Internal conversion

Internal conversion is an electromagnetic decay process in atomic nuclei in which an excited nuclear state transfers its energy directly to one of the atom's orbital electrons, ejecting it rather than emitting a gamma ray.^[1]^[2] This process typically follows beta or alpha decay that leaves the daughter nucleus in an excited state, allowing the nucleus to de-excite without photon emission.^[3] The mechanism involves the interaction of the nucleus's multipole electromagnetic fields with the atomic electrons, most commonly those in inner shells such as the K-shell, resulting in the ejection of a monoenergetic electron whose kinetic energy equals the nuclear transition energy minus the electron's binding energy.^[4]^[1] For instance, in the de-excitation of the 279 keV excited state of thallium-203 following mercury-203 electron capture decay, the K-shell conversion electron has a kinetic energy of approximately 194 keV after subtracting the 85.5 keV K-binding energy.^[2] The resulting atomic vacancy is filled by electrons from higher shells, often producing characteristic X-rays or Auger electrons.^[3] Unlike beta particles, these conversion electrons originate from atomic shells and carry away the full transition energy adjusted for binding.^[1] Internal conversion competes directly with gamma decay, with the relative probability quantified by the internal conversion coefficient α, defined as the ratio of the number of conversion electrons (N_e) to the number of gamma rays (N_γ) emitted in the same transition.^[4] This coefficient varies by electron shell (e.g., α_K for K-shell) and totals α = α_K + α_L + α_M + ..., increasing for low-energy transitions, high atomic numbers (Z), or magnetic multipole types.^[4] In cases like the 35 keV transition in tellurium-125, α ≈ 13.3, meaning over 93% of de-excitations occur via internal conversion rather than gamma emission.^[2] For cesium-137's 662 keV transition, internal conversion accounts for about 9.6% of decays, carrying roughly 5% of the total decay energy.^[3] This process is crucial in nuclear spectroscopy for determining transition multipolarities, electron binding energies, and nuclear structure, as the discrete energy spectra of conversion electrons from different shells (K, L, M) can be resolved experimentally.^[1] It also influences radiation detection and dosimetry, reducing observable gamma yields in some radionuclides, and has applications in medical physics, such as in Auger electron therapy for cancer treatment using high-conversion emitters like silver-109m.^[4]

Introduction

Definition and overview

Internal conversion (IC) is an electromagnetic process in which an excited atomic nucleus transfers its excitation energy directly to an orbital electron of the surrounding atom, ejecting the electron with kinetic energy equal to the difference between the nuclear transition energy and the electron's binding energy, thereby producing a conversion electron instead of a gamma ray.^[1]^[5] This non-radiative de-excitation mode competes directly with gamma decay in the relaxation of low-lying excited nuclear states.^[1]^[6] IC plays a key role in nuclear decay schemes, particularly following processes such as beta decay, alpha decay, or other reactions that populate excited states in daughter nuclei.^[6] It becomes especially significant for low-energy transitions (below 100 keV) and in nuclei with high atomic numbers (Z > 50), where the probability of internal conversion often exceeds that of gamma emission due to stronger electromagnetic coupling between the nucleus and inner electrons.^[7]^[4] The conversion electron is typically ejected from one of the inner atomic shells, such as the K, L, or M shell, owing to their proximity to the nucleus and higher electron density at the nuclear surface.^[8]^[9] This ejection creates a vacancy in the atomic shell, ionizing the atom and leading to subsequent relaxation through characteristic X-ray emission or Auger electron cascades as the outer electrons fill the hole.^[10]^[9]

Historical background

Conversion electrons were first noted shortly after the discovery of radioactivity in 1896 by Henri Becquerel, but these discrete lines in beta-ray spectra were initially misinterpreted as secondary beta particles or other artifacts of decay.^[11] Clearer observations of these monoenergetic electron lines emerged in the early 20th century, particularly in the decay chains of thorium and radium, with systematic spectra recorded around 1910–1920 using early magnetic spectrographs.^[12] These findings puzzled researchers, as they deviated from the expected continuous beta spectrum, prompting investigations into alternative nuclear de-excitation modes. Key insights came from Lise Meitner and Otto Hahn, whose 1924 work provided the first explicit interpretation of monoenergetic electrons in radioactive decay as arising from internal conversion of nuclear gamma energy directly to an orbital electron, distinguishing the process from true beta decay.^[11] Building on this, Meitner's collaboration with Charles D. Ellis during 1922–1924, involving exchanges on beta and gamma spectra from the Cavendish Laboratory and Berlin, facilitated systematic studies of these lines in radium B and C decays; Ellis's work in the 1920s helped establish "conversion electrons" as standard nomenclature for these emissions.^[11] By the 1930s, internal conversion was integrated into emerging quantum mechanical models of nuclear transitions, with theoretical treatments aligning it with electromagnetic interactions.^[13] Quantitative measurements advanced in the same decade through refined magnetic spectrometers, enabling precise energy determinations and intensity ratios in various isotopes. Post-World War II improvements in detector technology, such as scintillation counters, further solidified internal conversion's role in nuclear spectroscopy by enhancing resolution and efficiency for studying excited nuclear states.^[13]

Physical Mechanism

Process description

In internal conversion, an excited atomic nucleus undergoes a transition to a lower energy state by interacting electromagnetically with one of its orbital electrons, rather than emitting a gamma ray. The process begins with the nucleus in an excited state, characterized by a multipole field—either electric or magnetic—that couples directly to the electromagnetic field of a nearby orbital electron. This interaction is mediated by the exchange of a virtual photon, which transfers the nuclear excitation energy to the electron without the emission of a real photon.^[14]^[5] The energy transfer ejects the electron from its orbit, imparting it with kinetic energy given by E_k = E - B_e, where E is the energy difference between the initial and final nuclear states, and B_e is the binding energy of the electron in its shell. This ejection occurs primarily from the K-shell due to the electron's proximity to the nucleus, which maximizes the overlap of their wave functions and thus the interaction probability; for transitions with higher energies or those forbidden for K-shell conversion, electrons from the L- or M-shells may be involved instead.^[5]^[15]^[16] Following ejection, the atom is left with a vacancy in its electron shell, resulting in an ionized state that relaxes through subsequent atomic processes: an electron from a higher shell fills the vacancy, releasing energy either as characteristic X-ray fluorescence or, more commonly for inner shells, as Auger electrons. The nucleus, having de-excited without radiating a gamma ray, reaches its ground state, completing the internal conversion process. This mechanism competes with gamma decay, where the nuclear energy is instead carried away by an electromagnetic photon.^[3]^[5]^[16] Conceptually, the process can be visualized as a virtual photon bridging the nuclear transition and the electron's orbit, facilitating direct energy handover while the electron departs with discrete kinetic energy characteristic of the transition.^[14]

Theoretical framework

Internal conversion is fundamentally a quantum mechanical process in which an excited nucleus undergoes a non-radiative transition by coupling its electromagnetic multipole field to the wavefunction of an orbital electron, ejecting the electron in the process. This interaction is described within the semiclassical approximation, where the nuclear transition is treated as generating a time-varying electromagnetic field that interacts with the atomic electrons, leading to their excitation without the emission of a photon. The theoretical foundation emphasizes the electromagnetic nature of the coupling, distinguishing internal conversion from other decay modes like direct electron capture.^[17] The transition rate for internal conversion, \lambda_{IC}, is proportional to the square of the matrix element of the electromagnetic interaction Hamiltonian, \lambda_{IC} \propto |\langle f | \hat{H}_{EM} | i \rangle|^2, where \hat{H}_{EM} represents the Hamiltonian describing the interaction between the nuclear transition current and the electron's vector potential, and |i\rangle and |f\rangle denote the initial and final states of the combined nucleus-electron system. This matrix element encapsulates the overlap between the nuclear multipole operator and the electron's radial and angular wavefunctions. The process is classified by the multipolarity of the transition: electric $2^L-pole (EL) or magnetic L-pole (ML), with higher multipolarities L favoring internal conversion due to the slower variation of the nuclear field, which allows greater overlap with the electron wavefunction and thus a longer effective interaction time.^[17] Relativistic effects play a crucial role in the accurate description of internal conversion, particularly for inner-shell electrons in high-Z nuclei, where the electron velocities approach fractions of the speed of light. In such cases, the Dirac equation is employed to obtain the electron wavefunctions, accounting for spin-orbit coupling and finite nuclear size corrections, which enhance the conversion probabilities compared to non-relativistic treatments. For low-Z atoms, non-relativistic Schrödinger wavefunctions provide sufficient accuracy, simplifying the calculations while still capturing the essential multipole interactions. These relativistic formulations were pivotal in early theoretical developments, enabling precise predictions for K-shell conversions.^[18]^[19]

Conversion Coefficients

Definition and types

In nuclear physics, the internal conversion coefficient, denoted as \alpha, quantifies the probability of internal conversion relative to gamma emission for a given nuclear transition. It is defined as the ratio of the number of conversion electrons emitted (N_{IC}) to the number of gamma photons emitted (N_\gamma) from the same excited state, \alpha = N_{IC} / N_\gamma. The total conversion coefficient, \alpha_{tot}, is the sum of the partial coefficients over all atomic shells involved, \alpha_{tot} = \sum \alpha_i, where each \alpha_i corresponds to electrons ejected from a specific shell.^[20]^[21] Conversion coefficients are classified by the atomic shell from which the electron is ejected. The K-conversion coefficient \alpha_K applies to electrons from the K-shell (n=1), while \alpha_L covers the L-shell (n=2), subdivided into subshells as \alpha_L = \alpha_{L1} + \alpha_{L2} + \alpha_{L3}, corresponding to the 2s_{1/2}, 2p_{1/2}, and 2p_{3/2} orbitals, respectively. Similarly, the M-conversion coefficient \alpha_M accounts for the M-shell (n=3), often broken down into subshells like \alpha_{M1} through \alpha_{M5} for more precise analysis in higher-Z nuclei. These shell-specific coefficients reflect the varying probabilities due to differences in electron wavefunction overlap with the nuclear field.^[21]^[22] Coefficients are further categorized by the type of nuclear transition, distinguishing between electric multipole (EL) and magnetic multipole (ML) transitions, where L denotes the multipole order (e.g., E1 for electric dipole, M1 for magnetic dipole). For pure transitions, \alpha is computed specifically for the dominant multipolarity. In cases of mixed multipolarities, such as E2/M1 or M1/E2, the effective coefficient is a weighted combination based on the mixing ratio \delta, which parameterizes the relative admixture of the two multipoles.^[23]^[24] These coefficients are typically measured indirectly, as direct detection of low-energy electrons can be challenging. One common method uses high-resolution electron spectroscopy to identify and quantify conversion electrons from specific shells, often with magnetic or electrostatic spectrometers. Alternatively, they are inferred from intensity ratios of gamma rays to characteristic X-rays or Auger electrons, which arise from the atomic relaxation following inner-shell ionization by internal conversion.^[25]^[21]

Factors influencing coefficients

The internal conversion coefficients are strongly influenced by the atomic number Z of the emitting nucleus, primarily due to the scaling of the electron density at the nuclear surface. For K-shell conversion, the coefficient \alpha_K increases approximately as Z^4 to Z^5, reflecting the tighter binding and higher probability density of s-electrons near the nucleus in heavier elements. This dependence arises from the Coulomb interaction in the atomic potential, which enhances the overlap between the nuclear transition field and the electron wavefunction. For high-Z nuclei (Z > 70), relativistic effects, such as Dirac-Fock corrections to the electron orbitals, become essential, altering the coefficients by up to several percent compared to non-relativistic approximations.^[26]^[27] The transition energy E_\gamma exerts a pronounced inverse effect on the coefficients, with \alpha decreasing rapidly as E_\gamma increases. For electric L-pole (EL) transitions, this follows the approximate scaling \alpha \propto 1/E_\gamma^{2L+1}, stemming from the momentum transfer in the electron-nucleus interaction; lower energies favor conversion over gamma emission because the virtual photon wavelength matches the atomic scale better. Internal conversion dominates for E_\gamma < 150 keV, especially in heavy nuclei, where \alpha can exceed unity, making electron emission the primary decay mode.^[28]^[29] Multipolarity L and transition type (electric vs. magnetic) also modulate the coefficients significantly. Higher L values yield larger \alpha, as the multipole field penetrates more effectively into the atomic region; notably, pure electric monopole (E0) transitions proceed exclusively via internal conversion or pair production, with no gamma ray emitted due to angular momentum conservation forbidding photon decay. For the same L, electric transitions exhibit higher \alpha than magnetic ones, because the electric field couples more strongly to the electron charge distribution than the magnetic field does to the current.^[23]^[29] A widely used semi-empirical approximation for K-shell electric transitions is \alpha_K(\mathrm{EL}) \approx C_L \left( Z^{2L+1} / E_\gamma^{2L+1} \right), where C_L is a multipolarity-dependent constant derived from the radial integral of the electron wavefunction. More precise values are obtained from tabulated calculations, such as those employing the Rose (point-nucleus, no-penetration) or Sliv-Rose (finite-nuclear-size, surface-current) approximations, which account for relativistic kinematics and screening effects across ranges of Z, E_\gamma, and L.^[30]^[31]

Occurrence and Probability

Conditions favoring internal conversion

Internal conversion becomes the dominant de-excitation process over gamma emission when the nuclear transition energy E_\gamma is low, typically below 50-100 keV. At these energies, the phase space for photon emission is reduced, making gamma decay less probable, while the electromagnetic interaction with atomic electrons is more efficient due to the longer wavelength of the virtual photon involved. This preference is particularly evident in transitions around 35 keV, where conversion coefficients can exceed 10, indicating over 90% conversion probability.^[2]^[15] High multipolarity of the transition further favors internal conversion, especially for forbidden transitions involving large angular momentum changes (\Delta L > 1) or parity changes, as these suppress gamma decay rates while enhancing electron coupling through higher-order multipole fields. Electric monopole (E0) transitions exemplify this extreme, where no angular momentum transfer occurs (\Delta J = 0) and parity is conserved, prohibiting gamma emission entirely; such transitions proceed solely via internal conversion, achieving 100% conversion efficiency.^[15]^[32]^[33] In heavy nuclei with high atomic number Z, internal conversion is strongly preferred due to the intensified Coulomb field, which boosts electron-nucleus overlap and interaction strength, particularly for K-shell electrons. This trend is pronounced in elements like mercury (Hg), lead (Pb), and uranium (U), where conversion coefficients increase systematically with Z. The selection rules for internal conversion mirror those of gamma decay—conservation of angular momentum and parity—but uniquely permit pure \Delta J = 0, no-parity-change scenarios in E0 transitions that are inaccessible to photons.^[2]^[15] Although primarily a nuclear process, internal conversion involving outer-shell electrons (L, M, etc.) can exhibit slight sensitivity to environmental conditions, such as the chemical state or solid matrix, which alter electron binding energies and densities. For low-energy transitions, these effects manifest as small half-life variations, on the order of a few percent, between different compounds, enabling probes of atomic surroundings. The overall dominance of internal conversion in these scenarios is quantified by the conversion coefficient \alpha, which rises under the above conditions.^[34]^[15]

Comparison to gamma emission

Internal conversion and gamma emission represent competing pathways for the de-excitation of excited nuclear states, where the total decay rate is given by \lambda_{\text{total}} = \lambda_\gamma + \lambda_{\text{IC}}, with \lambda_\gamma and \lambda_{\text{IC}} denoting the rates for gamma emission and internal conversion, respectively.^[6] The internal conversion coefficient \alpha = \lambda_{\text{IC}} / \lambda_\gamma quantifies this competition, and the branching ratio for internal conversion is \alpha / (1 + \alpha).^[15] Internal conversion dominates when \alpha > 1, which occurs more frequently for low transition energies or high multipolarities.^[6] In terms of detection, gamma rays from electromagnetic transitions penetrate matter easily, allowing straightforward spectroscopy with detectors like scintillators or semiconductors, but they suffer from Compton scattering that can broaden energy peaks.^[35] Conversion electrons, in contrast, have shorter ranges in matter due to their charge and mass, enabling higher energy resolution through magnetic spectrometers in vacuum environments, though this requires more specialized equipment.^[36] Both processes conserve the transition energy E_\gamma, but in gamma emission, the nucleus experiences a small recoil kinetic energy of approximately E_\gamma^2 / (2Mc^2), whereas in internal conversion, the recoil is transferred primarily to the ejected electron and the residual atom, minimizing nuclear recoil.^[6] The presence of internal conversion reduces the observable intensity of gamma rays, as the branching ratio lowers the effective \lambda_\gamma, complicating intensity measurements in decay schemes.^[15] This competition is particularly useful for identifying forbidden transitions, where high \alpha values suppress gamma emission relative to internal conversion, aiding in the determination of transition multipolarities.^[37]

Aspect	Gamma Emission Advantages/Disadvantages	Internal Conversion Advantages/Disadvantages
Applicability to Transitions	Standard for high-energy electric/magnetic multipoles (E1, M1); forbidden for pure E0 (monopole) transitions due to no dipole radiation.^[35]	Essential for E0 transitions, enabling de-excitation where gamma emission is prohibited; less efficient for high E_\gamma.^[3]
Detection and Analysis	High penetration facilitates remote detection; but poorer energy resolution from scattering.^[35]	Precise electron energies reveal shell binding; shorter range aids resolution but demands vacuum setups.^[36]
Nuclear Insights	Provides transition probabilities via intensity; recoil affects Doppler broadening minimally.^[6]	Reveals multipolarity through \alpha; reduces gamma yield, requiring correction for true rates.^[15]

Examples

Decay of 203Hg

The isotope ^{203}Hg undergoes \beta^- decay with a half-life of 46.61 days, with nearly 100% of decays populating the 279.196 keV first excited state ($3/2^+) in ^{203}Tl, which subsequently de-excites to the $1/2^+ ground state via a mixed magnetic dipole (M1) plus electric quadrupole (E2) transition.^[38] This transition exemplifies internal conversion, where the excitation energy is transferred electromagnetically to an atomic electron rather than emitted as a \gamma-ray.^[2] The total internal conversion coefficient for the 279 keV transition is \alpha_\text{tot} = 0.2250 \pm 0.0012, indicating that for every \gamma-ray emitted, approximately 0.225 conversion electrons are produced across all shells.^[39] The K-shell conversion dominates with \alpha_K \approx 0.163 \pm 0.003, accounting for about 72% of the total, while L- and M-shell conversions contribute the remainder (\alpha_L \approx 0.049, \alpha_M \approx 0.013), reflecting the high atomic number (Z=81) of thallium, which favors inner-shell interactions.^[40] Conversion electrons from the K-shell are ejected with kinetic energy E_k \approx 279 - 85.5 = 193.7 keV, where 85.5 keV is the K-shell binding energy in ^{203}Tl; L- and M-shell electrons appear at slightly higher energies due to lower binding energies (10-20 keV for L, <3 keV for M).^[38] This decay was first studied experimentally in the 1950s using magnetic spectrometers, which revealed a discrete electron spectrum with prominent K, L, and M conversion lines alongside the \gamma-ray continuum, confirming the mixed M1+E2 multipolarity through conversion ratios (e.g., K/L \approx 3.4).^[40] Early measurements, such as those by Wapstra and collaborators, established the relative intensities and served as benchmarks for later refinements using coincidence techniques.^[41] As a classic case in an odd-mass (A=203) nucleus, the ^{203}Hg decay highlights internal conversion's role in low-energy, mixed-parity transitions where multipole mixing enhances conversion probabilities.^[42] Its well-characterized electron lines have made it a standard source for calibrating high-resolution electron spectrometers in nuclear spectroscopy.^[39]

Other nuclear examples

Internal conversion manifests in a variety of nuclear transitions, highlighting its dependence on transition energy, multipolarity, and atomic number. A prominent low-energy E0 example occurs in ^{235m}U at 0.077 keV, where the total internal conversion coefficient exceeds 1000, resulting in a pure monopole process with no observable gamma emission due to the overwhelming dominance of conversion over radiation.^[43] In high-Z heavy nuclei like ^{191}Ir, the 42 keV E3 transition displays a K-shell conversion coefficient α_K ≈ 10, underscoring its prevalence in the osmium region where relativistic effects and strong Coulomb fields favor conversion.^[44] Forbidden transitions also exhibit significant internal conversion, as seen in the 14.4 keV M1 transition of ^{57}Fe used in Mössbauer spectroscopy, with α_tot ≈ 9 and conversion primarily from the L-shell because the low energy limits K-shell participation.^[45] An exotic instance is the 35 keV E3 transition in ^{125}Te following ^{125}I decay, featuring high internal conversion branching that approaches 93% of the total decay rate.^[46] The following table summarizes trends across selected nuclei, illustrating how lower energies and higher multipolarities, combined with elevated Z, elevate α_tot:

Nucleus	E_γ (keV)	Multipolarity	α_tot
^{235m}U	0.077	E0	>1000
^{191}Ir	42	E3	≈14
^{57}Fe	14.4	M1	≈9
^{125}Te	35	E3	≈13

High atomic numbers enhance internal conversion, as the increased nuclear charge strengthens electron-nucleus interactions.

Internal pair production

Internal pair production is a radiative de-excitation process in which an excited atomic nucleus directly creates an electron-positron pair, rather than emitting a gamma photon, provided the available transition energy exceeds the threshold of 1.022 MeV (twice the electron rest mass energy).^[47] This process competes with both gamma emission and internal conversion, becoming a minor but measurable decay mode for high-energy nuclear transitions.^[47] The mechanism involves the nuclear electromagnetic multipole field coupling to the pair creation operator, where the nucleus emits a virtual photon that interacts with the nuclear Coulomb field to produce the e⁺e⁻ pair in the continuum.^[48] This is analogous to the multipole expansion used in gamma decay and internal conversion but replaces the photon emission or electron ejection with the pair production operator.^[49] The resulting pairs carry most of the transition energy, shared between the electron and positron, with the nucleus absorbing minimal recoil.^[48] The probability of internal pair production is quantified by the conversion coefficient κ, defined as the ratio of the number of pairs produced to the number of gamma rays that would otherwise be emitted (κ = N_pair / N_γ).^[50] This coefficient is typically small, on the order of 10⁻⁵ to 10⁻³, and increases with transition energy, becoming more significant above approximately 2 MeV due to the rising pair production cross section.^[47] Theoretical calculations of κ account for multipolarity (electric or magnetic) and nuclear charge Z, often using relativistic approximations for accurate predictions.^[50] Unlike internal conversion, which has a low-energy threshold set by atomic binding energies (tens to hundreds of keV) and strong dependence on electron shell structure, internal pair production requires the higher 1.022 MeV threshold and shows no such shell selectivity since the pairs are created as free particles.^[47] Additionally, its probability scales roughly with Z², similar to external pair production cross sections, making it more favorable in high-Z nuclei due to enhanced Coulomb screening effects that facilitate the virtual photon interaction. Internal pair production is rare for transitions below 3 MeV, where gamma emission dominates, but it has been observed in specific high-energy cases. A notable example is the 6.05 MeV 0⁺ excited state in ¹⁶O, which undergoes an electric monopole (E0) transition with a small pair production branching ratio, contributing to the e⁺e⁻ continuum spectrum alongside double gamma emission.^[51] In this light nucleus (Z=8), the measured pair yield provides a calibration standard for detecting such processes in nuclear reactions.^[51]

Auger effect

The Auger effect is a non-radiative atomic de-excitation process that follows the creation of an inner-shell vacancy, such as that produced by internal conversion in nuclear decay. In this process, an electron from an outer shell fills the vacancy, releasing energy that ejects a second electron from the same or another outer shell; this ejected electron, called the Auger electron, carries kinetic energy equal to the difference between the transition energy and the binding energy of the ejected electron.^[52] Unlike radiative de-excitation via X-ray emission, the Auger effect results in no photon production, instead producing low-energy electrons typically in the range of 20–500 eV.^[52] A prototypical example is the KLL Auger transition, where a vacancy in the K-shell is filled by an L-shell electron, and the released energy ejects another L-shell electron, leaving the atom with multiple vacancies that may trigger further cascades.^[53] The probability of the Auger process competing with fluorescence (X-ray emission) depends strongly on the atomic number Z: for light elements (Z < 30), the Auger yield dominates due to lower electron binding energies and higher overlap of wavefunctions, with fluorescence yields approaching zero, whereas for heavier elements (Z > 30), fluorescence becomes predominant as the radiative transition rate increases.^[54] This Z-dependence arises from the scaling of transition probabilities, where Auger rates follow a Z^4 dependence similar to photoelectric absorption, but fluorescence yields rise more rapidly with Z.^[55] In the context of internal conversion, the Auger effect occurs as the primary atomic relaxation mechanism following the ejection of an inner-shell electron by the nuclear transition, with the process taking place in effectively 100% of cases where an inner-shell vacancy is created, though the specific Auger branching ratio varies from near 100% for low-Z atoms to as low as 10% or less for high-Z atoms in K-shell events.^[52] The overall de-excitation cascade after internal conversion thus includes a combination of characteristic X-rays, Auger electrons, and secondary effects like shake-off ionization, where additional electrons are ejected due to the sudden atomic perturbation.^[2] This atomic process is distinct from the nuclear internal conversion, focusing solely on the relaxation of the ionized atom rather than energy transfer within the nucleus. Historically, the effect was first described by Lise Meitner in 1923 in the context of beta decay observations and independently observed by Pierre Auger in 1925 using X-rays, leading to its recognition as the Auger-Meitner effect.

Applications

Nuclear structure determination

Internal conversion plays a pivotal role in determining the multipolarity of nuclear transitions by providing detailed information on the electromagnetic character of de-excitations. The ratios of internal conversion coefficients for different atomic shells, particularly α_K/α_L and α_K/α_M, are highly sensitive to whether a transition is electric (EL) or magnetic (ML) in nature. For instance, in mid-mass nuclei with transition energies around 100-500 keV, M1 transitions typically exhibit α_K/α_L ratios greater than 10, reflecting stronger K-shell coupling due to the magnetic field's penetration, whereas E2 transitions show ratios less than 5, indicative of more uniform electric quadrupole interactions across shells. These ratios allow unambiguous assignment of multipolarities when compared to theoretical tables computed using relativistic approximations.^[56] Mixing ratios, denoted as δ², quantify the admixture of competing multipolarities (e.g., M1 + E2) in a single transition and are extracted by fitting experimental internal conversion coefficients against theoretical values for pure multipoles. This is often combined with γ-γ angular correlation data to resolve ambiguities, as the conversion process weights the matrix elements differently from photon emission. Such analyses probe relative transition strengths, revealing details about nuclear wave function overlaps and deformation. For example, in deformed nuclei, deviations in observed δ² from single-particle predictions indicate collective enhancements.^[21] Internal conversion data also test the validity of nuclear structure models by confronting predictions with observed coefficients, particularly in distinguishing collective rotational behavior from single-particle excitations. In even-even nuclei, high conversion rates for low-energy E2 transitions support the rotational model, where collective motion enhances quadrupole strengths. Conversely, in proton-odd nuclei, penetration effects—arising from the finite nuclear size and the odd proton's influence on the electromagnetic field inside the nucleus—alter M1 conversion coefficients beyond point-nucleus approximations. These effects enable extraction of effective spin g-factors (g_s^{eff}) and radial integrals, validating shell-model calculations with configuration mixing.^[57]^[58] Experimentally, multipolarity and mixing ratios are determined through high-resolution conversion electron spectroscopy, employing Si(Li) detectors to measure electron intensities from specific shells relative to coincident γ-rays, achieving resolutions sufficient to resolve K, L, and M lines even for low-energy transitions. Lifetime measurements, essential for absolute transition probabilities, utilize the Doppler-shift attenuation method (DSAM) applied to conversion electrons emitted from fast-recoiling ions, where the shift and attenuation in electron lines yield picosecond-scale lifetimes when analyzed with Monte Carlo simulations of stopping powers.^[59]^[60]

Spectroscopic and clock technologies

Internal conversion plays a pivotal role in Mössbauer spectroscopy, particularly with the 57Fe nucleus, where the 14.4 keV transition exhibits a high total internal conversion coefficient of approximately 9.7, facilitating the detection of conversion electrons in techniques like conversion electron Mössbauer spectroscopy (CEMS).^[61] This process enables recoilless emission and absorption of gamma rays when the nucleus is bound in a solid lattice, minimizing recoil energy loss and allowing hyperfine interactions to be resolved at nuclear timescales.^[62] Applications extend to materials science, where CEMS probes surface and near-surface properties of thin films and catalysts, and to magnetism, revealing spin alignments and hyperfine fields in ferromagnetic materials like iron alloys.^[63]^[64] In electron spectroscopy, internal conversion electrons provide high-resolution signatures for determining nuclear level schemes, as their kinetic energies directly reflect transition energies minus binding energies, with resolutions down to a few eV in modern spectrometers.^[65] This technique, known as conversion electron spectroscopy, is particularly useful for studying low-energy nuclear transitions in solids, where chemical shifts arise from variations in electron density at the nucleus due to the local chemical environment.^[34] For instance, in solid-state samples, these shifts—on the order of 10-100 eV—enable differentiation of oxidation states or coordination geometries without the need for gamma detection, enhancing sensitivity to surface phenomena.^[25] Nuclear clocks leverage low-energy internal conversion transitions, such as the ~8 eV isomeric state in 229Th, to achieve ultra-precise timekeeping by exploiting the nucleus's insensitivity to external perturbations compared to atomic electrons.^[66] In isolated ions, the isomer decays predominantly via internal conversion with a coefficient α_IC >> 1, but embedding 229Th in solid-state hosts like CaF2 or YSO crystals can enhance or suppress IC rates by tuning the electronic band structure, potentially shortening lifetimes from hours to milliseconds for practical clock operation.^[67] This solid-state approach allows laser excitation of the isomer and readout via fluorescence or electron emission, promising frequency stabilities exceeding 10^{-19}, far surpassing current optical clocks.^[68] In medical applications, particularly radiotherapy, 125I brachytherapy employs internal conversion electrons from its electron capture decay to deliver targeted radiation doses, with the isotope's low-energy emissions (averaging ~28 keV photons and conversion/Auger electrons) confining damage to millimeter scales around implanted seeds.^[69] The decay chain produces approximately 13-15 conversion electrons and over 20 Auger electrons per disintegration, primarily from K- and L-shell processes, which are highly cytotoxic when localized near DNA, enhancing efficacy in prostate and ocular cancers.^[70] Auger electrons from these internal conversion events contribute to clustered DNA damage, amplifying therapeutic impact while minimizing off-target effects compared to beta emitters.^[71] Recent advances since 2020 have focused on vacuum ultraviolet (VUV) lasers to probe internal conversion in 229Th for nuclear clock development, including the demonstration of continuous-wave VUV sources at 149 nm with linewidths below 1 MHz, enabling direct excitation of the isomer in solid-state matrices.^[72] These lasers facilitate spectroscopy of the IC-dominated decay, with experiments in 2024 achieving isomer lifetimes under 30 minutes in doped crystals via laser quenching, paving the way for integrated clock systems.^[73] In July 2025, the first continuous-wave VUV laser at 148.4 nm was demonstrated using four-wave mixing in cadmium vapor, advancing precision spectroscopy of the isomer.^[72] Such progress, including VUV frequency combs for precise calibration and October 2025 measurements of the transition's sensitivity to the fine-structure constant, underscores the potential for nuclear clocks to test fundamental physics, like varying constants, with sensitivities orders of magnitude beyond atomic standards.^[74]^[75]