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We present a numerical evaluation of the loop-after-loop contribution to thesecond-order self-energy for the ground state of hydrogenlike atoms with lownuclear charge numbers Z. The calculation is carried out in the Fried-Yenniegauge and without an expansion in Z \alpha. Our calculation confirms theresults of Mallampalli and Sapirstein and disagrees with the calculation byGoidenko and coworkers. A discrepancy between different calculations isinvestigated. An accurate fitting of the numerical results provides a detailedcomparison with analytic calculations based on an expansion in the parameter Z\alpha. We confirm the analytic results of order \alpha^2 (Z\alpha)^5 butdisagree with Karshenboim's calculation of the \alpha^2 (Z \alpha)^6 \ln^3(Z\alpha)^{-2} contribution.Comment: RevTex, 19 pages, 4 figure

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Loop-after-loop contribution to the second-order Lamb shift in hydrogenlike low-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Z</mml:mi></mml:math>atoms

Loop-after-loop contribution to the second-order Lamb shift in hydrogenlike low-Zatoms