Helium-3 in the context of Fermionic

Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortices that continue to rotate indefinitely. Superfluidity occurs in two isotopes of helium (helium-3 and helium-4) when they are liquefied by cooling to cryogenic temperatures. It is also a property of various other exotic states of matter theorized to exist in astrophysics, high-energy physics, and theories of quantum gravity. The semi-phenomenological theory of superfluidity was developed by Soviet theoretical physicists Lev Landau and Isaak Khalatnikov.

Superfluidity often co-occurs with Bose–Einstein condensation, but neither phenomenon is directly related to the other; not all Bose–Einstein condensates can be regarded as superfluids, and not all superfluids are Bose–Einstein condensates. Even when superfluidity and condensation co-occur, their magnitudes are not linked: at low temperature, liquid helium has a large superfluid fraction but a low condensate fraction; while a weakly interacting BEC, with almost unity condensate fraction, can display a vanishing superfluid fraction.

Solid is a state of matter in which atoms are closely packed and are difficult to move past each other. Solids resist compression, expansion, or external forces that would alter its shape, with the degree of resistance being dependent upon the specific material under consideration. Solids also always possess the least amount of kinetic energy per atom/molecule relative to other phases or, equivalently stated, solids are formed when matter in the liquid / gas phase is cooled below a certain temperature. This temperature is called the melting point of the substance and is an intrinsic property; i.e. independent of how much of the matter there is. The vast majority of substances, when in the solid state, can be arranged in one of a few ubiquitous structures.

Solids are characterized by structural rigidity and resistance to applied external forces and pressure. Unlike liquids, solids do not flow to take on the shape of their container, nor do they expand to fill the entire available volume like a gas. Much like the other three fundamental phases, solids also expand when heated, the thermal energy put into increasing the distance and reducing the potential energy between atoms. However, solids do this to a much lesser extent. When heated to their melting point or sublimation point, solids melt into a liquid or sublimate directly into a gas, respectively. For solids that directly sublimate into a gas, the melting point is replaced by the sublimation point. As a rule of thumb, melting will occur if the subjected pressure is higher than the substance's triple point pressure, and sublimation will occur otherwise. Melting and melting points refer exclusively to transitions between solids and liquids. Melting occurs across a great extent of temperatures, ranging from 0.10 K for helium-3 under 30 bars (3 MPa) of pressure, to around 4,100 K at 1 atm for the composite refractory material hafnium carbonitride.

A fermionic condensate (or Fermi–Dirac condensate) is a superfluid phase formed by fermionic particles at low temperatures. It is closely related to the Bose–Einstein condensate, a superfluid phase formed by bosonic atoms under similar conditions. Examples of fermionic condensates include superconductors and the superfluid phase of helium-3. The first fermionic condensate in dilute atomic gases was created by a team led by Deborah S. Jin using potassium-40 atoms at the University of Colorado Boulder in 2003.

Nuclear transmutation is the conversion of one chemical element or an isotope into another chemical element. Nuclear transmutation occurs in any process where the number of protons or neutrons in the nucleus of an atom is changed.

A transmutation can be achieved either by nuclear reactions (in which an outside particle reacts with a nucleus) or by radioactive decay, where no outside cause is needed.

Liquid helium is a physical state of helium at very low temperatures at standard atmospheric pressures. Liquid helium may show superfluidity.

At standard pressure, the chemical element helium exists in a liquid form only at the extremely low temperature of −269 °C (−452.20 °F; 4.15 K). Its boiling point and critical point depend on the isotope of helium present: the common isotope helium-4 or the rare isotope helium-3. These are the only two stable isotopes of helium. See the table below for the values of these physical quantities. The density of liquid helium-4 at its boiling point and a pressure of one atmosphere (101.3 kilopascals) is about 125 g/L (0.125 g/ml), or about one-eighth the density of liquid water.

In quantum mechanics, indistinguishable particles (also called identical or indiscernible particles) are particles that cannot be distinguished from one another, even in principle. Species of identical particles include, but are not limited to, elementary particles (such as electrons), composite subatomic particles (such as atomic nuclei), as well as atoms and molecules. Although all known indistinguishable particles only exist at the quantum scale, there is no exhaustive list of all possible sorts of particles nor a clear-cut limit of applicability, as explored in quantum statistics. They were first discussed by Werner Heisenberg and Paul Dirac in 1926.

There are two main categories of identical particles: bosons, which can share quantum states, and fermions, which cannot (as described by the Pauli exclusion principle). Examples of bosons are photons, gluons, phonons, helium-4 nuclei and all mesons. Examples of fermions are electrons, neutrinos, quarks, protons, neutrons, and helium-3 nuclei.

Deuterium fusion, also called deuterium burning, is a nuclear fusion reaction that occurs in stars and some substellar objects, in which a deuterium nucleus (deuteron) and a proton combine to form a helium-3 nucleus. It occurs as the second stage of the proton–proton chain reaction, in which a deuteron formed from two protons fuses with another proton, but can also proceed from primordial deuterium.

Sir Marcus Laurence Elwin Oliphant, commonly known as Mark Oliphant (8 October 1901 – 14 July 2000), was an Australian physicist and humanitarian who played an important role in the first experimental demonstration of nuclear fusion and in the development of nuclear weapons.

Born and raised in Adelaide, South Australia, Oliphant graduated from the University of Adelaide in 1922. He was awarded an 1851 Exhibition Scholarship in 1927 on the strength of the research he had done on mercury, and went to England where he studied under Sir Ernest Rutherford at the University of Cambridge's Cavendish Laboratory. There, he discovered the respective nuclei of helium-3 (helions) and of tritium (tritons). He also discovered that when they reacted with each other, the particles that were released had far more energy than they started with. Energy had been liberated from inside the nucleus, and he realised that this was a result of nuclear fusion.

A quantum fluid refers to any system that exhibits quantum mechanical effects at the macroscopic level such as superfluids, superconductors, ultracold atoms, etc. Typically, quantum fluids arise in situations where both quantum mechanical effects and quantum statistical effects are significant.

Most matter is either solid or gaseous (at low densities) near absolute zero. However, for the cases of helium-4 and its isotope helium-3, there is a pressure range where they can remain liquid down to absolute zero because the amplitude of the quantum fluctuations experienced by the helium atoms is larger than the inter-atomic distances.

Superfluid helium-4 (helium II or He-II) is the superfluid form of helium-4, the most common isotope of the element helium. The substance, which resembles other liquids such as helium I (conventional, non-superfluid liquid helium), flows without friction past any surface, which allows it to continue to circulate over obstructions and through pores in containers which hold it, subject only to its own inertia.

The formation of the superfluid is a manifestation of the formation of a Bose–Einstein condensate of helium atoms. This condensation occurs in liquid helium-4 at a far higher temperature (2.17 K) than it does in helium-3 (2.5 mK) because each atom of helium-4 is a boson particle, by virtue of its zero spin. Helium-3, however, is a fermion particle, which can form bosons only by pairing with itself at much lower temperatures, in a weaker process that is similar to the electron pairing in superconductivity.

The neutron–proton ratio (N/Z ratio or nuclear ratio) of an atomic nucleus is the ratio of its number of neutrons to its number of protons. Among stable nuclei and naturally occurring nuclei, this ratio generally increases with increasing atomic number. This is because electrical repulsive forces between protons scale with distance differently than strong nuclear force attractions. In particular, most pairs of protons in large nuclei are not far enough apart, such that electrical repulsion dominates over the strong nuclear force, and thus proton density in stable larger nuclei must be lower than in stable smaller nuclei where more pairs of protons have appreciable short-range nuclear force attractions.

For many elements with atomic number Z small enough to occupy only the first three nuclear shells, that is up to that of calcium (Z = 20), there exists a stable isotope with N/Z ratio of one. The exceptions are beryllium (N/Z = 1.25) and every element with odd atomic number between 9 and 19 inclusive (though in those cases N = Z + 1 always allows for stability). Hydrogen-1 (N/Z ratio = 0) and helium-3 (N/Z ratio = 0.5) are the only stable isotopes with neutron–proton ratio under one. Uranium-238 has the highest N/Z ratio of any primordial nuclide at 1.587, while mercury-204 has the highest N/Z ratio of any known stable isotope at 1.55. Radioactive decay generally proceeds so as to change the N/Z ratio to increase stability. If the N/Z ratio is greater than 1, alpha decay increases the N/Z ratio, and hence provides a common pathway towards stability for decays involving large nuclei with too few neutrons. Positron emission and electron capture also increase the ratio, while beta decay decreases the ratio.

A helion (symbol h) is the nucleus of a helium atom, a doubly positively charged cation. The term helion is a portmanteau of helium and ion, and in practice refers specifically to the nucleus of the helium-3 isotope, consisting of two protons and one neutron. The nucleus of the other (and far more common) stable isotope of helium, helium-4, consisting of two protons and two neutrons, is called an alpha particle or an alpha for short.

This particle is the daughter product in the beta-minus decay of tritium, an isotope of hydrogen:

Fermi liquid theory (also known as Landau's Fermi-liquid theory) is a theoretical model of interacting fermions that describes the normal state of the conduction electrons in most metals at sufficiently low temperatures. The theory describes the behavior of many-body systems of particles in which the interactions between particles may be strong. The phenomenological theory of Fermi liquids was introduced by the Soviet physicist Lev Davidovich Landau in 1956, and later developed by Alexei Abrikosov and Isaak Khalatnikov using diagrammatic perturbation theory. The theory explains why some of the properties of an interacting fermion system are very similar to those of the ideal Fermi gas (collection of non-interacting fermions), and why other properties differ.

Fermi liquid theory applies most notably to conduction electrons in normal (non-superconducting) metals, and to liquid helium-3. Liquid helium-3 is a Fermi liquid at low temperatures (but not low enough to be in its superfluid phase). An atom of helium-3 has two protons, one neutron and two electrons, giving an odd number of fermions, so the atom itself is a fermion. Fermi liquid theory also describes the low-temperature behavior of electrons in heavy fermion materials, which are metallic rare-earth alloys having partially filled f orbitals. The effective mass of electrons in these materials is much larger than the free-electron mass because of interactions with other electrons, so these systems are known as heavy Fermi liquids. Strontium ruthenate displays some key properties of Fermi liquids, despite being a strongly correlated material that is similar to high temperature superconductors such as the cuprates. The low-momentum interactions of nucleons (protons and neutrons) in atomic nuclei are also described by Fermi liquid theory.