Approximate numerical calculation of the self-energy of a bound electron

• Published in: Annals of physics Vol. 327; no. 2; pp. 297 - 328
• Main Author: Zamastil, J.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.02.2012; Elsevier BV
• Subjects: Bound state QED; Radiation corrections; Radiation corrections; Bound state QED
• ISSN: 0003-4916; 1096-035X
• DOI: 10.1016/j.aop.2011.09.002

The evaluation method of the self-energy of the bound electron in the one-loop approximation is described. It is based on the expansion of physical momentum of the electron around the momentum of the electron at rest. The method is applied to 1 S , 2 P 3 / 2 and 3 D 5 / 2 states of the hydrogen-like ions. It is for the first time the results for D states for Z from 5 to 55 are presented. For P states and for nuclear charges up to Z about 40 the accuracy of the results is comparable to that of the most accurate calculations made so far. If the exact value of the coefficient A 50 in the expansion of the self-energy is used as an additional input, the relative difference between the present method and the most accurate value given so far in the literature for 1 S state of the hydrogen atom is 4 parts in 10 6 . Reliable predictions for the self-energy are obtained up to Z about 90 for all states. The calculation is analytic up to the one-dimensional integration over continuous part of the hydrogen spectrum. The separation of the low and high energy regions and their matching is avoided. ► The results for 3 D 5 / 2 states for Z ∈ ( 5 , 55 ) are given here for the first time. ► The results for 2 P 3 / 2 states up to Z about 40 are very accurate. ► Reliable predictions are obtained up to Z about 90 for all states. ► Up to 1D integration the calculation is analytic. ► The separation into the low and high energy regions and their matching are avoided.