Clustering in nuclear systems: from finite nuclei to neutron stars

Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10−15 meters, a nucleus is quite small compared to the radius of the entire atom, which is about 10−10 meters. Nuclei are extremely dense compared to bulk matter, averaging 1.8 × 1014 grams per cubic centimeter. If the earth’s density were equal to the average nuclear density, the earth’s radius would be only about 200 meters.
To hold positively charged protons together...

Neutron Stars and Black HolesWhen massive stars reach the end of their life cycle, they can collapse into two extreme objects: neutron stars and black holes. Neutron stars are incredibly dense, with a mass greater than the Sun packed into a small space. Black holes are regions of space where gravity is so strong that nothing, not even light, can escape. Studying neutron stars and black holes helps scientists understand the most powerful forces in the universe.Science and Engineering Practices...

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.

Star ClusterStars are not always found alone in space. Many stars form in groups called star clusters, which are collections of stars that share a common origin and move together through space. There are two main types of star clusters: open clusters and globular clusters. Open clusters contain young, bright stars and are loosely packed, while globular clusters are tightly packed groups of older stars. Studying star clusters helps scientists understand how stars form, evolve, and interact with...

In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.

NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...