Visualizing the Nucleus

MIT Department of Physics — transcript of https://youtu.be/ach9JLGs2Yc

Humans have long wondered about the structure of matter and what makes up our world. The Greek philosopher Democritus first developed the concept of atomos, an indivisible building block of matter. He believed it came in many shapes depending on what kind of matter it made up. Over two millennia later these shapes were unified into solid spheres. Around 1900 the electron was discovered, which was proposed to exist scattered within the sphere. A few years later the nucleus was discovered and the model evolved to electrons traveling in fixed orbits around the nucleus. Uncertainty principles introduced us to the concept of quantum mechanics and the wave-like electrons became a probability cloud surrounding the nucleus.

But what about the world of the nucleus — a tiny point of positive charge a trillion times smaller than the atom itself? Before we dive in, let's back up way back. The diameter of the Earth is 10,000 km. Zooming in on Boston, the size of the MIT campus is 1 km — four orders of magnitude smaller. Let's add a fictional child's pool of water on top of the MIT Dome with a scale of 1 m. Diving into its water three orders of magnitude in we reach a cube of water with a scale of 1 mm. Three more orders of magnitude in we reach a scale of 1 micrometer. When we reach the scale of 1 nanometer we start to see the motion of the water molecules. Zoom in by a factor of 10 we reach the size of a hydrogen atom. Five more orders of magnitude in we arrive at its nucleus — the proton. Inside this proton things are moving at incredible speeds in an infinitesimal volume. We are now deep in the quantum realm.

The hydrogen atom has a nucleus consisting of a single proton. The size of a nucleus is measured in units of femtometers — a proton has a radius of nearly 1 fm, 100,000 times smaller than the size of its hydrogen atom. This proton exists in a quantum state that changes based on how you observe it: at a high shutter speed we see an ocean of gluons; at a medium shutter speed we see a sea of gluons and quark-antiquark pairs; and at a low shutter speed we see the dominance of the valence quarks.

More complex nuclei contain not only positively charged protons but neutrally charged neutrons. While the proton can exist by itself in a stable form, neutrons on their own are unstable and will quickly decay into a proton, electron and anti-neutrino — but neutrons remain stable when bound to a proton by the strong force in nuclei. Oxygen-16 contains eight protons and eight neutrons. If we look deeper the fundamental quark-gluon constituents appear, but for our purposes they are hidden. We will concentrate on the structure of the nucleus in terms of protons and neutrons. In future work we will illustrate how quarks and gluons can get impacted by the nucleus they live in.

Oxygen-16 has a charge radius of 2.7 fm. To better define the velocities of particles at such small distance scales we established the "babyc" as 10⁻²³ seconds. A photon moving at the speed of light crosses 3 fm — a bit more than the radius of Oxygen-16 — in one babyc.

In this animation of the nucleus the protons and neutrons are randomly distributed and contained within a radius limiting their motions. The neutrons are distinguishable by their blue tones. The individual protons and neutron particles will both attract and repel each other based on proximity, to mimic the strong nuclear force, and a noise field is introduced to stir them around randomly. The protons and neutrons inside move on average about 1/3 the speed of light. In the period of a babyc, protons and neutrons traverse 1 fm — compare this motion with that of the point-like photon that moves at the speed of light across our femtometer ruler.

Shown here is helium-4, the most abundant multinucleon system. When peering inside the protons and neutrons, the quarks and gluons move with the speed of light. It would take a proton about 3 babyseconds to traverse a helium-4 nucleus, and for a larger nucleus like copper-64 about 10 babyseconds. Both helium-4 and copper-64 nuclei are predominantly round shapes, but some even heavier nuclei can be quite deformed with elongations by a factor of three. This is caused by the nucleus vibrating and rotating with protons and neutrons moving in lock step. The typical period of such a nuclear rotation is about 100 babyseconds. The period for nuclear vibrations is shorter — about 20 babyseconds — roughly the same time for a proton to do a round trip in a medium-heavy nucleus.

The size of most nuclei grows with the number of protons and neutrons inside them, though there are striking exceptions. Lithium-11 — with three protons and eight neutrons — has a similar radius as lead-208 with 82 protons and 126 neutrons. Lithium-11 is called a "halo" nucleus and can be visualized as a core with two additional neutrons circling in the periphery. Many heavy nuclei such as lead-208 have a surplus of neutrons that one would expect to be on the outside and form a "neutron skin." Indeed the radius that neutrons occupy in lead-208 is larger than that of the protons, but despite the large surplus of 44 neutrons the difference is only 0.2 fm — this is due to the specifics of the proton-neutron force.

Carbon-12 and Oxygen-16 are crucial to life. The cornerstone of life is the chemical process in plants where sunlight converts carbon dioxide and water into plant food glucose and oxygen. The elements hydrogen, oxygen and carbon account for 93% of the mass of the human body. Carbon-12 consists of six protons and six neutrons that occupy a sphere with a radius of 2.5 fm. Oxygen-16 packs two more protons and neutrons each in a sphere with a radius of 2.7 fm. Those additional protons and neutrons make a huge difference: oxygen is a gas, the most abundant element in Earth's crust, and after hydrogen and helium it is the third most abundant element in the universe. Oxygen is continually being replenished in Earth's atmosphere by photosynthesis.

Carbon is a solid. Carbon's abundance, its unique diversity of organic compounds and its unusual ability to form polymers at temperatures commonly encountered on Earth enables it to serve as a common element of all known life. Oxygen, carbon and the elements that make up our universe are all created with the same basic quantum building blocks. By just adding or removing protons, neutrons and electrons, the matter they create at the macro level varies with an incredible diversity of properties.

Despite the dominance of these elements, a large variety of nuclei are used in technical applications benefiting humankind: tritium (hydrogen-3) powers exit signs; carbon-14 dates our Earth's history and art; fluorine-18 traces brain and biological imaging; cobalt-60 reduces disease and extends food shelf life; technetium-99 is widely used in nuclear medical imaging; samarium-153 treats bone metastasis; americium-241 is used in smoke detectors.

By adding or removing these quantum building blocks of the proton and neutron, an incredible diversity of nuclei can exist. These elements play a critical role in human life, in our bodies, our health and safety, and the world around us.

Substrate mappings (moore26)

• The shutter-speed triad — the video's most portable idea: structure depends on observation timescale. Our registers split the same way: packets = the fast sea (in-flight flux), incipients = the medium shutter (standing-offer negotiation cloud), winding/mass = the slow shutter (bound structure). A census at each register layer is a shutter-speed read.
• "babyc" = 10⁻²³ s — the natural nuclear timescale. Our 0.1 fm node at c=1 hop/tick runs ~100× finer than a babyc (~0.01 babyc/tick); nucleon-scale dynamics span ~10²–10³ ticks.
• Nucleons move ~1/3 c — bound-state constituent speeds; our measured mass-flow ceiling (~0.033c knot drift) is an order lower, while the internal packet sea runs at c — consistent with "constituents fast, bound motion slow."
• Nuclear rotation ~100 babycs, vibration ~20 — our closed- ring circulation and knot-oscillation periods live in the same 10²–10³-tick regime.
• Halo nuclei / neutron skin — species-dependent radial layering; our lump-radius / accretion-radius probes are the same measurement (peripheral vs core population).
• "Attract and repel based on proximity" — the strong-force mimic: our proximity-dependent exchange/binding (chain toll, surplus protection, bondDist feedback) is the analog.