Ionization

Ionization creates ions by changing a system's electron number, commonly by removing an electron from a neutral chemical atom or molecule. The required ionization energy is supplied by an absorbed photon, an energetic collision, or work done by a sufficiently strong electric field.

In photoionization of an isolated atom from a specified state, energy above the threshold can appear as photoelectron kinetic energy, with recoil included in a complete balance. In a detector gas, many ionization events produce collectable electric charge. Observation of charge alone does not identify the initiating process: collection efficiency, recombination and background must also be considered.

An energetic secondary electron knocked out by a charged particle. It can radiate above a Cherenkov radiation threshold even when the primary particle is below threshold.

The continuous set of scattering states consisting of a residual ion and a free electron, beginning at the relevant ionization threshold. A bound Rydberg series approaches this threshold; the continuum is a set of states rather than the act of ionization.

The fraction of nuclei in a specified ionized state. For pure singly ionized hydrogen, $x=n_e/(n_H+n_e)$ by charge neutrality; a different species or normalization requires a different definition.

The fraction of a specified population of chemical atoms that has become ionized. For singly ionized atoms with no external charge source, charge neutrality gives equal free-electron and ion number densities. Its equilibrium value depends on both temperature and total number density through the Saha ionization equation.

Tunnel ionization is ionization through quantum tunnelling across a field-distorted binding barrier.

An ionization cascade in which electrons accelerated by an electric field produce further free electrons through collisional ionization.

Three-body recombination captures an electron while a second free electron carries away energy, the inverse of direct electron-impact ionization. Its rate scales as the parent-ion density times the square of electron density. It is usually negligible compared with two-body radiative recombination and dielectronic recombination in the low-density solar corona, but matters in sufficiently dense plasmas.

A free electron is resonantly captured while exciting the ionic core, producing a doubly excited state above the parent-ion threshold. Capture becomes permanent recombination only if the state undergoes radiative stabilization rather than autoionization. For resonance $d$, entrance ion $i$, and Maxwellian electrons, ${\alpha }_d=(g_d/(2g_i))(h^2/(2\pi mkT){)}^{3/2}{e}^{-E_d/kT}{A}_{di}^a{A}_{\mathrm{stab}}^r/(A_{\mathrm{tot}}^a+A_{\mathrm{tot}}^r)$. Detailed balance determines the capture rate; a steady population balance determines the survival factor. The rate coefficient has dimensions volume per time.

For temperature-independent atomic rates and an isolated positive-energy resonance, dielectronic recombination has the displayed dependence. Differentiating its logarithm gives a maximum at $kT=2E_d/3$. A sum of resonances can have several peaks, and near-threshold resonances change the low-temperature behavior. Collisional destruction of captured high levels can introduce density dependence.

Radiative stabilization occurs when a photon emission from an autoionizing state leads to a bound state, preventing electron re-ejection. For one radiative channel and one autoionization channel, its probability is $A_r/(A_a+A_r)$. With several channels, use summed losses and the total rate of successful stabilizing decays; a cascade through another autoionizing state requires its eventual survival probability.

Dielectronic capture is the resonant capture stage inverse to a specified autoionization channel. For an entrance ion of weight $g_i$ and resonance of weight $g_d$ and energy $E_d>0$, its Maxwellian coefficient is $C_d=(g_d/(2g_i))(h^2/(2\pi mkT){)}^{3/2}{e}^{-E_d/kT}{A}_{di}^a$. This follows by equating capture and autoionization fluxes at thermodynamic equilibrium. Capture alone need not produce a permanently recombined ion.

An excited atom or ion above an electron-emission threshold can decay without a photon by ejecting an electron and leaving a more highly charged ion. This is autoionization. Its rate competes with radiative stabilization in dielectronic recombination; the inverse electron-capture channel is dielectronic capture.

Photoionization removes a bound electron when an atom or ion absorbs a sufficiently energetic photon. The threshold is its ionization energy. The excess photon energy becomes kinetic energy of the products; subsequent collisions can heat the gas or cause secondary ionizations. A photoionization rate and a photoionization equilibrium are distinct concepts: equilibrium also requires specified recombination and other reaction rates.

A photoionization cross section $\sigma (\nu )$ quantifies the probability that an incident photon of frequency $\nu$ ionizes a specified atomic or molecular target. For a weak monochromatic beam with photon number flux $F_{\gamma }$, the ionization rate per target is $\Gamma =F_{\gamma }\sigma$; the cross section has dimensions of area.

The cross section depends on photon energy, target state and accessible final channels. In an isotropic radiation field with mean specific intensity $J_{\nu }$, $\Gamma ={\int }_{{\nu }_0}^{\infty }[4\pi J_{\nu }/(h\nu )]\sigma (\nu )d\nu$. Energy-resolved photoelectron measurements probe the resulting channels; interpreting a count rate requires photon-flux normalization and detector calibration.^[ref]

The ionization parameter compares the local density of hydrogen-ionizing photons with the hydrogen number density. For an unattenuated isotropic source the displayed form uses its ionizing photon production rate $Q_H$. Ionic fractions depend on $U$ together with the radiation spectrum, temperature, recombination rates and shielding, so $U$ alone does not determine every emission-line ratio.

An electron ejected following photon absorption. For a free residual ion with negligible recoil, the emitted electron's kinetic energy equals incident photon energy minus the ionization binding energy.

For isotropic specific intensity $J_{\nu }$, absorption cross-section ${\sigma }_{\nu }$, and threshold frequency ${\nu }_0$, the photoionization rate per target atom isFor a directed incident flux, replace $4\pi J_{\nu }$ by its spectral flux density. The factor $h\nu$ converts energy flux into photon flux. This rate alone does not imply photoionization equilibrium.

At an unattenuated inner boundary, define photon-weighted cross section moments $⟨{\sigma }^k⟩=Q^{-1}\int {\sigma }_{\nu }^k{L}_{\nu }/(h\nu )d\nu$. Across a layer $dr$, the inverse-square geometrical factor contributes $-2dr/r$, and expanding $e^{-n_H(1-\zeta ){\sigma }_{\nu }dr}$ contributes $-n_H(1-\zeta )dr⟨{\sigma }^2⟩/⟨\sigma ⟩$. Both are first order; a plane-parallel treatment can suppress the former only as a separate geometrical approximation. The second moment occurs because the photoionization rate weights an already attenuated spectrum by another cross section.

Absorption of an ionizing photon leaves energy in a photoelectron above the binding energy. Thermalization supplies heat to the gas. Photoionization heating competes with the astrophysical cooling function, can establish thermal equilibrium, and can raise the pressure enough to inhibit baryon accretion into shallow dark-matter haloes.

A free electron can be captured by an ion while a photon carries away binding and kinetic energy. This radiative recombination process contributes free-bound radiation to plasma cooling and balances collisional ionization in a collisional-equilibrium plasma.

In an optically thin plasma, radiative recombination removes the kinetic energy of captured electrons. A radiative recombination photon can also carry the binding energy released when a free electron becomes bound; that part is stored ionization energy, rather than newly removed thermal energy. The kinetic contribution per event is the recombination-weighted electron energy, which need not be $3k_{B}T/2$.

Equality with mean photoelectron heating requires two balances. If photoionization is the only ionization and heating process, and radiative recombination the only recombination and cooling process, photoionization equilibrium equates their event rates. Separately imposing thermal equilibrium then equates the mean heating energy per ionization to the mean kinetic cooling energy per recombination. Photoionization equilibrium alone does not do this: at the same balanced event rate, unequal energies can still heat or cool the gas. Additional atomic line cooling, collisional ionization or trapping of emitted photons changes the energy accounting.

The mean kinetic energy removed per recombination is $⟨E{⟩}_{\mathrm{rec}}=\int E{f}_T(E){\sigma }_{\mathrm{rec}}(E)v(E)dE/\int f_T(E){\sigma }_{\mathrm{rec}}(E)v(E)dE$. The capture-rate weighting generally differs from averaging an unselected Maxwell distribution, so $⟨E{⟩}_{\mathrm{rec}}=3k_{B}T/2$ is only an additional approximation.

A recombination line is a spectral line produced after a free electron is captured, often through a subsequent radiative cascade among bound levels. Its emissivity is computed with an effective recombination coefficient, distinct from the free-bound recombination continuum.

The effective recombination coefficient for a spectral line counts recombinations and subsequent radiative cascades producing that line. At sufficiently low density, its photon production rate per volume is $n_e{n}_{\mathrm{parent}}{\alpha }_{\ell }^{\mathrm{eff}}$. It depends on gas temperature, optical-depth assumptions such as Case B recombination, and sometimes density. It differs from the total rate coefficient removing the parent ion.

In collisional ionization, an energetic collision frees a bound electron. The process consumes kinetic energy and changes the electron and ion populations controlling plasma cooling. In a thermal gas its rate competes with recombination and depends strongly on the ionization threshold relative to temperature.

Electron impact can excite an ion into a state above an electron-emission threshold, which then ejects a bound electron by autoionization. This two-stage excitation-autoionization contributes to collisional ionization in addition to direct impact removal.

In collisional ionization equilibrium, collision-driven ionization and recombination balance for the populated ion stages, determining their relative abundances at a given temperature. The resulting cooling curve includes the loss of line-emitting bound states as temperature increases. Rapidly cooling gas or external photoionization can invalidate this equilibrium assumption.

The coronal approximation treats an optically thin, low-density plasma with electron-impact ionization balanced by radiative and dielectronic recombination. Excited-level populations are determined mainly by collisional excitation and radiative decay, not by a Boltzmann distribution over levels. Ion fractions can depend primarily on electron temperature while metastable populations retain density dependence; this distinction enables density diagnostics.