Fourth-Order Electrodynamic Corrections to the Lamb Shift

The fourth-order radiative correction to the slope at q’= 0 of the Dirac form factor of the free electron vertex is calculated using computer techniques. The result, m28 F(4)(0)/8 q2 = (o!/7q2 10.48 i 0.071, disagrees with previous calculations, and implies a new theoretical value for the order a2(Z~)4mc2 contribution to the Lamb shift. The new values for the 2s 4 2P, z separation in H and D are increased by (0.35 f 0.07) MHz and are in good agreement with the results of recent experiments. (Submitted to The Physical Review) t Work supported by the U. S. Atomic Energy Commission.