Calculation of the electron self-energy for low nuclear charge

We present a nonperturbative numerical evaluation of the one-photon electro n self-energy for hydrogenlike ions with low nuclear charge numbers Z = 1 t o 5. Our calculation for the 1S state has a numerical uncertainty of 0.8 Hz for hydrogen and 13 Hz for singly ionized helium. Resummation and converge nce acceleration techniques that reduce the computer time by about 3 orders of magnitude were employed in the calculation. The numerical results are c ompared to results based on known terms in the expansion of the self-energy in powers of Z alpha. [S0031-9007(98)08043-0].