Speaker
Description
The two-loop electron self-energy correction induces one of the two dominant uncertainties in theory of the Lamb shift in hydrogen and He$^+$ [1]. It is currently obtained by extrapolating results of numerical all-order (in $Z\alpha$) calculations for $Z\ge 10$ [2] in combination with available $Z\alpha$-expansion results [3,4]. The present accuracy of the all-order numerical calculations is limited by the convergence of the partial-wave expansion. Recently, methods with improved the partial-wave expansion convergence were developed for the one-loop self-energy problem [5,6]. I will discuss the present status of numerical two-loop calculations in the low-$Z$ region and the generalization of the methods with the improved partial-wave convergence to the two-loop case, and will present preliminary results of improved numerical computations.
[1] E. Tiesinga, P. J. Mohr, D. B. Newell, and B. N. Taylor, Rev. Mod. Phys. 93, 025010 (2021).
[2] V. A. Yerokhin, Phys. Rev. A 80, 040501(R) (2009).
[3] K. Pachucki and U. D. Jentschura, Phys. Rev. Lett. 91, 113005 (2003).
[4] S. G. Karshenboim, A. Ozawa, and V. G. Ivanov, Phys. Rev. A 100, 032515 (2019).
[5] V. A. Yerokhin, K. Pachucki, and V. M. Shabaev, Phys. Rev. A 72, 042502 (2005).
[6] J. Sapirstein, K. T. Cheng, Phys. Rev. A 108, 042804 (2023).
