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Title: S -matrix calculations of energy levels of sodiumlike ions

Journal Article · · Physical Review A - Atomic, Molecular, and Optical Physics
 [1];  [2]
  1. Univ. of Notre Dame, IN (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

A recent S -matrix-based QED calculation of energy levels of the lithium isoelectronic sequence is extended to the general case of a valence electron outside an arbitrary filled core. Emphasis is placed on modifications of the lithiumlike formulas required because more than one core state is present, and an unusual feature of the two-photon exchange contribution involving autoionizing states is discussed. Here, the method is illustrated with a calculation of the energy levels of sodiumlike ions, with results for 3s1/2, 3p1/2, and 3p3/2 energies tabulated for the range Z = 30 – 100 . Comparison with experiment and other calculations is given, and prospects for extension of the method to ions with more complex electronic structure discussed.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE; National Science Foundation (NSF)
Grant/Contract Number:
AC52-07NA27344; PHY-1068065
OSTI ID:
1234599
Alternate ID(s):
OSTI ID: 1188515
Report Number(s):
LLNL-JRNL-670986; PLRAAN
Journal Information:
Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 91, Issue 6; ISSN 1050-2947
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 16 works
Citation information provided by
Web of Science

References (56)

Many-body perturbation-theory calculations of energy levels along the copper isoelectronic sequence journal August 1990
The lamb shift in hydrogen-like atoms, 1 ⩽ Z ⩽ 110 journal November 1985
Two-loop QED corrections with closed fermion loops for the bound-electron g factor journal October 2013
Evaluation of two-photon exchange graphs for excited states of highly charged heliumlike ions journal October 2000
Wavelength measurement of n = 3 to n = 3 transitions in highly charged tungsten ions journal May 2010
Many-body perturbation-theory formulas for energy levels of excited states of closed-shell atoms journal November 1992
Foundations of the relativistic theory of many-electron bound states journal January 1984
Tenth-Order QED Contribution to the Electron g 2 and an Improved Value of the Fine Structure Constant journal September 2012
Nonperturbative Calculation of the Two-Loop Lamb Shift in Li-Like Ions journal December 2006
Measurement of the D -line doublet in high- Z highly charged sodiumlike ions journal July 2009
Many-body perturbation-theory calculations of energy levels along the lithium isoelectronic sequence journal April 1988
Hydrogenic and screened self-energies for d states journal January 2006
Vacuum polarization calculations for hydrogenlike and alkali-metal-like ions journal October 2003
Reformulation of the theory of the mass shift journal November 1987
Nuclear and Relativistic Effects in Atomic Spectra journal March 1961
Effective lagrangians for bound state problems in QED, QCD, and other field theories journal February 1986
Testing Three-Body Quantum Electrodynamics with Trapped Ti 20 + Ions: Evidence for a Z -dependent Divergence Between Experiment and Calculation journal October 2012
Calculations of the screened self-energy and vacuum polarization in Li-like, Na-like, and Cu-like ions journal March 1993
Table of experimental nuclear ground state charge radii: An update journal January 2013
E2 and E4 deformations in 232Th and 239,240,242Pu journal February 1986
CODATA recommended values of the fundamental physical constants: 2010 journal November 2012
On Bound States and Scattering in Positron Theory journal January 1951
QED theory of the nuclear recoil effect in atoms journal January 1998
Nuclear recoil corrections to the 2p 3/2 state energy of hydrogen-like and high-Z lithium-like atoms in all orders in alpha Z journal December 1995
Lamb-shift calculations for non-Coulomb potentials journal March 1993
Some Observable Effects of the Quantum-Mechanical Fluctuations of the Electromagnetic Field journal November 1948
Model operator approach to the Lamb shift calculations in relativistic many-electron atoms journal July 2013
Electron self-energy for the K and L shells at low nuclear charge journal March 2001
Relativistic Z-Dependent Corrections to Atomic Energy Levels book January 1969
Two-loop self-energy for the ground state of medium- Z hydrogenlike ions journal October 2009
Recoil corrections in highly charged ions journal October 2007
On the interaction of two electrons
  • Brown, G. E.; Ravenhall, D. G.
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 208, Issue 1095, p. 552-559 https://doi.org/10.1098/rspa.1951.0181
journal September 1951
QED calculation of the n = 1 and n = 2 energy levels in He-like ions journal June 2005
S -matrix calculations of energy levels of the lithium isoelectronic sequence journal January 2011
Two-time Green's function method in quantum electrodynamics of high-Z few-electron atoms journal January 2002
The size of the proton journal July 2010
Two-Body System in Quantum Electrodynamics. Energy Levels of Positronium journal August 1954
Resonance transition energies of Li-, Na-, and Cu-like ions journal July 1991
Nuclear and Relativistic Effects in Atomic Spectra: II journal May 1963
Relativistic nuclear recoil corrections to the energy levels of hydrogenlike and high- Z lithiumlike atoms in all orders in α Z journal September 1995
Calculation of properties with the coupled-cluster method journal January 1977
The Influence of Nuclear Structure on the Hyperfine Structure of Heavy Elements journal January 1950
Reduction of Relativistic Two-Particle Wave Equations to Approximate Forms. III journal July 1955
Fine structure of helium and light helium-like ionsThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at École de Physique, les Houches, France, 30 May – 4 June, 2010. journal January 2011
Many-body perturbation-theory calculations of energy levels along the sodium isoelectronic sequence journal September 1988
Determination of the two-loop Lamb shift in lithiumlike bismuth journal July 2001
S -Matrix Formalism for Level-Shift Calculations journal September 1957
E 2 and E 4 Deformations in U 2 3 3 , 2 3 4 , 2 3 5 , 2 3 8 journal November 1984
Transition energies of the 3 s 3 p 3 / 2 resonance lines in sodiumlike to phosphoruslike uranium journal August 2003
EXPERIMENT AND THEORY IN COMPUTATIONS OF THE He ATOM GROUND STATE journal June 2006
Relativistic configuration-interaction calculations of the n = 3 -3 transition energies in highly charged tungsten ions journal July 2011
Finite basis sets for the Dirac equation constructed from B splines journal January 1988
Theoretical Determination of the Dissociation Energy of Molecular Hydrogen journal September 2009
Calculation of the Lamb shift in neutral alkali metals journal October 2002
Erratum: Accurate variational calculations of energies of the 2 S 2 , 2 P 2 , and 3 D 2 states and the dipole, quadrupole, and dipole-quadrupole polarizabilities and hyperpolarizability of the lithium atom journal June 1996
Nuclear-polarization contribution to the Lamb shift in actinide nuclei journal February 1995

Cited By (4)

Introduction to Bound-State Quantum Electrodynamics book October 2016
QED calculation of electron-electron correlation effects in heliumlike ions journal December 2019
Identification and Plasma Diagnostics Study of Extreme Ultraviolet Transitions in Highly Charged Yttrium journal September 2017
Introduction to Bound-State Quantum Electrodynamics book January 2016

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