Concept

Degenerate matter — where it appears

Matter so dense and cold that its fermions fill every available state up to a sharp energy, as the exclusion principle requires. Its pressure comes from that stacking rather than from temperature, and it holds up white dwarfs and neutron stars.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

$Hydrogen ionised by heat at one end and by crowding at the other. The ionised fraction of hydrogen against the density of nuclei, at 5,000 K, 10,000 K, 20,000 K, from Saha's equation with the binding energy lowered by the neighbouring charges (solid) and without the lowering (dashed). Thin gas is ionised by the room a free electron gains; compression takes the room away and the gas recombines, as the dashed curves continue to do for ever. The solid curves turn round: at 5,000 K the gas is least ionised, 2.5·10⁻⁴ per cent, near 10²⁶ per cubic metre; at 10,000 K the gas is least ionised, 0.41 per cent, near 10²⁷ per cubic metre; at 20,000 K the gas is least ionised, 12 per cent, near 10²⁸ per cubic metre, and by 6·10²⁸ per cubic metre — 0.10 g/cm³ — every curve is fully ionised, because the ground state no longer exists. That density does not depend on the temperature at all.$

The pressure that ionises

Squeeze a hot gas of hydrogen and Saha's equation says it recombines: a free electron has less room to be in, and room was what paid for its freedom. Squeeze it far enough and it comes apart again, completely, at any temperature — not because the room has grown but because the atom has nowhere left to be. Crowded to within a few atomic radii of each other, hydrogen atoms have no bound state, and their electrons, freed by pressure alone, form a metal. Deep inside Jupiter most of the planet's hydrogen is in that state.

thermodynamics · Chemical potential $The proton fraction a cold star settles at. The fraction of nucleons that are protons in cold matter in beta equilibrium, where the neutron's chemical potential equals the proton's plus the electron's, against density on logarithmic axes, for free neutrons, protons and electrons with no nuclear forces. Below 1.22·10⁷ g/cm³ the electrons cannot pay the 1.29 MeV difference between a neutron and a proton and the matter is all protons. Above it the fraction collapses, to 0.014 per cent at its lowest near 7.9·10¹¹ g/cm³, and at nuclear density, 2.66·10¹⁴ g/cm³, it is 0.49 per cent. At higher densities it climbs slowly towards one ninth, 11 per cent, which it never reaches. The dashed part lies where real matter is made of nuclei rather than free nucleons.$

The protons a star cannot afford

A free neutron decays in fifteen minutes into a proton, an electron and an antineutrino. Inside a neutron star it cannot, and the star is made of neutrons because of it. Beta decay is a reaction like any other, and at equilibrium the neutron's chemical potential must equal the proton's plus the electron's. In a crowded star an electron can only be added at the top of a sea tens of megaelectronvolts deep. So the matter settles where protons are rare: half a per cent of the nucleons at nuclear density, if nucleons were free, and never more than one in nine at any density.

thermodynamics · Chemical potential

Named alongside it

The objects these essays reach for when they reach for this one.

Chemical potential Beta equilibrium Electron capture Fermi energy Ionisation Metallic hydrogen Mott transition Neutron star Pauli exclusion Pressure ionisation Saha equation Screening

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