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Photoionization

Photoionization is the physical process in which a photon interacts with an atom or molecule, ejecting a bound electron if the photon's energy exceeds the ionization potential, thereby forming a positive ion and a free photoelectron.^[1] This interaction, fundamentally described by the photoelectric effect as explained by Albert Einstein in 1905, underpins the quantum mechanical understanding of light-matter interactions in gaseous media.^[2] In atomic physics, the process is governed by the electric dipole approximation within the interaction Hamiltonian, where the cross-section for photoionization depends on matrix elements between bound and continuum states, often influenced by electron correlations such as particle-hole interactions.^[3] Theoretically, photoionization can occur directly via absorption to a continuum state or resonantly through quasi-bound intermediate states, with the ejected electron's kinetic energy given by E_k = h\nu - I_p, where h\nu is the photon energy and I_p is the ionization potential.^[4] In astrophysical environments, it serves as the primary ionization mechanism in regions irradiated by ultraviolet or X-ray photons, such as active galactic nuclei (AGN) and H II regions around hot stars, balancing with recombination to determine gas ionization states and temperatures typically around 10^4 K.^[1] The ionization parameter, defined as the ratio of photon flux to gas density, quantifies these dynamics and influences observable spectral features like recombination continua and emission lines.^[1] Beyond astrophysics, photoionization is crucial in laboratory applications, including photoelectron spectroscopy for probing molecular electronic structure and dynamics, as well as in mass spectrometry techniques like atmospheric pressure photoionization (APPI) for analyzing nonpolar compounds.^[4] In environmental monitoring, photoionization detectors (PIDs) utilize ultraviolet lamps to ionize volatile organic compounds, enabling sensitive detection in air quality assessments and leak detection without requiring oxygen.^[5] Advances in attosecond science, including X-ray pulses as of 2024, have enabled time-resolved studies of photoionization delays and chiroptical effects, revealing ultrafast electronic processes on femtosecond timescales.^[6]^[7]

Fundamentals

Definition and Process

Photoionization is the physical process in which a photon interacts with an atom or molecule, ejecting one or more bound electrons if the photon's energy exceeds the ionization potential of the system, thereby forming a positively charged ion and a free photoelectron.^[1] This interaction occurs when the photon energy h\nu is sufficient to overcome the binding energy of the electron, distinguishing it from other photon-matter interactions that do not result in electron ejection.^[8] In the basic single-photon process, the absorbed photon promotes the electron from a discrete bound orbital to the continuum of free states, leaving the residual ion in its ground or excited state. The kinetic energy of the ejected photoelectron is then given by E_{\text{kin}} = h\nu - \text{IP}, where \text{IP} is the ionization potential of the atom or molecule.^[9] The minimum photon energy required, known as the threshold energy, precisely equals the ionization potential; for the hydrogen atom in its ground state, this threshold is 13.6 eV, corresponding to ultraviolet photons with wavelengths below approximately 91 nm.^[10] A representative example is the photoionization of the hydrogen atom, where a photon above 13.6 eV directly ionizes the 1s electron, producing \text{H}^+ and a photoelectron with kinetic energy determined by the excess photon energy.^[11] For molecules, such as water (H₂O), the ionization potential is about 12.62 eV, allowing photoionization by photons in the vacuum ultraviolet range and leading to the formation of \text{H}_2\text{O}^+ along with a free electron; this process has been studied through photoionization efficiency curves that reveal the onset and fragmentation pathways.^[12] Unlike photoexcitation, which involves the promotion of an electron to a higher discrete bound state without ejection, photoionization specifically transitions the electron to unbound continuum states, resulting in permanent charge separation.^[8]

Quantum Mechanical Basis

Photoionization is fundamentally a quantum mechanical process involving the absorption of a photon by an atom or molecule, leading to a transition from a bound initial state |i⟩ to a continuum final state |f⟩ comprising an ion and a free photoelectron. This transition is analyzed using time-dependent perturbation theory, where the photon-atom interaction perturbs the unperturbed Hamiltonian describing the isolated system.^[13] In the electric dipole approximation, valid for photon wavelengths much longer than atomic dimensions, the interaction Hamiltonian simplifies to H_{\text{int}} = - \vec{\mu} \cdot \vec{E}, where \vec{\mu} = -e \vec{r} is the electric dipole moment operator and \vec{E} is the electric field of the incident light. The probability of ionization is then determined by the transition rate from Fermi's golden rule:

W = \frac{2\pi}{\hbar} \left| \langle f | H_{\text{int}} | i \rangle \right|^2 \rho(E_f),

where \rho(E_f) is the density of final states at energy E_f, ensuring energy conservation through a delta function in the full derivation. This rate quantifies the likelihood of ejecting an electron with specific kinetic energy matching the excess photon energy above the ionization threshold.^[13] Selection rules govern allowed transitions in the dipole approximation, arising from the symmetry of the interaction operator. For the orbital angular momentum quantum number l of the ejected electron, the change must satisfy \Delta l = \pm 1, reflecting the vector nature of the dipole operator. Additionally, parity is conserved such that the initial and final states must have opposite parity (odd number of electrons changing parity). These rules prohibit certain transitions, such as s → s, and dictate the possible final state symmetries.^[13] Resonant enhancements can occur through autoionization, where a discrete excited state embedded in the continuum decays into the ion-plus-electron continuum, as seen in Feshbach resonances formed by electron capture into a bound state above the ionization threshold. The role of angular momentum is central, with partial photoionization cross sections computed separately for each final-state l (e.g., s, p, d waves), influencing the total cross section and photoelectron angular distributions via interference between channels.^[13]

Photoionization Cross Section

The photoionization cross section, denoted as \sigma(\omega), quantifies the probability that an atom absorbs a photon of angular frequency \omega and undergoes ionization, expressed as an effective geometric area per atom. It is derived from the quantum mechanical transition rate between the initial bound state and the final continuum state, with typical units of square centimeters (cm²) or megabarns (Mb; 1 Mb = $10^{-18} cm²). This quantity is fundamental in single-photon ionization processes, where the linear response to the electromagnetic field determines the ionization yield.^[14]^[15] For hydrogenic atoms, the Wigner threshold law is modified by the long-range Coulomb potential, resulting in a finite non-zero cross section at threshold rather than vanishing as in short-range potentials. The near-threshold behavior reflects the p-wave (l=1) character of the ejected electron from an initial s-state and the normalization of the Coulomb continuum wave function, but does not follow a simple power law in (ℏ ω - I_p) due to the Coulomb interaction; for the hydrogen ground state, σ ≈ 6.3 Mb at I_p, decreasing with increasing photon energy.^[11]^[15] For the hydrogen atom in its ground state, the exact total photoionization cross section is obtained by integrating the differential cross section over ejection angles, yielding an analytic expression involving the dipole matrix element and Coulomb factors:

\sigma_H(\omega) = \frac{2^{9} \pi^{2} \alpha a_0^{2}}{3} \left( \frac{I_H}{\hbar \omega} \right)^{4} g\left( \frac{I_H}{\hbar \omega} \right),

where \alpha is the fine-structure constant, a_0 is the Bohr radius, I_H = 13.6 eV is the ionization energy, and g is the Gaunt factor accounting for Coulomb distortion, approximated near threshold as g \approx \frac{2\pi \eta}{1 - e^{-2\pi \eta}} with Sommerfeld parameter \eta = \frac{2\pi }{k} (in atomic units), where k \propto \sqrt{\hbar \omega - I_H} is the photoelectron wave number. At threshold, \sigma_H \approx 6.3 Mb, decreasing monotonically with increasing \hbar \omega. This form originates from exact solutions of the Schrödinger equation for the hydrogen atom.^[16]^[17]^[18] Several factors influence the magnitude and shape of the photoionization cross section. For hydrogenic atoms, the threshold value scales as \sigma \propto Z^{-2}, where Z is the atomic number, due to the contraction of the atomic orbital size with increasing nuclear charge. Asymptotically at high photon energies (\hbar \omega \gg Z^2 I_H), certain partial cross sections exhibit a Z^{-4} dependence, arising from the scaling of the radial matrix elements in the Born approximation. In molecules, the cross section is modified by effects such as shape resonances, where quasi-bound states in the continuum lead to enhanced absorption peaks above the threshold. Measurements of cross sections are performed using techniques like photoelectron spectroscopy, yielding typical near-threshold values of \sim 10^{-18} cm² for alkali metals; for instance, the 3p state of sodium has \sigma \approx 7.63 \times 10^{-18} cm² at threshold.^[18]^[19]^[20]^[21] A notable feature in many atomic systems is the Cooper minimum, a pronounced dip in the cross section at specific energies where the radial part of the dipole matrix element vanishes, causing a sign change and destructive interference between contributing channels. This minimum, first identified in noble gases, provides insight into electron correlations and is particularly evident in subshells like np orbitals of alkali atoms.^[22]

Ionization Mechanisms

Single-Photon Ionization

Single-photon ionization occurs when an atom or molecule absorbs a single photon with energy h\nu exceeding the ionization potential (IP), leading to the ejection of an electron in a process governed by the perturbative regime. This mechanism is typically analyzed using the first-order electric dipole approximation, where the photon's magnetic field and higher-order multipole contributions are negligible, simplifying the interaction to the electric field's coupling with the atomic dipole moment.^[23] In this linear response regime, the ionization operates as a one-step absorption event, distinct from nonlinear processes, and the resulting photoelectron carries kinetic energy E_k = h\nu - \mathrm{IP}.^[24] The ionization rate in this process is directly proportional to the incident light intensity I, reflecting its linear dependence on photon flux. Consequently, the number of ions produced, N_\mathrm{ion}, scales as N_\mathrm{ion} \propto \sigma I / (h\nu), where \sigma is the photoionization cross section, which quantifies the probability of ionization per unit photon flux.^[25] A representative example is the vacuum ultraviolet (VUV) photoionization of noble gases like helium, where the threshold lies at 24.6 eV, corresponding to a wavelength of approximately 50 nm; above this energy, the process efficiently produces He^+ ions and photoelectrons.^[26] Upon ionization, the process can lead to various final states, characterized by branching ratios that determine the distribution of outcomes. For helium, the dominant channel yields ground-state He^+ (1s) plus a free electron, but a fraction—typically a few percent near threshold—results in shake-up satellites, such as He^+ (2s or 2p) plus a lower-energy electron due to electron correlation effects during the rapid charge rearrangement.^[27] These ratios vary with photon energy, providing insights into intra-atomic interactions. This mechanism is limited to scenarios where photon energies suffice to overcome the IP directly; at lower intensities or longer wavelengths (e.g., visible or near-infrared), where h\nu < IP, single-photon ionization is negligible, and multi-photon processes may dominate under high-intensity conditions.^[8] Historically, precise measurements of absolute cross sections for single-photon ionization, such as those for helium, were enabled by early synchrotron radiation experiments starting in the 1960s, which provided tunable VUV light sources for quantitative studies.^[28]

Multi-Photon Ionization

Multi-photon ionization occurs when an atom or molecule absorbs two or more photons whose combined energy exceeds the ionization potential (IP), even though the energy of each individual photon is below the IP threshold, requiring intense laser fields in the perturbative regime. This process can be sequential, involving intermediate bound states, or simultaneous, and is distinct from single-photon ionization by its nonlinear dependence on laser intensity. In the perturbative multiphoton regime, the k-photon ionization rate R_k is proportional to the laser intensity I raised to the power k, expressed as R_k \propto I^k |M_k|^2, where |M_k|^2 represents the square of the k-th order transition matrix element involving the atomic wavefunctions and the laser field. This rate arises from time-dependent perturbation theory applied to the Schrödinger equation, with the generalized cross section \sigma_k incorporating the matrix elements such that R_k = \sigma_k I^k. The perturbative approach holds when the Keldysh parameter \gamma \gg 1, indicating that photon absorption dominates over field-driven tunneling.^[29] A key phenomenon in multi-photon ionization is above-threshold ionization (ATI), where the atom absorbs more than the minimum number k of photons required for ionization, resulting in photoelectrons with discrete kinetic energies spaced by the photon energy h\nu. The kinetic energy of these electrons is given by E_{\text{kin}} = k h\nu - \text{IP} - U_p, where U_p = \frac{e^2 E^2}{4 m \omega^2} is the ponderomotive potential, representing the average quiver energy of the electron in the laser field E at frequency \omega. ATI was first experimentally observed in xenon atoms using six-photon absorption, revealing peaks in the photoelectron spectrum shifted by U_p.^[30]^[31] Multi-photon ionization finds applications in laser-based detection and spectroscopy, particularly with femtosecond pulses for efficient ionization of alkali atoms such as sodium. For example, three-photon ionization of sodium has been demonstrated using 589 nm dye laser pulses, where the process involves resonant excitation via the 3p intermediate state followed by ionization to the continuum, enabling selective detection in vapor cells. These short pulses minimize thermal effects and allow control over the ionization dynamics at intensities around $10^{12} W/cm².^[32] At sufficiently high intensities, the ionization yield saturates and plateaus, as the neutral atom population depletes and the process transitions toward complete ionization within the laser focal volume. This saturation intensity depends on the atomic species and laser wavelength but typically occurs when the Rabi frequency exceeds the inverse pulse duration, leading to a balance between excitation and depletion rates. In such regimes, the simple perturbative rate equation underestimates the yield, requiring numerical solutions of the time-dependent Schrödinger equation.^[33] Unlike single-photon ionization, which requires photon energies above the IP and operates linearly with intensity at low fields, multi-photon ionization demands peak intensities on the order of $10^{12} W/cm² or higher to achieve appreciable rates, exhibits a power-law dependence I^k, and allows ionization with longer wavelengths below the single-photon threshold, providing greater flexibility in experimental setups.

Tunnel Ionization

Tunnel ionization occurs in the presence of intense laser fields, typically exceeding intensities of I > 10^{14} W/cm², where the strong electric field distorts the atomic Coulomb potential, suppressing the potential barrier and allowing a bound electron to quantum mechanically tunnel from its orbital into the continuum without the absorption of real photons.^[34] This non-perturbative mechanism dominates when the laser frequency is low enough that the field acts quasi-statically over the timescale of the tunneling process, contrasting with perturbative regimes at lower intensities.^[35] The boundary between tunneling and multi-photon ionization regimes is characterized by the Keldysh parameter, \gamma = \omega \sqrt{2 I_p} / E, where \omega is the angular frequency of the laser, I_p is the atomic ionization potential, and E is the peak electric field strength (in atomic units).^[34] For \gamma \ll 1, the ponderomotive energy U_p = E^2 / (4 \omega^2) exceeds I_p, and the electron experiences the field as nearly static, favoring tunneling over stepwise photon absorption.^[36] Theoretical description of the tunneling rate is provided by the Ammosov-Delone-Krainov (ADK) model, which employs a quasi-classical approximation based on the saddle-point method for the ionization amplitude from hydrogen-like wave functions.^[35] The ionization rate w is given by

w \approx \left( \frac{2 I_p}{E} \right)^{2(2 s_p - 1)} \exp\left[ -\frac{2 (2 I_p)^{3/2}}{3 E} \right],

where s_p = Z / \sqrt{2 I_p} is the effective quantum number accounting for the nuclear charge Z.^[35] This expression captures the exponential dependence on field strength and has been validated for multielectron atoms and ions in linearly polarized fields.^[37] Experimental realizations of tunnel ionization frequently involve noble gases exposed to Ti:sapphire laser pulses at 800 nm wavelength and intensities near $10^{15} W/cm², where argon, for example, exhibits efficient single and double ionization in the tunneling limit (\gamma < 1).^[36] In such setups, the process is confirmed by the spatial distribution of ionization within the laser focus, with tunneling prevailing in the high-intensity core.^[36] The applied field not only suppresses the barrier height but also induces a linear Stark shift in the ionization potential, \Delta I_p \approx (3/2) n^2 E for hydrogenic states with principal quantum number n, which lowers the effective binding energy and enhances the tunneling probability.^[38] Barrier suppression ionization emerges at even higher fields when the barrier vanishes entirely, transitioning the process to over-the-barrier escape.^[38] Upon tunneling, the electron emerges with near-zero initial velocity and is subsequently driven by the laser field, undergoing classical acceleration that imparts high kinetic energies up to several tens of eV, depending on the birth phase within the optical cycle.^[39] This post-ionization dynamics underpins phenomena like above-threshold ionization, where the electron's final momentum distribution reflects the vector potential of the field at the instant of escape.^[39]

Applications and Detection

In Atomic and Molecular Spectroscopy

Photoelectron spectroscopy (PES) employs photoionization as a fundamental process to investigate the electronic structure of atoms and molecules by ejecting electrons with photons of sufficient energy and analyzing their kinetic energies, which directly relate to the binding energies of the occupied orbitals. This technique maps orbital energies and symmetries, providing insights into atomic and molecular configurations. In X-ray photoelectron spectroscopy (XPS), a core-level variant of PES, X-rays ionize inner-shell electrons, revealing element-specific signatures due to the distinct binding energies of core orbitals across the periodic table, enabling identification of chemical environments and surface compositions.^[40] In molecular applications, photoionization often results in dissociative photoionization, where the ionized molecule breaks apart, yielding fragment ions that disclose bond strengths and dissociation mechanisms; for instance, in water, the reaction \ce{H2O + h\nu -> [OH+](/page/Oh) + H + e-} produces hydroxyl and hydrogen fragments, aiding the study of aqueous reaction dynamics.^[41] Threshold photoelectron spectroscopy (TPES), a high-resolution method, selectively detects near-zero kinetic energy electrons close to the ionization threshold, yielding detailed spectra of vibrational and rotational progressions in molecular ions and elucidating subtle structural details in polyatomic species.^[42] Site-specific photoionization further refines molecular analysis by targeting electrons from particular orbitals or atomic sites, such as distinguishing valence from core ionization in biomolecules like amino acids, where core-level ejection localizes charge on specific functional groups, facilitating the mapping of electronic delocalization.^[43] This selectivity arises from variations in photoionization cross sections across orbitals, which modulate spectral intensities and enable differentiation of contributions from equivalent sites.^[44] The element-specific nature of ionization potentials in PES variants like XPS and ultraviolet photoelectron spectroscopy (UPS) offers key advantages, including precise elemental detection and surface sensitivity, as demonstrated in UPS studies of adsorbates on metal substrates, where valence band shifts reveal bonding interactions.^[45]^[46] Interpreting PES data requires deconvolution or peak fitting of spectra to resolve overlapping features, assigning them to ionic states while correcting for instrumental resolution and inelastic scattering, thus enabling accurate determination of electronic transitions and molecular symmetries.^[47] Single-photon ionization predominates in these spectroscopic applications due to its simplicity and tunability with synchrotron sources.

In Astrophysics and Plasma Physics

In astrophysics, photoionization serves as the primary mechanism for ionizing hydrogen in H II regions surrounding hot, massive O and B stars, where ultraviolet photons from the stellar photosphere excite electrons from neutral hydrogen atoms to create fully ionized plasma. These regions are characterized by the Strömgren sphere, an idealized spherical volume where the rate of ionizations balances recombinations, yielding a radius given by R_s = \left( \frac{3 Q}{4 \pi \alpha_B n^2} \right)^{1/3}, where Q is the total number of ionizing photons emitted per second by the star, \alpha_B the case-B recombination coefficient, and n the hydrogen density.^[48] This model, first derived for uniform density media, delineates the boundary beyond which the interstellar medium remains neutral, influencing the structure and dynamics of galactic disks. In photoionized plasmas, the traditional Saha equation, which assumes thermal equilibrium, is modified to account for the radiation field dominance over collisions, leading to an ionization fraction approximated as x \approx \sqrt{\Gamma / (n \alpha_B)}, where \Gamma = \int \sigma(\nu) (4\pi J_\nu / h\nu) \, d\nu is the photoionization rate and J_\nu the mean specific intensity. This balance highlights how photoionization rates, integrated over the cross section and radiation field, determine the degree of ionization in low-density environments like the interstellar medium, where ultraviolet radiation from O stars ionizes diffuse gas, shaping the warm ionized medium phase. Similarly, in planetary nebulae, photoionization by the central post-asymptotic giant branch star creates stratified ionization structures, with inner regions highly ionized and outer shells showing He II and higher ions near the nucleus. Recent computational advances, such as the 2024 HOMERUN modeling framework and the 2025 release of the Cloudy code, have improved simulations of photoionized gas by better accounting for complex emission lines and radiation transfer.^[49]^[50] In plasma physics, photoionization plays a key role in laser-produced plasmas, where it contributes to Rosseland mean opacity through bound-free transitions, affecting radiation transport and energy balance in high-temperature, dense conditions.^[51] During recombination following intense laser pulses, photoionization influences cascade processes as electrons recombine stepwise, populating excited states that can lead to population inversions and enhanced emission in x-ray or extreme ultraviolet regimes.^[52] Non-equilibrium effects become prominent in transient astrophysical events, such as supernovae, where time-dependent photoionization alters ionization states on timescales shorter than recombination times, resulting in delayed responses to evolving radiation fields from the expanding ejecta.^[53] Observationally, photoionized regions exhibit signatures in recombination emission lines, such as Hα from hydrogen cascades, which trace the density and temperature of the plasma and provide diagnostics for the underlying ionizing spectrum. These lines, arising from transitions in recombining ions, dominate spectra of H II regions and planetary nebulae, enabling inferences about stellar content and interstellar conditions without reliance on collisionally excited forbidden lines.

Experimental Techniques

Experimental techniques for studying photoionization rely on advanced light sources to initiate the process and sophisticated detection systems to capture the resulting ions and electrons. Synchrotron radiation facilities provide tunable vacuum ultraviolet (VUV) and extreme ultraviolet (XUV) light, enabling precise control over photon energy for threshold and above-threshold ionization studies. For instance, the Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory utilizes merged-beam setups where ion beams intersect with synchrotron photons to measure absolute cross sections for multiply charged ions. Similarly, the Photon-Ion spectroscopy at PETRA III Experiment (PIPE) at DESY employs synchrotron radiation for photoionization of atomic ions, offering high-resolution data on resonance features. Free-electron lasers (FELs), such as the Linac Coherent Light Source (LCLS) at SLAC, generate attosecond XUV pulses, allowing time-resolved observations of electron dynamics during photoionization. As of 2025, these pulses have enabled measurements of photoionization time delays probing electron correlations in atoms and attosecond control of chiral photoionization in oriented molecules, providing insights into ultrafast stereochemical dynamics.^[54]^[7]^[55]^[56]^[57] Detection methods focus on resolving the kinematics of photoelectrons and ions to infer cross sections and angular distributions. Time-of-flight (TOF) mass spectrometry identifies ion masses and measures their kinetic energies by recording flight times through a field-free region, commonly integrated into photoionization mass spectrometry (PIMS) setups for studying reaction dynamics in molecular systems. Velocity map imaging (VMI) projects photoelectrons onto a 2D detector using electrostatic lenses, providing angular distributions that reveal orbital symmetries and dynamics; this technique has been optimized for low-energy electrons in photoionization studies of noble gases. Coincidence techniques, such as photoelectron-photoion coincidence (PEPICO) spectroscopy, detect correlated electron-ion pairs to suppress background and enable isomer-selective analysis, often combined with VMI for multidimensional momentum mapping.^[58]^[59]^[60] Setup examples illustrate the integration of these components for specific investigations. In PIMS, a tunable light source ionizes gas-phase samples within a TOF spectrometer, tracking dissociation pathways in real time, as demonstrated in studies of interstellar analog ices. Coincidence setups at synchrotron beamlines, like those at DESY, use position-sensitive detectors to record joint electron-ion spectra, revealing fragmentation channels in polyatomic molecules. For high-resolution angular studies, VMI spectrometers are aligned with FEL pulses at LCLS to capture attosecond-scale photoionization delays.^[58]^[61]^[57] Intensity regimes span from low-fluence continuous-wave (CW) sources to ultrahigh intensities for nonlinear processes. Low-intensity CW VUV lamps, such as those based on rare-gas discharges, facilitate single-photon ionization in gas cells for baseline cross-section measurements. At higher intensities, Ti:sapphire amplifiers deliver femtosecond pulses up to 10^14 W/cm², enabling multi-photon and tunnel ionization regimes, as used in tabletop experiments probing strong-field dynamics.^[62]^[63] Calibration ensures accurate quantification of photoionization yields. Absolute cross sections are determined using gas cells with known target densities and photon fluxes, often calibrated against standard atomic resonances like those in argon or xenon. Photon flux is measured via calibrated photodiodes or electron yield from clean metal surfaces, achieving uncertainties below 5% in synchrotron experiments.^[64]^[65] Challenges in these experiments include managing background signals and space-charge effects. Background subtraction is critical in coincidence setups to isolate true photoionization events from stray photons or collisions, often requiring time-gating or differential pulsing. In dense targets or high-flux regimes, space-charge effects distort electron trajectories, broadening images in VMI; mitigation involves low-repetition-rate pulsing or retarding fields to reduce ion-electron repulsion.^[66]^[67]

Historical Development

Early Discoveries

The initial observations of photoionization emerged from Heinrich Hertz's experiments on electromagnetic waves in 1887, during which he noted that ultraviolet radiation from a spark gap enhanced the conductivity of surrounding air, enabling easier spark discharge across a gap; this effect was attributed to the ionization of air molecules by the UV light, marking the first reported instance of photoionization.^[68] Although Hertz did not fully explore the phenomenon, his incidental discovery highlighted the ability of short-wavelength light to ionize gases. Philipp Lenard, building on Hertz's work, conducted systematic investigations starting around 1900, confirming that ultraviolet light could ionize various gases over distances of several centimeters without relying on secondary radiation or contact effects; he demonstrated this using quartz windows to transmit UV from sparks into evacuated tubes filled with gases like air and hydrogen.^[69] In further experiments around 1902, Lenard extended these studies to alkali metal vapors, such as sodium, where he observed a sharp threshold frequency for ionization, analogous to the photoelectric effect in solids but occurring in the gas phase, thus establishing photoionization as a distinct process for atomic systems.^[69] Lenard received the 1905 Nobel Prize in Physics for his research on cathode rays, including the photoelectric effect from solids; his gas-phase ionization studies further advanced the understanding of light-induced ionization. In 1905, Albert Einstein provided the first theoretical explanation by applying his quantum hypothesis of light to photoionization, positing that photons with energy h\nu exceeding the ionization potential I could eject electrons from atoms, with the kinetic energy of the photoelectrons given by h\nu - I; this unified the observed thresholds in both solid and gaseous systems under a single framework. Robert Millikan's precise measurements in 1916 verified this law experimentally for metals, determining the long-wavelength cutoff corresponding to ionization thresholds and yielding Planck's constant h = 6.57 \times 10^{-27} erg·s, while noting similarities to gas-phase ionization processes. During the 1920s, James Franck and Gustav Hertz advanced the field through comparative studies of electron impact and photoionization, revealing discrete energy levels in atoms; in 1920, Franck, Paul Knipping, and Fritz Reiche measured the ionization potential of helium as approximately 24.6 eV using electron impact methods, identifying metastable states and supporting quantum models of atomic structure.^[70] These experiments distinguished collision-induced processes from photoionization and highlighted the role of discrete energy levels in both. In 1923, Hendrik Kramers introduced a semi-classical approximation for the photoionization cross section at high photon energies (h\nu \gg I), expressed as \sigma \approx 6.3 \times 10^{-18} \left( \frac{I}{h\nu} \right)^{7/2} (Z+1)^2 cm², where Z is the atomic number, providing a foundational estimate for absorption probabilities in atomic systems. Early photoionization studies relied on fixed-wavelength sources like spark discharges and gas-filled lamps (e.g., hydrogen or mercury arcs) to produce vacuum ultraviolet radiation, enabling threshold measurements but restricting detailed cross-section profiles. A significant challenge was the absence of tunable light sources, which limited experiments to discrete emission lines and broad continua, hindering precise spectroscopy until synchrotron radiation facilities emerged in the 1960s. The seminal contributions of figures like Philipp Lenard and James Franck (Nobel Prize 1925) underscored the experimental foundations of photoionization, bridging classical optics with emerging quantum theory.

Theoretical Advancements

The theoretical understanding of photoionization advanced significantly in the late 1920s with J. Robert Oppenheimer's seminal calculations within quantum mechanics for the cross section of the hydrogen atom, treating transitions from bound to continuum states. This work established the foundational framework for treating photoionization as an aperiodic quantum process, highlighting the role of the continuum wavefunction in determining the ionization probability. In the 1930s, the development of the Hartree-Fock approximation by Vladimir Fock extended these models to multi-electron atoms, incorporating antisymmetrization via Slater determinants and self-consistent fields to account for electron-electron interactions and exchange effects in bound and continuum orbitals. This independent-particle model improved accuracy for inner-shell ionizations and provided a basis for estimating cross sections in complex atoms, though it neglected explicit electron correlation. Post-World War II advancements in the 1950s introduced close-coupling methods, pioneered by David R. Bates and colleagues, which solved coupled integro-differential equations for multi-channel scattering to yield precise continuum wavefunctions incorporating target excitation effects. These methods enhanced predictions for near-threshold photoionization by treating the ejected electron's interaction with the residual ion more rigorously than single-channel approximations. The 1960s saw the emergence of R-matrix theory for atomic processes, formulated by Philip G. Burke and Michael J. Seaton, which partitioned configuration space into an inner region for strong correlations and an outer region for asymptotic behavior, enabling accurate handling of resonances and bound-continuum coupling. This approach proved essential for modeling autoionizing states where discrete levels embed in the continuum. Key contributions during this era included Michael J. Seaton's calculations of photoionization cross sections for astrophysically relevant ions in the 1950s, which quantified opacity in stellar atmospheres by integrating bound-free transitions over atomic configurations. Complementing this, Ugo Fano's 1961 theory described the characteristic asymmetric line profiles of autoionizing resonances, arising from interference between direct ionization and discrete excitation pathways, formalized through configuration interaction parameters q and \Gamma. Further developments in the 1970s involved numerical solutions of the time-dependent Schrödinger equation (TDSE) for atoms in intense laser fields, allowing non-perturbative treatments of multi-photon and above-threshold ionization beyond the dipole approximation. In the 1980s, density functional theory (DFT) was adapted for molecular photoionization, using Kohn-Sham orbitals to compute continuum states efficiently for polyatomic systems, capturing exchange-correlation effects in vibrational and rotational frames. Modern computational tools, such as the CIV3 code developed by Alan Hibbert, employ configuration interaction to incorporate electron correlation beyond Hartree-Fock limits, yielding high-precision cross sections for transition metals and ions.^[71] Similarly, B-spline basis methods expand continuum wavefunctions over a discrete radial grid, facilitating accurate matrix elements for photoionization in both atomic and molecular targets while addressing limitations of independent-particle models through explicit inclusion of correlation via multi-configuration expansions.^[72]

Modern Contributions

Since the 1990s, photoionization research has advanced significantly through the development of attosecond science, enabling the probing of ultrafast electron dynamics on timescales of 10^{-18} seconds. High-harmonic generation (HHG) driven by intense femtosecond laser pulses has been pivotal, producing coherent extreme ultraviolet (XUV) attosecond pulse trains that initiate photoionization and reveal electron motion in atoms and molecules. Paul Corkum's three-step model, which describes tunnel ionization, electron acceleration, and recollision, provided the foundational semiclassical framework for understanding strong-field HHG and subsequent photoionization processes in the 1990s.^[73] The 2023 Nobel Prize in Physics, awarded to Anne L'Huillier, Pierre Agostini, and Ferenc Krausz, recognized their pioneering work in generating and applying attosecond pulses to study electron dynamics. Strong-field advances have further refined photoionization studies, particularly through techniques like RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions), which measures photoionization time delays and atomic phase shifts with attosecond precision. Introduced in 2001, RABBITT uses an attosecond pulse train and a delayed infrared probe to interfere two-photon pathways, allowing extraction of the spectral phase of photoelectrons. This method has been extended to angle-resolved measurements, providing insights into the angular dependence of photoionization amplitudes in complex systems.^[74] In molecular and cluster studies, modern photoionization has enabled site-selective ionization, particularly in biomolecules like proteins, where XUV pulses target specific amino acid residues to probe local electronic structure without global disruption. Such selectivity emerged in the 2000s through inner-shell photoionization experiments, revealing charge migration dynamics in peptides. For clusters, photoionization investigations have elucidated solvation effects, showing how surrounding solvent molecules shift ionization potentials and alter fragmentation pathways, as demonstrated in water-solvated organic clusters where hydrogen bonding influences electron ejection. Interdisciplinary impacts include quantum control of photoionization using shaped laser pulses, which manipulate interference pathways to enhance or suppress ionization yields. Femtosecond pulse shaping has achieved coherent control over multiphoton ionization rates in molecules, opening avenues for selective chemistry.^[75] Attosecond metrology, leveraging these techniques, now calibrates electron clocks with sub-attosecond accuracy, aiding precision measurements in quantum optics.^[76] Recent milestones encompass free-electron laser (FEL) experiments, such as those at FLASH since 2005, which have enabled inner-shell photoionization of heavy atoms at high intensities, uncovering nonlinear effects like two-photon absorption in xenon.^[77] In the 2020s, machine learning models have predicted photoionization cross sections for large datasets of organic molecules, achieving accuracies comparable to quantum chemistry calculations and facilitating high-throughput simulations for atmospheric and combustion modeling.^[78] As of 2025, advances in attosecond X-ray pulses have enabled time-resolved studies of photoionization delays in the photoelectric effect, revealing ultrafast electron correlations. Additionally, attosecond chiroptical spectroscopy has demonstrated control over chiral photoionization dynamics in oriented molecules, enhancing understanding of stereoselective processes.^[6]^[7] Looking forward, tabletop XUV sources based on HHG continue to democratize attosecond photoionization experiments, offering compact alternatives to FELs for real-time dynamics studies.^[79] Quantum computing simulations promise to tackle many-body correlations in photoionization, with algorithms now computing vertical ionization energies for complex systems beyond classical limits.^[80]

References

[1]
[PDF] What is photoionization? - HEASARC
Photoionization is the removal of a bound electron by a photon, where photons ionize atoms in a gas.
[2]
Einstein and The Photoelectric Effect - American Physical Society
Jan 1, 2005 · In 1887, German physicist Heinrich Hertz noticed that shining a beam of ultraviolet light onto a metal plate could cause it to shoot sparks.
[3]
None
### Summary of Atomic Photoionization Theory
[4]
Photoionization - an overview | ScienceDirect Topics
Photoionization (PI) of atoms and ions is described as one of the fundamental process occurring in many astrophysical systems such as stars and nebulae. In the ...
[5]
Photoionisation Detectors - A Basic Guide From ION Science Ltd
A Basic Guide to Photoionization Detectors ... PIDs are fully functional in applications where it is necessary to measure toxic compounds without oxygen present.
[6]
Photoionization in the time and frequency domain - Science
Nov 2, 2017 · The ability to produce attosecond pulses of light provides access to some of the fastest electronic processes occurring within atoms.Photoionization In The Time... · Abstract · Photoionization Time Delays
[7]
Photoemission and photoionization time delays and rates - PMC - NIH
We give a brief overview of some of the most important ionization processes and how to resolve the associated time delays and rates. With regard to time delays, ...
[8]
A general formula for the calculation of atomic photo-ionization cross ...
X~ i, E), E being the electron kinetic energy. The energy conservation condition is h~' =1+ E where I is the threshold ionization energy.
[9]
Photoionization Equilibrium - The Intergalactic Medium - P. Madau
The photoionization cross-section for hydrogen in the ground state by photons with energy hP nu (above the threshold hP nu L = 13.6 eV) can be usefully ...
[10]
[PDF] Photoionization of Atoms - UNL Digital Commons
This chapter outlines the theory of atomic photoion- ization, and the dynamics of the photon-atom collision process. Those kinds of electron correlation that ...Missing: overview | Show results with:overview
[11]
[PDF] Mass spectrometric study of photoionization. V. Water and ammonia
Photoionization efficiency curves are obtained for the molecule and fragment ions of H2 0 and. NH3 in the wavelength region extending from onset of ...
[12]
https://nvlpubs.nist.gov/nistpubs/jres/70A/jresv70An6p459_A1b.pdf
[13]
Photo-Ionization - Richard Fitzpatrick
In this phenomenon, a photon of angular frequency $ \omega$ is absorbed by an electron that occupies the ground state of a hydrogen atom.
[14]
Statistical and quantum photoionization cross sections in plasmas
Statistical models combined with the local plasma frequency approach applied to the atomic electron density are employed to study the photoionization cross- ...<|control11|><|separator|>
[15]
Photoionization Cross Sections of He and H2 - IOP Science
The photoionization cross sections of H, H2, and He are important parameters in the determination of the ionization structure of cosmic gas subjected to ...
[16]
[PDF] Photoionization Cross Sections of He and H 2 - Harvard DASH
at photon energies between 18. H. 2 and 113 eV to within an uncertainty of ^3%. There have been earlier measurements down to the threshold energy of. 15.4 eV.<|separator|>
[17]
Photoionization and Electron-Ion Recombination of n = 1 to Very ...
Sep 4, 2004 · Ground State Photoionization Cross Sections of Hydrogen. The exact analytical form for the ground state photoionization ... Bethe, J.A.; Salpeter ...2.1. Photoionization Of... · 2.1. 2. Ground State... · 2.2. Electron-Ion...
[18]
[PDF] A hyperspherical close-coupling calculation of photoionization from ...
The intensities of partial cross section decline with different Z dependence, with of. Z-4 and σN=1 of. Z-2. As a result of diminishing intershell ...<|separator|>
[19]
[PDF] Absolute Cross Sections for Molecular Photoabsorption, Partial ...
Molecular photoionization processes are of fundamen- tal importance' and find application in a large number of scientific contexts, including studies in ...
[20]
Measurement of Photoionization Cross-Section for the Excited ...
Oct 2, 2004 · In hydrogen, the photoionization cross-section is maximum at the ionization threshold (13.606 nm) and it decreases monotonically at higher ...
[21]
[PDF] arXiv:2212.00577v1 [physics.atom-ph] 1 Dec 2022
Dec 1, 2022 · The ground-state photoabsorption cross sections of alkali metal atoms are known to have distinct minima called Cooper minima [1, 2], just above ...
[22]
Photon Momentum Transfer in Single-Photon Double Ionization of ...
Jan 29, 2020 · The dipole approximation is commonly used in the theoretical treatment of the interaction of photons or light pulses with atoms and molecules.
[23]
Photoemission and photoionization time delays and rates
A single photon can remove an electron from a physical system if the photon energy is high enough to promote the electron from its initial bound state into the ...
[24]
Breakdown of the single-active-electron approximation for one ...
Jun 8, 2010 · (7) show that for one-photon ionization, the ion yield is proportional to the one-photon absorption cross section and the laser intensity, P ion ...
[25]
Photoelectron Imaging of Helium Droplets | Phys. Rev. Lett.
Article Text · 2 shows the total electron yield (TEY) following photoexcitation between 22.5 to 24.6 eV along with the location of He atomic n p Rydberg states.
[26]
[PDF] Lawrence Berkeley National Laboratory - eScholarship
Jun 1, 1986 · Photoionization of helium and neon to excited satellite states,. +. + ... If the monochromator width is decreased to 0.09, then the branching ...
[27]
Partial Photoionization Cross Sections and Angular Distributions for ...
Dec 8, 2005 · In 1963 Madden and Codling [1] investigated the double excitation of helium into P 0 1 states using synchrotron radiation. These measurements ...
[28]
Multiphoton Ionization of Hydrogen and Rare-Gas Atoms | Phys. Rev.
A perturbation theory of the ionization of atoms by simultaneous absorption of several photons, each of whose energy is less than the ionization potential, ...Missing: equation | Show results with:equation
[29]
Free-Free Transitions Following Six-Photon Ionization of Xenon Atoms
Apr 23, 1979 · Agostini, F. ... We have shown that the discrete absorption of photons above the six-photon ionization threshold was observable under specified ...
[30]
Role of the ponderomotive potential in above-threshold ionization
Ponderomotive scattering strongly affects photoelectron spectra in above-threshold ionization. We review experimental studies of intensity-dependent angular ...
[31]
[PDF] and two-photon ionization of the sodium 4s state - NB Baranova, IM ...
This laser was a dye laser using the dye rhodamine 6G, with 2 = 589 nm. This dye laser was pumped by the second har- monic produced inside the resonator of ...
[32]
Multiphoton ionization saturation intensities and generalized cross ...
Abstract. A simple method for the determination of saturation intensities and in some cases generalized cross sections in multiphoton ionization is presented.
[33]
[PDF] ionization in the field of a strong electromagnetic wave
1965. IONIZATION IN THE FIELD OF A STRONG ELECTROMAGNETIC WAVE. L. V. KELDYSH. P. N. Lebedev Physics Institute, Academy of Sciences, U.S.S.R.. Submitted to JETP ...
[34]
[PDF] Tunnel ionization of complex atoms and of atomic ions in an ...
B19 ( 1986). 'M. V. Ammosov, N. B. Delone, and V. P. Krainov, Preprint No. 83,. Inst. Gen. Phys. USSR Acad. Sci., 1986. 'L. P. Rappoport, B. A. Zon, and ...
[35]
In situ characterization of laser-induced strong field ionization ...
Apr 21, 2025 · When the laser pulse interacts with the gas jet, the gas molecules and atoms undergo ionization within the pulse's relatively short duration, ...
[36]
Theory of molecular tunneling ionization | Phys. Rev. A
We have extended the tunneling ionization model of Ammosov-Delone-Krainov (ADK) for atoms to diatomic molecules by considering the symmetry property and the ...
[37]
Polarizability, Stark shifts, and field ionization of highly charged ions ...
Mar 6, 2023 · The tunneling time under the barrier [30–32] is impacted by the polarization and Stark shift of the tunneling electron. Tunneling ionization is ...
[38]
Unveiling Under-the-Barrier Electron Dynamics in Strong Field ...
May 27, 2025 · Investigating both theoretically and experimentally the nonadiabatic tunneling in strong-field ionization across a wide range of laser intensities,
[39]
Introduction to x-ray photoelectron spectroscopy - AIP Publishing
Sep 24, 2020 · An important advantage of XPS over other techniques is the ability to determine the chemical environment of the atoms present in a sample.<|separator|>
[40]
Dissociative Photo ionization of H 20 - AIP Publishing
Relative Cross Sections. A modulated water vapor beam was crossed with a tributed predominately to the HzO+ count. Relative cross sections measured in this way ...Missing: H2O | Show results with:H2O
[41]
[PDF] Advances in threshold photoelectron spectroscopy (TPES ... - Pure
Apr 28, 2017 · Photoionization has thus been used as the preferred analytical tool for detecting the products of radical – molecule reactions in gaseous flow ...
[42]
Site-selective photoemission from delocalized valence shells ...
May 9, 2014 · This separation allows one to monitor the molecular orbital (MO) extension at different atomic sites, and hence to map the composition of MOs.
[43]
Atomic photoionization cross sections beyond the electric dipole ...
Jan 29, 2019 · Photoionization is the physical process in which atoms, molecules, or solids emit electrons upon irradiation. It constitutes the basis for ...Ii. Theory · Iii. Computational Details · B. Magnitude Of The Nd...<|control11|><|separator|>
[44]
X-ray photoelectron spectroscopy: Towards reliable binding energy ...
XPS is moreover referred to as a finger-print technique, as each element has a unique set of associated core-level peaks that allow for unambiguous ...
[45]
Ultraviolet photoelectron spectroscopy: Practical aspects and best ...
UPS measures valence band energies of surfaces using UV light, measuring ionization energies of valence shell electrons, and work function.
[46]
Practical guide for curve fitting in x-ray photoelectron spectroscopy
Oct 6, 2020 · This guide discusses the physics and chemistry involved in generating XPS spectra, describes good practices for peak fitting, and provides examples of ...
[47]
[PDF] Opacity of photoionization plasmas generated by laser-produced ...
We measured opacity of non-LTE photoionized silicon plasmas generated by a laser-produced blackbody radiator having two roles as for a radiation source and ...
[48]
Recombination and population inversion in plasmas generated by ...
Jun 2, 2006 · The principal aim of this work is to investigate the nature of the relaxation and recombination in the cascade following tunneling ionization.Missing: opacity | Show results with:opacity
[49]
Time-dependent effects in photospheric-phase Type II supernova ...
Time dependence operates through the energy gain from changes in ionization and excitation and, perhaps more universally across SN types, from the competition ...<|control11|><|separator|>
[50]
[PDF] Photoionization of Multiply Charged Ions at the Advanced Light Source
Experiments are performed using a merged-beams end station at the Advanced Light Source (ALS). An ion beam from an electron-cyclotron-resonance (ECR) ion.
[51]
The photon‐ion merged‐beams experiment PIPE at PETRA III—The ...
Apr 12, 2019 · Pioneering work using the photon-ion merged-beams technique was carried out at the Daresbury Synchrotron Radiation Source.3 Since then, the ...
[52]
Physics - Clocking Electrons During Photoionization
Sep 24, 2024 · Crucial to its success was LCLS's ability to produce isolated, attosecond pulses of adjustable energy. Also crucial was the use of a second, ...
[53]
Exploiting Photoionization Reflectron Time-of-Flight Mass ...
Dec 1, 2020 · This Account presents recent advances in our understanding on the formation pathways of complex organic molecules (COMs) within interstellar analog ices.
[54]
[2503.16339] Velocity Map Imaging Spectrometer Optimized for ...
Mar 20, 2025 · Velocity map imaging spectroscopy is a powerful technique for detecting the momentum distribution of photoelectrons resulting from an ionization ...
[55]
Electron-ion coincidence measurements of molecular dynamics with ...
Jan 12, 2021 · Molecules can sequentially absorb multiple photons when irradiated by an intense X-ray pulse from a free-electron laser.
[56]
Photoelectron-Photoion Coincidence Experiments with Synchrotron ...
The study of molecular photoionization processes was revolutionized by the development of angle-resolved photoelectron-photoion coincidence techniques in the ...
[57]
[PDF] Time-of-Flight Mass Spectrometry Technical Overview | Agilent
Dec 11, 2003 · Time-of-flight mass spectrometry (TOF MS) uses improved resolution and ion sources for analysis of small and large molecules. Mass is assigned ...
[58]
A 50-EW/cm 2 Ti:sapphire laser system for studying relativistic light ...
A 10-Hz repetition rate, 60-TW peak power, Ti:sapphire laser system was developed for use in experiments where relativistic effects dominate the physics. The ...
[59]
Absolute Photoionization Cross-Section of the Methyl Radical
The photon energy is calibrated by measurement of known atomic resonances of Xe, absorption resonances of Ar (using the gas filter as an absorption cell), and ...
[60]
Absolute high-resolution Se photoionization cross-section ...
For the present measurements the photon energy scale was calibrated on a side-branch gas cell permanently installed at beamline 10 using well-known doubly ...
[61]
Breaking through the false coincidence barrier in electron–ion ...
Oct 31, 2016 · Photoelectron Photoion Coincidence (PEPICO) spectroscopy holds the promise of a universal, isomer-selective, and sensitive analytical technique ...
[62]
Suppression of the vacuum space-charge effect in fs-photoemission ...
May 6, 2021 · Here, we present an approach to effectively suppress space-charge artifacts in momentum microscopes and photoemission microscopes. A retarding ...
[63]
Photoelectric Effect - The Physics Hypertextbook
The photoelectric effect was first observed in 1887 by Heinrich Hertz during experiments with a spark gap generator (the earliest device that could be called a ...
[64]
None
### Summary of Early Discoveries in Photoionization from Philipp E. A. von Lenard’s Nobel Lecture (1906)
[65]
James Franck, the ionization potential of helium ... - ScienceDirect.com
In 1920, James Franck and Paul Knipping measured the ionization potential of helium. · With Fritz Reiche, they found that the ground state of helium was a ...Missing: photoionization | Show results with:photoionization
[66]
Three Notes on the Quantum Theory of Aperiodic Effects | Phys. Rev.
The theory is applied to the ionization of hydrogen atoms in a constant electric field. The period of ionization in a field of 1 volt per cm is sec.Missing: photoionization cross
[67]
CIV3 — A general program to calculate configuration interaction ...
A general program to calculate configuration interaction wave functions and electric-dipole oscillator strengths. Author links open overlay panel
[68]
Spline methods for resonances in photoionisation cross sections
Spline-based methods for continuum state wavefunctions are evaluated by applying these techniques to the study of the resonance structure in the photoionisation ...
[69]
Plasma perspective on strong field multiphoton ionization
Sep 27, 1993 · During strong-field multiphoton ionization, a wave packet is formed each time the laser field passes its maximum value.
[70]
Angle-resolved RABBITT: theory and numerics - IOPscience
Jun 29, 2017 · Angle-resolved (AR) RABBITT measurements offer a high information content measurement scheme, due to the presence of multiple, interfering, ionization channels.
[71]
Control of nitromethane photoionization efficiency with shaped ...
Apr 15, 2011 · The applicability of adaptive femtosecond pulse shaping is studied for achieving selectivity in the photoionization of low-density ...
[72]
Attosecond physics | Rev. Mod. Phys.
Feb 2, 2009 · Attosecond physics is the science of electrons in motion, both collective and individual, on atomic and molecular scales and in high-density ...
[73]
Two-Photon Inner-Shell Ionization in the Extreme Ultraviolet
Jun 29, 2010 · We have observed the simultaneous inner-shell absorption of two extreme-ultraviolet photons by a Xe atom in an experiment performed at the short-wavelength ...
[74]
Machine Learning for Ionization Potentials and Photoionization ...
Apr 6, 2023 · This study employs several methods of machine learning (ML) to predict IP and σ values at 10.6 eV (117 nm) for a dataset of 1251 gaseous organic species.
[75]
High order harmonic generation-based attosecond light sources and ...
Jan 31, 2025 · The remarkable advances in both tabletop HHG-based XUV-sources as well as FELs providing ultrashort light pulses ranging from XUV to x-ray ...
[76]
Quantum Algorithm for the Direct Calculations of Vertical Ionization ...
Mar 16, 2021 · In this work, we propose a modified quantum circuit for the direct calculations of spin state energy gaps to reduce the number of qubits and quantum gates.