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In electron-phonon scattering, an electron changes its energy by $\pm \hslash {\omega }_{\mathbf{q}}$ while its crystal momentum changes by a phonon wavevector modulo a reciprocal lattice vector. Charge-transport relaxation weights a scattering angle $\theta$ by $1-\cos \theta$. Small-angle events can therefore relax heat efficiently while relaxing electrical current weakly. At temperatures above the phonon excitation scale, scattering becomes approximately elastic in the electron thermal shell; residual elastic disorder often dominates at very low temperature.

The annihilation of an electron with a Positron, producing other particles; a common final state consists of two photons.

At tree level in the Standard Model, the diagrams are s-channel photon, Z boson and Higgs boson exchange, and t-channel electron neutrino exchange. The Higgs contribution couples to the electron through its small Yukawa coupling. In a zero-electron-mass approximation that diagram vanishes, leaving the three gauge diagrams. The gauge contributions interfere; their sum has the high-energy behavior required by the electroweak gauge structure.

Thermal electron-positron pairs in chemical equilibrium with photons have opposite chemical potentials when the one-particle energy includes rest energy. For negligible degeneracy and $k_{B}T\ll m_e{c}^2$, the zero-chemical-potential density per charge species is $n_0=2[m_e{k}_{B}T/(2\pi {\hslash }^2){]}^{3/2}{e}^{-m_e{c}^2/(k_{B}T)}$. In that nondegenerate limit, charge neutrality and the classical equilibrium product $n_{-}{n}_{+}=n_0^2$ give $n_{+}=(\sqrt{n_b^2+4n_0^2}-n_b)/2$, with net electron density $n_b$. Pairs are important when $n_0\gtrsim n_b$. At arbitrary temperature the zero-chemical-potential marker uses the integral $n_0=({\pi }^2{\hslash }^3{)}^{-1}{\int }_0^{\infty }{p}^2[\exp (\sqrt{m_e^2{c}^4+p^2{c}^2}/k_{B}T)+1{]}^{-1}dp$. Its ultrarelativistic limit is $3\zeta (3)(k_{B}T/\hslash c{)}^3/(2{\pi }^2)$. A nonzero net chemical potential shifts the exact abundance boundary; the zero-potential curve is an approximate crossover marker.

The condition $p_F=m_{e}c$ gives ${\rho }_{\ast }=[{\mu }_e{m}_u/(3{\pi }^2)](m_{e}c/\hslash {)}^3\simeq 9.74\times 10^5{\mu }_e\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}$. Degenerate electrons are nonrelativistic for $\rho \ll {\rho }_{\ast }$ and ultrarelativistic for $\rho \gg {\rho }_{\ast }$. This density threshold differs from thermal relativity in a nondegenerate gas.

The electron single-particle spectral function $A(\mathbf{k},ϵ)=-\mathrm{Im}{G}^R(\mathbf{k},ϵ)/\pi$, in a convention normalized to unit energy integral per orbital and spin, describes addition and removal energies. For the fermionic retarded Green function, $G^R(\mathbf{k},t)=-i\Theta (t)⟨\{c_{\mathbf{k}}(t),c_{\mathbf{k}}^{†}(0)\}⟩$, energy is referenced to the chemical potential. The occupied removal spectrum is $f(ϵ)A(\mathbf{k},ϵ)$, with Fermi-Dirac distribution $f$. In the noninteracting limit, $A$ is a delta peak at the band energy; interactions can shift, broaden, and redistribute its weight.

Electron repulsion is the repulsive electrostatic interaction between electrons. In a metal complex it affects pairing costs and many-electron transition energies, so a measured absorption maximum is not always identical to a one-electron orbital splitting.

A change of direction of an electron through interaction with matter. It can redistribute a transmitted beam outside a detector's collection region without stopping every diverted electron.

The fermion self-energy of an electron in quantum electrodynamics. After renormalization, its contribution in a bound chemical atom is one source of the Lamb shift; other radiative corrections and nuclear structure also affect the observed energy levels.

An electron shell collects the allowed electronic quantum states sharing a principal quantum number $n$. Its occupancy is the number of electrons assigned to those states in an electron configuration. An electron shell is not a material surface or a prescribed orbit.

An electron spectrometer measures an electron energy distribution. A time of flight design infers kinetic energy from calibrated travel times.

Spectroscopy based on the energy distribution of electrons, including photoemission spectroscopy.

An electron has spin one-half. Its intrinsic spin angular momentum has two possible components, $\pm \hslash /2$, along a specified unit vector $\mathbf{n}$. These are the two eigenvalues of the corresponding spin measurement; the spin is distinct from the electron's orbital angular momentum.

The average loss of electron kinetic energy per path length, including collisional and radiative contributions.

An electron subshell groups the allowed electronic quantum states within an electron shell by their orbital angular momentum quantum number $\ell$. Labels $s$ and $p$ mean $\ell =0$ and $\ell =1$, respectively; their capacities are two and six electrons. The leading number in $2p$ identifies the electron shell, while $p$ identifies the electron subshell.

The bookkeeping steps $\mathrm{Na}\to {\mathrm{Na}}^{+}+e^{-}$ and $\mathrm{Cl}+e^{-}\to {\mathrm{Cl}}^{-}$ conserve electric charge and describe the electron inventories of separated species. They do not establish a chronological mechanism in which a labeled electron jumps between two pre-existing chemical atoms and becomes a classical object owned exclusively by one of them. In a bound material, quantum mechanics determines the electron density and the total energy.

Ionic bonding and a covalent bond are useful limiting descriptions with a continuum between them. Electronegativity helps anticipate unequal sharing of electron density, but a numerical cutoff does not measure a universal fraction of ionic bonding. A partial atomic charge depends on how the electron density is partitioned; integer formal charges are a bookkeeping convention. Using $\pm e$ in a point-charge model therefore does not claim that every partition of the actual electron density assigns exactly those values.^[ref][ref]

An electron transport chain transfers electrons from an electron donor through electron carriers to a terminal electron acceptor. In the mitochondrial respiratory chain, some transfers drive protons across the inner mitochondrial membrane; their return through ATP synthase can drive ATP formation.^[ref]

The useful separation is between an electron route and a proton route. The former ends in a redox chemical reaction; the latter changes an electrochemical gradient across a membrane. Energy coupling connects them without making electrons and protons interchangeable. An oxygen readout consequently need not be an ATP readout.

This article focuses on the mitochondrial respiratory chain. Bacteria can use other terminal electron acceptors in anaerobic respiration. In chloroplast light-dependent reactions, light supplies energy and linear electron transport connects water oxidation to NADP+ reduction, releasing oxygen. Thus neither oxygen consumption nor the mitochondrial arrangement defines every electron transport chain.^[ref]

A substituent that reduces electron density in a specified molecular region by induction or chemical resonance. The sign and size of its effect depend on connectivity and the measured property.

With the conventional electroweak vacuum value $v\simeq 246\mathrm{GeV}$, the electron Yukawa coupling is $y_e\simeq 2.9\times 10^{-6}$ and the physical Higgs-electron vertex coefficient is $m_e/v\simeq 2.1\times 10^{-6}$. Direct s-channel Higgs production in electron-positron annihilation is consequently very small away from a compensating resonance enhancement. This suppression belongs to the coupling at the initial vertex, not to a prohibition on the Higgs boson coupling to W bosons.

Electrostatics studies time-independent electric charge distributions and their electric fields. In vacuum, its local equations in SI units areHere $\rho$ is charge density, ${ϵ}_0$ is vacuum permittivity, and $\Phi$ is electric potential. Gauss's law supplies the divergence equation; the static form of Faraday's law of induction supplies the zero curl. The Poisson equation becomes Laplace's equation where there is no electric charge. Prescribed electric charges give electric fields through Coulomb's law and the superposition principle; mobile electric charges on an electrical conductor instead require solving for their distribution together with the electric potential. ^[ref].

The useful distinction is between prescribed sources and prescribed boundary conditions. On a grounded electrical conductor, an external connection fixes its electric potential relative to an electrical reference potential and allows electric charge to enter or leave. On an isolated electrical conductor, total electric charge is fixed and its constant electric potential is an unknown. A neutral isolated electrical conductor can therefore have a nonzero local surface charge density through electrostatic induction. Equal electric potentials also do not imply equal electric charges: charge sharing between distant connected spheres gives a simple geometric example. ^[ref].

Electrostatics is useful because a spatial boundary value problem replaces the need to follow every moving charge carrier during charge relaxation. It describes the settled state of a capacitor and explains electrostatic shielding of sensitive equipment. Its assumptions must match the apparatus: stationary boundaries and sources, negligible time variation of the magnetic field, and enough time for charge relaxation. A metal carrying a maintained electric current through finite electrical resistance generally needs a nonzero internal electric field by Ohm's law; it is not a conductor in electrostatic equilibrium. Static macroscopic electric charge also does not mean that every electron is motionless. ^[ref].