Energetic Degenerates
If systems “seek” the lowest possible energy, why don't atomic electrons all cascade down into the ground state? Since the electronic properties of all atoms would be essentially the same, there'd be no need for the periodic table—we'd have no chemistry, and no life.
To the rescue comes the famous “Pauli exclusion principle,” which says that no two electrons may occupy the same quantum state. Imagine building up an atom by starting with a nucleus and adding electrons one by one. As each energy level is filled, it becomes unavailable for the next electron, which then must go in the next higher energy level, and so on.
Fermi gas Energy Levels — Degenerate Fermi gas of particles with spin 1/2. Because of the Pauli exclusion principle, no two identical particles may occupy the same state. The particles are shown in each possible spin state, up and down. In this system, the particle energy is independent of its spin.
Bose gas Energy Levels —Bose gas at low temperature. All particles are free to occupy the lowest-energy state, also called the ground state. The particle energy is independent of its spin
The other family, Bose particles or bosons, have integer spin. They do not obey the exclusion principle and therefore can occupy the same quantum state at the same time, as shown in the diagram. Notice the difference in energy between the boson and fermion systems, which have the same number of particles.
Following groundbreaking low-temperature experiments with a gas of Bose atoms, which resulted in a form of matter called a Bose-Einstein Condensate (BEC) [See Matters of State], other researchers cooled fermionic atoms, looking for a degenerate Fermi gas, but this proved much more difficult. At a crucial stage in the cooling, the more energetic atoms are allowed to escape, and collisions among the remaining atoms ordinarily would redistribute their energy to bring the system back into thermal equilibrium at a lower temperature. In a degenerate Fermi gas, however, the low-energy states are already filled, so if two atoms collide, there are no lower-energy states available for the atoms to go to after the collision and they must stay in the original ones. Consequently, cold fermionic atoms cannot exchange energy by collisions, preventing the cooling of some of the atoms from lowering the temperature of the whole sample, as can be done with bosonic atoms.
Beyond electrons in atoms, the Pauli exclusion principle applies to any system of identical “fermions”—the family of particles with half-integer “spin,” the property that specifies intrinsic angular momentum. Fermions include the electron, proton, neutron, and other subatomic particles. A system of identical Fermions is called a “Fermi gas.” If the temperature is low enough, the Fermi gas is “degenerate,” which means the low-lying states are filled up to a well-defined maximum energy, as shown in the diagram. The degenerate Fermi gas provides a good model of the conduction electrons in a metal, even at room temperature. Also, in a white dwarf star, the electrons form a degenerate Fermi gas, and their pressure stabilizes the star against its gravity.
