Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Calculation of the Electron Self Energy for Low Nuclear Charge



U Jentschura, Peter J. Mohr, G Soff


We present a nonperturbative numerical evaluation of the one-photon electron self-energy for hydrogen like ions with low nuclear charge numbers Z = 1 to 5. Our calculation for 1S state has a numerical uncertainty of 0.8 Hz for hydrogen and 13 Hz for singly-ionized helium. Resummation and convergence acceleration techniques that reduce the computer time by about three orders of magnitude were employed in the calculation. The numerical results are compared to results based on known terms in the expansion of the self energy in powers of Zα.
Physical Review Letters
No. 1


calculations and mathematical techniques, computational techniques, detrmination of fundamental constants, electrodynamic effects in atoms, electrodynamic effects in molecules, numerical approximation and analyasis, quantum electrodynamic effects, quantum electrodynamics, relativistic electrodynamic effects


Jentschura, U. , Mohr, P. and Soff, G. (1999), Calculation of the Electron Self Energy for Low Nuclear Charge, Physical Review Letters (Accessed July 12, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created January 1, 1999, Updated February 17, 2017