Va. Yerokhin, Loop-after-loop contribution to the second-order Lamb shift in hydrogenlike low-Z atoms - art. no. 012508, PHYS REV A, 6201(1), 2000, pp. 2508
We present a numerical evaluation of the loop-after-loop contribution to th
e second-order self-energy for the ground state of hydrogenlike atoms with
low nuclear charge numbers Z. The calculation is carried out in the Fried-Y
ennie gauge and without an expansion in Z alpha. Our calculation confirms t
he results of Mallampalli and Sapirstein and disagrees with the calculation
by Goidenko and co-workers. A discrepancy between different calculations i
s investigated. An accurate fitting of the numerical results provides a det
ailed comparison with analytic calculations based on an expansion in the pa
rameter Z alpha. We confirm the analytic results of order alpha(2()Z alpha)
(5) but disagree with Karshenboim's calculation of the a(2)(Z alpha)(6) 1n(
3)(Z alpha)(-2) contribution.