Hall A Experiments on Nuclear Few-Body Form Factors*

The Few-Body Nuclear Systems

The deuterium nucleus is comprised of two nucleons: one proton and one neutron. It is the simplest nuclear system, the “two-body” system, also called the deuteron. Deuterium exists in very large quantities in sea water.

The Few-Body Nuclear Systems

A stable helium nucleus can contain either three or four nucleons:

• Two protons and one neutron making up a He-3 nucleus, a “three-body” nuclear system. He-3 is rare on earth but is abundant on the surface of the moon.

• Two protons and two neutrons making up a He-4 nucleus, a “four-body” nuclear system. Twenty five percent of the Universe is He-4. Supermarket Helium balloons contain He-4 gas!

The He-3 nucleus is a spinning round object. In simple terms, it rotates about itself much the same way that the earth rotates about itself. The spin can be in two distinct orientations, “up” or “down”. Any nucleus with these two spin orientations has two form factors: a charge one and a magnetic one. The charge form factor provides information on the distribution of the electrically charged protons in the nucleus, and the magnetic form factor on the magnetization created by the moving charged protons (a moving electrically charged particle always creates a magnetic field!).

The He-4 nucleus is a round object, which has no spin. This is because the spinning motion of the two protons cancels the spinning motion of the two neutrons. Like all nuclei with no spin, it has only one form factor, a charge form factor.

The deuterium nucleus can exist in three different spin states. This results in the deuteron having three form factors, a charge form factor, a magnetic form factor, and a quadrupole form factor. The existence of the quadrupole form factor is ultimately due to the fact that the deuteron is not exactly a round object but close to an egg-like object.

The nucleons inside nuclei constantly interact with each other. The force between two nucleons, the nucleon-nucleon force, is what holds the nucleons together to form the nucleus. One of the goals of nuclear physics research is to study all aspects of this force.

The form factors of the few-body nuclear systems give us, in general, information on the internal structure and dynamics of these systems, and in particular on their shape, size, composition, quantum mechanical wave function, and on the nucleon-nucleon force that holds their mutually interacting nucleons together.

The form factors of the few-body systems are measured in experiments where high energy electrons collide with deuterium or helium target nuclei. (The currently running experiment in Hall A, E04-018, is measuring the form factors of He-3 and He-4.)

The high energy electrons are provided by the Jefferson Lab Continuous Electron Beam Accelerator Facility (CEBAF).

The target nuclei are those of deuterium or helium atoms, which are stored in gaseous forms in metallic cans under high pressure and low temperature, the cryogenic targets.

Measuring the Form Factors

All matter is made up of atoms. Each atom is comprised of a positively charged nucleus consisting of protons (p) and neutrons (n), collectively called nucleons, and negatively charged electrons orbiting around the nucleus. Each nucleon is made up of 3 quarks, which are held together by massless particles, the gluons, acting like springs.

Collectively, the deuteron, the He-3 and He-4 nuclei, and another nucleus made up of two neutrons and a proton, the triton, are the “few-body” systems of nuclear physics.

What Do the Form Factors Tell Us?

Nuclei, as other subatomic objects are described by quantum mechanical wave functions. These are mathematical functions of space and time, in other words mathematical tools used to describe the state and whereabouts of these objects.

View of the target inside the scattering chamber, and the scattering chamber at the pivot.

E. Khrosinkova, M. Katramatou, M. Petratos (Kent State U.), M. Olson (St. Norbert College), A. Camsonne, J. Gomez (JLab) on behalf of the Hall A Collaboration

* Work supported in part by the National Science Foundation (Grant PHY-0355181)

The Hall A Facility of Jefferson Lab is pursuing an experimental program to measure the “Form Factors” of the lightest, simplest nuclear systems in nature, the nuclei of thedeuterium and helium atoms. The form factors provide fundamental information on the size, structure, and internal dynamics of these nuclear systems.

Most of the time, the incident electrons do not interact with the target nuclei, and end up mostly undisturbed at the end of the beam line in a water cooled damp.

Very rarely, the electrons do interact with the target nuclei resulting in elastic or inelastic collisions:

• In elastic collisions, the incident electrons bounce (scatter) off the heavy nuclei, which in turn break up from the atoms and recoil with fairly large speeds. In inelastic collisions, the target nucleus breaks up into fragments (smaller nuclei and/or free protons or neutrons and possibly other subatomic particles like pions).

The form factors are extracted from measurements of elastic collisions. In this case, both scattered electrons and recoiling nuclei are detected with the two state-of-the art High Resolution Spectrometers of Hall A.

Previous experiments on the form factors of the deuterium and helium nuclei have established their shape and size. Both are tiny objects, about one thousand million millions (1,000,000,000,000,000) times smaller than the size of a ping-pong ball or an egg!

The goal of the JLab experiments is to “look” now inside the helium and deuterium nuclei, with finer precision and resolution and study the shapes of the form factors at large collision impacts, which are a measure of how hard the target nuclei are hit by the incident electrons. JLab is the only place in the world where experiments such as these can be performed! Form factors may also provide us with valuable input into examining the light nuclei as systems of quarks and gluons and ultimately lead us to a complete understanding of the simplest, lightest nuclei in Nature!

The Hall A Spectrometers are made up of large superconducting electro-magnets, which gather the scattered electrons and recoiling nuclei, and focus them (like optical lenses focus light) onto two sets of subatomic particle detectors housed in the so-called shielded “huts”.

Every minute, CEBAF can deliver a beam with up to one thousand million millions (1,000,000,000,000,000) electrons per second onto a cryogenic target.

The electrons encounter in their path in the target, many many nuclei, for example, in the case of He-3, approximately fifty thousand billion billions (50,000,000,000,000,000,000,000) of He-3 nuclei.

State of the art, specialized nuclear electronics devices and high speed computers receive the information (“data”) for the particles identified by the detectors. The collection of the experimental data is directed and monitored by scientists in a “Counting House”, above the underground Hall A. Typically, it takes two years for a small group of scientists to analyze these data and publish the results.

Experimental Outcome

Calorimeter detector of the electron spectrometer

Scintillator detector of the recoil spectrometer

HRS recoil spectrometer

Counting House

Hall A Experiments on Nuclear Few-Body Form Factors