The generalized Bethe logarithm for tightly bound electrons

We derive a closed relativistic expression that makes it possible to calculate the self-energy of multiply charged ions in an external Coulomb field without resorting to a series expansion in powers of αZ. The expression contains the generalized Bethe logarithm for tightly bound electrons. We do numerical calculations of the self-energy for the 1s _1/2-electrons of multiply charged hydrogenlike ions. The proposed method allows for self-energy calculations for any values of the nuclear charge Z. Zh. éksp. Teor. Fiz. 112, 1197–1208 (October 1997)