Theory of Light Hydrogenlike Atoms

Abstract

The present status and recent developments in the theory of light hydrogenic atoms, electronic and muonic, are extensively reviewed. The discussion is based on the quantum field theoretical approach to loosely bound composite systems. The basics of the quantum field theoretical approach, which provide the framework needed for a systematic derivation of all higher order corrections to the energy levels, are briefly discussed. The main physical ideas behind the derivation of all binding, recoil, radiative, radiative-recoil, and nonelectromagnetic spin-dependent and spin-independent corrections to energy levels of hydrogenic atoms are discussed and, wherever possible, the fundamental elements of the derivations of these corrections are provided. The emphasis is on new theoretical results which were not available in earlier reviews. An up-to-date set of all theoretical contributions to the energy levels is contained in the paper. The status of modern theory is tested by comparing the theoretical results for the energy levels with the most precise experimental results for the Lamb shifts and gross structure intervals in hydrogen, deuterium, and helium ion $H{e}^{+}$, and with the experimental data on the hyperfine splitting in muonium, hydrogen and deuterium.

230 pages, 106 figures, 24 tables. Discussion of muonic hydrogen is added, list of references expanded, some minor corrections and amendments

References in corpus (8)

• Calculation of the Electron Self Energy for Low Nuclear Charge
• Measurement of the 1s-2s energy interval in muonium
• Coulomb Corrections to Elastic Electron-Proton Scattering and the Proton Charge Radius
• Higher-order binding corrections to the Lamb shift of 2P states
• The three loop slope of the Dirac form factor and the 1S Lamb shift in hydrogen
• Loop-after-loop contribution to the second-order Lamb shift in hydrogenlike low-Z atoms
• Logarithms of alpha in QED bound states from the renormalization group
• Lamb Shift of 3P and 4P states and the determination of $\alpha$

Cited by in corpus (291)

• CODATA Recommended Values of the Fundamental Physical Constants: 2010
• Search for New Physics with Atoms and Molecules
• CODATA Recommended Values of the Fundamental Physical Constants: 2014
• QCD and strongly coupled gauge theories: challenges and perspectives
• Precision physics of simple atoms: QED tests, nuclear structure and fundamental constants
• Muonic hydrogen and the proton radius puzzle
• Highly charged ions: optical clocks and applications in fundamental physics
• The Proton Radius Puzzle
• Searching for the light dark gauge boson in GeV-scale experiments
• Hydrogen-atom spectrum under a minimal-length hypothesis
• Quirky Composite Dark Matter
• Theory of the 2S-2P Lamb shift and 2S hyperfine splitting in muonic hydrogen
• Two-Photon Physics in Hadronic Processes
• Ultra-precise measurement of optical frequency ratios
• Precision Study of Positronium: Testing Bound State QED Theory
• The proton charge radius
• The RMS Charge Radius of the Proton and Zemach Moments
• Theoretical Constraints and Systematic Effects in the Determination of the Proton Form Factors
• Defining the Proton Radius: a Unified Treatment
• Higher order proton structure corrections to the Lamb shift in muonic hydrogen
• Lamb Shift in Light Muonic Atoms - Revisited
• ${\alpha }^4$ Ry corrections to singlet states of helium
• Nonrelativistic QED approach to the Lamb shift
• Relativistic, QED, and finite nuclear mass corrections for low-lying states of Li and Be${}^{+}$
• Spectroscopy as a test of Coulomb's law - A probe of the hidden sector
• QED tests with highly-charged ions
• Relativistic corrections of mα^6 order to the ro-vibrational spectrum of H_2^+ and HD^+ molecular ions
• Nucleon Polarizabilities: from Compton Scattering to Hydrogen Atom
• Two-Loop Bethe Logarithms
• Higher-order effective Hamiltonian for light atomic systems
• Proton radii and two-photon exchange
• Model independent analysis of proton structure for hydrogenic bound states
• Atomic Precision Tests and Light Scalar Couplings
• Validity of the Weizsäcker-Williams Approximation and the Analysis of Beam Dump Experiments: Production of an axion, a dark photon, or a new axial-vector boson
• Uncertainty Estimates for Theoretical Atomic and Molecular Data
• Rovibrational energy levels of the hydrogen molecule through nonadiabatic perturbation theory
• Nonadiabatic QED correction to the dissociation energy of the hydrogen molecule
• Theory of the Lamb shift in hydrogen and light hydrogen-like ions
• Nucleon Axial Radius and Muonic Hydrogen - A New Analysis and Review
• 2S Hyperfine splitting of muonic hydrogen
• Lamb Shift in Muonic Hydrogen
• Radiative corrections and parity nonconservation in heavy atoms
• QED effects in molecules: test on rotational quantum states of H${}_2$
• Proton Zemach radius from measurements of the hyperfine splitting of hydrogen and muonic hydrogen
• Zemach Moments for Hydrogen and Deuterium
• Noncommutative Point Sources
• New Physics and the Proton Radius Problem
• Corrections to the ns-levels of hydrogen atom in deformed space with minimal length
• Complete ${\alpha }^{6}m$ corrections to the ground state of H${}_2$
• Theory of the n=2 levels in muonic deuterium
• Isotope Shift Measurements of Stable and Short-Lived Lithium Isotopes for Nuclear Charge Radii Determination
• Electrophobic Scalar Boson and Muonic Puzzles
• Quantum field theory on toroidal topology: algebraic structure and applications
• Observation of Long-Lived Muonic Hydrogen in the 2S State
• Testing quantum electrodynamics in the lowest singlet states of beryllium atom
• The proton structure in and out of muonic hydrogen
• The Validity of the Weizsacker-Williams Approximation and the Analysis of Beam Dump Experiments: Production of a New Scalar Boson
• Spectroscopy of atomic hydrogen. How is the Rydberg constant determined?
• Hadronic contributions to the anomalous magnetic moment of the electron and the hyperfine splitting of muonium
• Fundamental constants and tests of theory in Rydberg states of hydrogen-like ions
• Non-perturbative evaluation of some QED contributions to the muonic hydrogen $\mathbf{n}=2$ Lamb shift and hyperfine structure
• Hyperfine structure in hydrogen and helium ion
• Nonadiabatic relativistic correction in H${}_2$, D${}_2$, and HD
• Helium energy levels including $m{\alpha }^6$ corrections
• Asymmetry of the natural line profile for the hydrogen atom
• Comprehensive theory of the Lamb shift in light muonic atoms
• $\mu -H$ Lamb shift: dispersing the nucleon-excitation uncertainty with a finite energy sum rule
• Proton polarizability effect in the Lamb shift of the hydrogen atom
• New precise spectroscopy of the hyperfine structure in muonium with a high-intensity pulsed muon beam
• Proton polarizability contribution to the hyperfine splitting in muonic hydrogen
• Current and future perspectives of positronium and muonium spectroscopy as dark sectors probe
• On the Minimal Length Uncertainty Relation and the Foundations of String Theory
• Constraints on a long-range spin-independent interaction from precision atomic physics
• Precise calculation of transition frequencies of hydrogen and deuterium based on a least-squares analysis
• Fundamental Physical Constants: Looking from Different Angles
• Higher-order recoil corrections for triplet states of the helium atom
• Natural Resolution of the Proton Size Puzzle
• New Measurement of the 2S Hyperfine Interval in Atomic Hydrogen
• Sympathetic cooling of ${}^4$He${}^{+}$ ions in a radiofrequency trap
• Precise determination of proton magnetic radius from electron scattering data
• Two-photon exchange correction to the Lamb shift and hyperfine splitting of S levels
• Reanalysis of the BFKL Pomeron at the next-to-leading logarithmic accuracy
• Muonic hydrogen ground state hyperfine splitting
• In-beam measurement of the hydrogen hyperfine splitting - towards antihydrogen spectroscopy
• Ab initio calculation of nuclear structure corrections in muonic atoms
• Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field
• Muonic Hydrogen and the Third Zemach Moment
• Non-relativistic contributions in order ${\alpha }^5{m}_{\mu }{c}^2$ to the Lamb shift in muonic hydrogen, deuterium and helium ion
• Ab initio potential energy curve for the ground state of beryllium dimer
• Ground state hyperfine splitting in ^6,7Li atoms and the nuclear structure
• Higher-order recoil corrections for singlet states of the helium atom
• The proton radius (puzzle?) and its relatives
• Dissociation Energy of Molecular Hydrogen Isotopologues
• Muonium hyperfine structure and hadronic effects
• Mode-sum construction of the covariant graviton two-point function in the Poincaré patch of de Sitter space
• Hyperfine Structure of the Ground and First Excited States in Light Hydrogen-Like Atoms and High-Precision Tests of QED
• Higher order corrections to the hydrogen spectrum from the Standard-Model Extension
• Contribution of Light-by-Light Scattering to Energy Levels of Light Muonic Atoms
• Calculation of radiative corrections to the effect of parity nonconservation in heavy atoms
• Hyperfine Splitting in Muonium: Accuracy of the Theoretical Prediction
• Nuclear Corrections to Hyperfine Structure in Light Hydrogenic Atoms
• Lamb shift in muonic deuterium atom
• Two-photon exchange correction to $2S$-$2P$ splitting in muonic helium-3 ions
• Two-photon exchange correction to the hyperfine splitting in muonic hydrogen
• Lamb shift in muonic helium ion
• Hyperfine structure of S-states in muonic deuterium
• The ${\alpha }^2(Z\alpha {)}^{4}m$ contributions to the Lamb shift and the fine structure in light muonic atoms
• Proton charge and magnetic rms radii from the elastic $ep$ scattering data
• Aspects of open-flavour mesons in a comprehensive DSBSE study
• Radiative-Recoil Corrections of Order $\alpha (Z\alpha {)}^5(m/M)m$ to Lamb Shift Revisited
• Radiative nonrecoil nuclear finite size corrections of order $\alpha (Z\alpha {)}^5$ to the hyperfine splitting of S-states in muonic hydrogen
• Hyperfine Structure of S-States in Muonic Helium Ion
• 2S hyperfine structure of atomic deuterium
• Two-Loop Polarization Contributions to Radiative-Recoil Corrections to Hyperfine Splitting in Muonium
• Model-independent determination of the two-photon exchange contribution to hyperfine splitting in muonic hydrogen
• Lamb shift in muonic ions of lithium, beryllium and boron
• Calculation of two-centre two-electron integrals over Slater-type orbitals revisited. III. Case study of the beryllium dimer
• Dynamic electron-phonon and spin-phonon interactions due to inertia
• Theory of muonic hydrogen - muonic deuterium isotope shift
• Nuclear structure corrections in the energy spectra of electronic and muonic deuterium
• Relativistic calculations of pionic and kaonic atoms hyperfine structure
• Forward two-photon exchange in elastic lepton-proton scattering and hyperfine-splitting correction
• Non-Perturbative Relativistic Calculation of the Muonic Hydrogen Spectrum
• Constraints on a long-range spin-dependent interaction from precision atomic physics
• Proton Radius, Darwin-Foldy Term and Radiative Corrections
• Hadron and light nucleus radii from electron scattering
• Probing new physics using Rydberg states of atomic hydrogen
• Particle-like solutions to classical noncommutative gauge theory
• Ground State Hyperfine Structure of Muonic Helium Atom
• The Lamb shift contribution of very light millicharged particles
• Hard Three-Loop Corrections to Hyperfine Splitting in Positronium and Muonium
• Magnetic Dipole Moment in Relativistic Quantum Mechanics
• Testing the Stability of the Fine Structure Constant in the Laboratory
• All-order relativistic computations for atoms and molecules using an explicitly correlated Gaussian basis
• Weak Interaction Contributions in Light Muonic Atoms
• Hadronic Light-by-Light Scattering in the Muonium Hyperfine Splitting
• Zemach moments and radii of 2,3H and 3,4He
• Hard Nonlogarithmic Corrections of Order $m{\alpha }^7$ to Hyperfine Splitting in Positronium
• QED calculation of transition probabilities in two-electron ions
• Electric Dipole Polarizabilities of Hydrogen and Helium Isotopes
• Hyperfine structure of P-states in muonic deuterium
• Second-order corrections to the non-commutative Klein-Gordon equation with a Coulomb potential
• D1 and D2 lines in ${}^{6,7}$Li including QED effects
• Two-Loop Bethe Logarithms for non-S Levels
• Double-Logarithmic Two-Loop Self-Energy Corrections to the Lamb Shift
• Electron Structure: Shape, Size and GPDs in QED
• Theoretical determination of polarizability and magnetic susceptibility of neon
• Radiative-nonrecoil corrections of order alpha^2 (Z alpha)^5 to the Lamb shift
• Two-Loop Bethe Logarithms for Higher Excited S Levels
• Three-Loop Reducible Radiative Photon Contributions to Lamb Shift and Hyperfine Splitting
• New treatment of the noncommutative Dirac equation with a Coulomb potential
• Expansion of bound state energies in powers of m/M and (1-m/M)
• Muonic hydrogen cascade time and lifetime of the short-lived $2S$ state
• Proton polarizability contribution to the hydrogen hyperfine splitting
• Three-Loop Radiative Corrections to Lamb Shift and Hyperfine Splitting
• Probing New Physics with Long-Range Neutrino Interactions: An Effective Field Theory Approach
• Precision spectroscopy of the hydrogen molecular ions HD${}^{+}$
• Radiative ${\mathbf{\alpha }}^7\mathbf{m}$ QED contribution to the helium Lamb shift
• First-principles calculation of the frequency-dependent dipole polarizability of argon
• Leading order relativistic corrections to the ro-vibrational spectrum of $\mbox{H}^+_2$ and $\mbox{HD}^+$ molecular ions
• Finite nuclear size effect on Lamb shift of s1/2, p1/2, and p3/2 atomic states
• Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting in Muonium
• The Structure of Light Nuclei and Its Effect on Precise Atomic Measurements
• Hadronic Vacuum Polarization Contribution to the Muonium Hyperfine Splitting
• Precision Spectroscopy of Molecular Hydrogen Ions: Towards Frequency Metrology of Particle Masses
• Hydrogen and muonic-Hydrogen Atomic Spectra in Non-commutative Space-Time
• Leading-order QED effects in the ground electronic state of molecular hydrogen
• Point-Particle Effective Field Theory III: Relativistic Fermions and the Dirac Equation
• Standard Model in multiscale theories and observational constraints
• Hyperfine splitting in ordinary and muonic hydrogen
• Vacuum polarization for compactified $QE{D}_{4+1}$ in a magnetic flux background
• New Polarization Operator Contributions to Lamb Shift and Hyperfine Splitting
• Higher-order corrections for the dynamic hyperfine structure of muonic atoms
• Ground state hyperfine splitting in the Be${}^{+}$ ion
• Thermal QED theory for bound states
• Muonic bound systems, virtual particles and proton radius
• Eta Decay and Muonic Puzzles
• Virtual Delbrück scattering and the Lamb shift in light hydrogen-like atoms
• Vacuum polarization in muonic and antiprotonic atoms: the fine structure at medium Z
• Light-by-Light Scattering Nonlogarithmic Corrections to Hyperfine Splitting in Muonium
• Two-loop electron self-energy for low nuclear charges
• Fine and hyperfine structure of the muonic ^3He ion
• One More Hard Three-Loop Correction to Parapositronium Energy Levels
• Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting Generated by One-Loop Fermion Factors
• Pseudoscalar pole terms contributions to hadronic light-by-light corrections to the muonium hyperfine splitting
• Hyperfine structure of the $2{}^{3}P$ state in ${}^9$Be and the nuclear quadrupole moment
• Precision calculation of the recoil--finite-size correction for the hyperfine splitting in muonic and electronic hydrogen
• Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting in Muonium: Diagrams with Polarization Loops
• Particle-physics constraints on multifractal spacetimes
• Can Galileons solve the muon problem?
• Few-electron atomic ions in non-relativistic QED: the Ground state energy
• Bound-state relativistic quantum electrodynamics: a perspective for precision physics with atoms and molecules
• Finite-nuclear-size effect in hydrogen-like ions with relativistic nuclear structure
• Variational Worldline Approximation for the Relativistic Two-Body Bound State in a Scalar Model
• Higher-order QED corrections to the hyperfine splitting in ${}^3$He
• Fine and hyperfine splitting of the low-lying states of ${}^9$Be
• Hyperfine structure of S-states in muonic ions of lithium, beryllium and boron
• Two-photon exchange on neutron and the hyperfine splitting
• Three-Loop Contributions to Hyperfine Splitting: Muon Loop Light-by-Light Insertion and Other Closed Lepton Loops
• Radiative nonrecoil nuclear finite size corrections of order $\alpha (Z\alpha {)}^5$ to the Lamb shift in light muonic atoms
• Three-Loop Corrections to Lamb Shift in Muonium and Positronium
• Finite nuclear size and Lamb shift of p-wave atomic states
• Breakdown of the expansion of finite-size corrections to the hydrogen Lamb shift in moments of charge distribution
• A constraint on antigravity of antimatter from precision spectroscopy of simple atoms
• Radiative-Recoil Corrections to Hyperfine Splitting: Polarization Insertions in the Muon Factor
• Study of hyperfine structure in simple atoms and precision tests of the bound state QED
• Quantum field theory meets Hopf algebra
• Bayesian analysis of nuclear polarizability corrections to the Lamb shift of muonic H-atoms and He-ions
• Pre-Born-Oppenheimer Dirac-Coulomb-Breit computations for two-body systems
• Reduced Theoretical Error for QED Tests with 4He+ Spectroscopy
• Two-Loop Electron Factor Contribution to Lamb Shift in Muonium and Positronium
• Breit Equation with Form Factors in the Hydrogen Atom
• Radiative-nonrecoil corrections of order alpha^2 (Z alpha) E_F to the hyperfine splitting of muonium
• Magnetic Field Focusing of Hyperfine Interaction in Hydrogen
• Extrapolation of the Zalpha-Expansion and Two--Loop Bound--State Energy Shifts
• Proposal for the determination of nuclear masses by high-precision spectroscopy of Rydberg states
• Non-spherical proton shape and hydrogen hyperfine splitting
• Relativistic and QED corrections to the $2p{\sigma }_u(\upsilon =1)$ vibrational state of the $H_2^{+}$ molecular ion
• Light-by-Light Scattering Single-Logarithmic Corrections to Hyperfine Splitting in Muonium
• Three-Loop Radiative-Recoil Corrections to Hyperfine Splitting in Muonium
• Non-Perturbative Lepton Sea Fermions in the Nucleon and the Proton Radius Puzzle
• QED corrections to the correlated relativistic energy: one-photon processes
• Radiative-Recoil Corrections to Hyperfine Splitting: Polarization Insertions in the Electron Factor
• Two-loop electron self-energy with accelerated partial-wave expansion
• Light-by-light-scattering contributions to the Lamb shift in light muonic atoms
• Hyperfine structure of excited state of muonic helium atom
• Hyperfine structure of the ground state muonic He-3 atom
• Isotope effects in the harmonic response from hydrogenlike muonic atoms in strong laser fields
• Cosmological Variation of the Fine Structure Constant versus a new Interaction
• Limits on a Dynamically Varying Fine Structure Constant
• Two-Loop Effects and Current Status of the 4He+ Lamb Shift
• Nuclear recoil correction to the hyperfine splitting in atomic systems
• Nuclear polarizability effects in ${}^3$He${}^{+}$ hyperfine splitting
• Low-lying electron energy levels in three-particle electron-muon ions $(\mu eLi)$, $(\mu eBe)$, $(\mu eB)$
• Exclusive photon-fusion production of even-spin resonances and exotic QED atoms in high-energy hadron collisions
• Hadronic vacuum polarization correction to atomic energy levels
• Ground state hyperfine structure of light muon-electron ions
• Hyperfine structure of P states in muonic ions of lithium, beryllium and boron
• Three-Loop Contribution to Hyperfine Splitting in Muonium: Polarization Corrections to Light by Light Scattering Blob
• Effects of Non-Commutativity on Light-Hydrogen-Like Atoms and Proton Radius
• Relativistic Ritz approach to hydrogen-like atoms I: theoretical considerations
• The higher-order black-body radiation shift of atomic energy-levels
• Worldline Variational Approximation: A New Approach to the Relativistic Binding Problem
• The MC-QTAIM: A framework for extending the atoms in molecules analysis beyond purely electronic systems
• The 4-particle hydrogen-antihydrogen system revisited: twofold Hamiltonian symmetry and natural atom antihydrogen
• On hydrogen-like bound states in $\mathcal{N}=4$ super Yang-Mills
• The quasiclassical theory of the Dirac equation with a scalar-vector interaction and its applications in the theory of heavy-light mesons
• Vacuum polarization and quadrupole corrections to the hyperfine splitting of P-states in muonic deuterium
• Lamb shift of interactive electron-hole pairs in spherical semiconductor quantum dots
• Quantum Gravity Constraints on Fine Structure Constant from GUP in Braneworlds
• Nucleus polarizability contribution to the hydrogen-deuterium isotope shift
• From First Principles of QED to an Application: Hyperfine Structure of P States of Muonic Hydrogen
• Energy interval 3S-1S in muonic hydrogen
• Lamb shift of non-degenerate energy level systems placed between two infinite parallel conducting plates
• Hydrogen energy-levels shifts induced by the atom motion. Crossover from the Lamb shifts to the motion-induced shifts
• Effective quantum electrodynamics: One-dimensional model of the relativistic hydrogen-like atom
• One-loop corrections of order (Z alpha)^6m_1/m_2, (Z alpha)^7 to the muonium fine structure
• Symmetry breaking in covalent chiral bond Hsub2, according to accurate vibrational levels from Kratzer bond theory
• A new method that automatically regularizes scattering amplitudes
• Nuclear structure corrections to gyromagnetic factor of the bound lepton
• Relativistic density functional theory with finite-light-speed correction for the Coulomb interaction: a non-relativistic-reduction based approach
• Laser excitation of the 1s-hyperfine transition in muonic hydrogen
• Precision Rydberg State Spectroscopy with Slow Electrons and Proton Radius Puzzle
• Finite-nuclear-size effect for hydrogenlike ions under high external pressure
• The zero-point energy of elementary quantum fields
• Toward high-precision values of the self energy of non-S states in hydrogen and hydrogen-like ions
• Bound state equations in Riemannian geometry
• Reexamination of vacuum-polarization corrections to the self-energy in muonic bound systems
• Rovibrational computations for He${}_2^{+}$ X ${\Sigma }_{\mathrm{u}}^{+}$ including non-adiabatic, relativistic and QED corrections
• Splitting Isotope Shift in the $1s2p{}^3{P}_{0,1,2}$ Fine-Structure Triplet in ${}^{12,13,14}$C${}^{4+}$: Experiment and Theory
• Physics beyond the Standard Model from hydrogen spectroscopy
• Improved constraints on exotic interactions between electron and proton in hydrogen
• CFNS Ad-Hoc meeting on Radiative Corrections Whitepaper
• Ground state hyperfine structure in muonic lithium ions
• Meaning of the nuclear wave function
• Precision study of hyperfine structure in simple atoms
• Clustering in hadrons and light nuclei from Lorentz boosted form factors
• Transformation of bound states of relativistic hydrogen-l ike atom into two-component form
• Flat Bundles on Function Manifolds and Evolution Equations in Quantum Field Theories
• Recoil corrections to $\mu$H hyperfine splitting
• Computation of the leading order contributions to the Lamb shift for the H atom using spectral regularization
• Relativistic correction of the Coulomb interaction in the local density approximation for energies and radii in doubly-magic nuclei
• Laser Excitation of Muonic 1S Hydrogen Hyperfine Transition: Effects of Multi-pass Cell Interference
• Properties of solutions of the "naive" functional Schroedinger equation for QCD
• Rovibrational computations for the He${}_2$ a ${}^3{\Sigma }_{\mathrm{u}}^{+}$ state including non-adiabatic, relativistic, and QED corrections
• Two-loop corrections to the Lamb shift
• Lyman-Alpha Spectroscopy in Non-Commutative Space-Time
• Møller maps for Dirac fields in external backgrounds
• Self-Localized Quasi-Particle Excitation in Quantum Electrodynamics and Its Physical Interpretation
• Effective Angular Momentum Operators in NRQED and Matching at One-Loop Order
• Double-Resonance g Factor Measurements by Quantum Jump Spectroscopy