Precise calculation of transition frequencies of hydrogen and deuterium based on a least-squares analysis.

We combine a limited number of accurately measured transition frequencies in hydrogen and deuterium, recent quantum electrodynamics (QED) calculations, and, as an essential additional ingredient, a generalized least-squares analysis, to obtain precise and optimal predictions for hydrogen and deuterium transition frequencies. Some of the predicted transition frequencies have relative uncertainties more than an order of magnitude smaller than that of the g factor of the electron, which was previously the most accurate prediction of QED.

[1]  Electron self-energy for higher excited S levels (2 pages) , 2004, hep-ph/0405137.

[2]  U. Jentschura,et al.  Two-loop Bethe-logarithm correction in hydrogenlike atoms. , 2003, Physical review letters.

[3]  Logarithmic two-loop corrections to the Lamb shift in hydrogen , 2000, physics/0011044.

[4]  B. M. Fulk.  MATH , 1992 .

[5]  C. W. Fabjan,et al.  SEPARATED OSCILLATORY FIELD MEASUREMENT OF THE LAMB SHIFT. , 1971 .

[6]  D. Andrews,et al.  A precision determination of the Lamb shift in hydrogen , 1979, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[7]  Hagley,et al.  Separated oscillatory field measurement of hydrogen 2S1/2-2P3/2 fine structure interval. , 1994, Physical review letters.

[8]  Theodor W. Hänsch,et al.  HYDROGEN-DEUTERIUM 1S-2S ISOTOPE SHIFT AND THE STRUCTURE OF THE DEUTERON , 1998 .

[9]  P. J. Mohr,et al.  Calculation of the Electron Self-Energy for Low Nuclear Charge , 1999 .

[10]  André Clairon,et al.  Absolute Frequency Measurement of the 2S-8S/D Transitions in Hydrogen and Deuterium: New Determination of the Rydberg Constant , 1997 .

[11]  Salomon,et al.  Measurement of the hydrogen 1S- 2S transition frequency by phase coherent comparison with a microwave cesium fountain clock , 2000, Physical review letters.

[12]  Julien,et al.  High resolution spectroscopy of the hydrogen atom: Determination of the 1S Lamb shift. , 1996, Physical review letters.

[13]  Howard Grotch,et al.  Theory of light hydrogenlike atoms , 2000, hep-ph/0002158.

[14]  Huber,et al.  Precision measurement of the 1S ground-state Lamb shift in atomic hydrogen and deuterium by frequency comparison. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[15]  Double-logarithmic two-loop self-energy corrections to the Lamb shift , 2002, hep-ph/0205019.

[16]  S. Karshenboim,et al.  LETTER TO THE EDITOR: Two-loop logarithmic corrections in the hydrogen Lamb shift , 1996 .

[17]  V. B. Berestet͡skiĭ,et al.  Quantum Electrodynamics , 2021, Introduction to Quantum Mechanics.

[18]  Asymptotic properties of self-energy coefficients. , 2003, Physical review letters.

[19]  André Clairon,et al.  Optical Frequency Measurement of the 2S-12D Transitions in Hydrogen and Deuterium: Rydberg Constant and Lamb Shift Determinations , 1999 .

[20]  Electron Self-Energy for the K and L Shells at Low Nuclear Charge , 2000, physics/0009090.

[21]  Glen W. Erickson,et al.  Energy levels of one‐electron atoms , 1977 .

[22]  K. Haller.  Quantum Electrodynamics , 1979, Nature.

[23]  Hinds,et al.  Precise optical measurement of lamb shifts in atomic hydrogen. , 1995, Physical review letters.

[24]  Radiative energy shifts induced by local potentials , 2003, hep-ph/0305066.

[25]  A. C. Aitken.  IV.—On Least Squares and Linear Combination of Observations , 1936 .

[26]  Perturbation approach to the self-energy of non- S hydrogenic states , 2003, physics/0304068.