Loop-after-loop contribution to the second-order Lamb shift in hydrogenlike low-Z atoms - art. no. 012508

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.