Bethe logarithm for the 1 S-1 and 2 S-1 states of helium

We present variational calculations of the Bethe logarithm for the 1 S-1 an d 2 S-1 states of helium. The approach is based on the explicit second-orde r perturbation formula and closely follows the method of Schwartz. The fina l values are In[K-0(1 S-1)/(1 Ry)] = 4.370 157 9(5) and ln[k(0)(2 S-1)/(1 R y)] = 4.366 409 1 (7). The latter result reduces the difference between the oretical and experimental values for the ionization potential of the 2, S-1 State to 0.15 MHz. [S1050-2947(99)03305-3].