models or poor models and help scientist come to a better understanding of the nuclear force.

This work was performed in 2000-2002. Since then another experiment using polarized Helium-3 as a neutron target has ran and is about it release its data for publication (early 2010). Three more experiments at Jefferson Laboratory are approved to run after the 12-GeV upgrade in 2013 to measure the electric form factor to even higher momentum transfers. More theoretical work has proceeded as well and measurements of the form factor at low momentum transfers have occurred as well to better understand how the distribution changes near the ‘hump’ in the above plot. I am still interested and involved in these experiments and you can find out more on the other research pages.